Magdalena Skurzok

Seminary IKP Jϋlich 05052011

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

hellipwhich I did in the frame of my diploma thesis

1 Introduction

2 Model of the quasi-free

production of T-h bound state

3 Simulations of h-mesic T

production and decay

4 Summary

2

1 Wiadomości ogoacutelne-co to są BS i jaki jest warunek ich istnienia

2 Reakcje prod I rozp BS kinematyka omoacutewienie detektora TOF

3 Akceptancje geom Eff detektora TOF roacuteżne założenia- gamma i pf model spektatora

4 Podsumowanie

1 At the beginning short introduction what are bound states the conditions of their existence 2 Then I would like to tell about kinematical model of the quasi-free production of T-eta BS which I used in my simulations 3 Next Irsquod like to show the simulation results- acceptances of COSY-TOF detector for quasi-free dd reaction in which eta-T is produced and decays in considered channel assumptions which used for simulations 4 At the end short summary

3

STRONG INTERACTION

n

p p

p

p p

n n

n n

n

n n p

p

p

n

p

p p

p p

n n

n

n

n

n n p

p

p

snp BmNmZm

n

n

p h

n

n

p

h

sTbs Bmmm h

2mcBs

Atomic nucleus h-mesic nucleus

T-h Those new kind of exotic matter consists of Helium nucleus bound with eta meson via strong interaction (the mass of the bound system is less then the sum of He and eta masses because of binding energy-similarly like in case of atomic nucleus) The mesonic helium was postulated by Haider and Liu over 20 years ago however till now none of experiments confirmed empirically its existence

4

-gt Przyciąganie -gt Przyciąganiegtabsorpcja

Obecne teoretyczne przewidywania hadronowej i foto-produkcji ety In the 1980rsquos the ndashmesic nuclei were considered to exists for A 12 only due to the relatively small value of the N scattering length (a_ηN = (028 + i019) fm )

Green

fma d 30h

Attractive interaction between h and N R Bhalerao L C Liu Phys Lett B54 685 (1985)

possible existence of h-mesic bound state for Agt12

Q Haider L C Liu Phys Lett B172 257 (1986)

nucleusnucleus

nucleus

aa

a

hh

h

ImRe

0ReConditions for the existence

of eta-mesic nuclei

Dotychczas nie odkryto stanoacutew związanych ety z jądrami lekkimi choć teoretycznie zostały one przewidziane około 20 lat temu Na początku myślano że powinny istnieć duże jądra mezonowe ze względu na oddziaływanie silne (fals) Możliwe istnienie BS ze względu na odpowiedni zakres długości rozpraszania

5

Odpowiednie warunki na długość rozpraszania Teoretyczne zakresy dł rozpraszania-możliwe istnienie BS trytu helu a nawet deuteronu Wcześniej sądzono (lata80) że możliwe dla Agt12 (małe dł Rozpraszania) poacuteźniej model optyczny i Skyrma Wilkin eksperyment Green Teoria wielokrotnego rozpraszania Wycech Teoria wielokrotnego rozpraszania Optyczny potencjał Obecne teoretyczne przewidywania hadronowej i foto-produkcji ety In the 1980rsquos the ndashmesic nuclei were considered to exists for A 12 only due to the relatively small value of the N scattering length (a_ηN = (028 + i019) fm )

Green

fma d 30h

fmafm

fmafm

N

N

390Im190

051Re270

h

h

(4He-h)bs

(3He-h) bs

Recent theoretical investigations of hadronic- and photoproduction of h meson

Q Haider L C Liu Phys Lett C66 045208 (2002)

(T-h) bs

(d-h) bs

MeVB

MeV

s )155(

)407(

4He-eta z dł Rozpr 3He-eta wykluczony ale eksperymentalne sygnały obiecujące WASA measurement in 2010 with deuteron beam and target performed for beam momentum value varying continousely around eta meson production threshold analysis in PROGRESS (3He-eta) was searched in experiments at COSY ANKE and COSY-11

MOTYWACJA Możliwe badanie własności rezonansoacutew mezonu eta oraz jego oddziaływania z materią jądrową

6

bull ANKE and COSY-11 bull dp rarr 3Heη bull J Smyrski et al Phys Lett B 649 258 (2007)

bull T Mersmann et al Phys Rev Lett 98 242301

bull (2007)

bull TAPS at MAMI

bull γ3He rarr pπ X bull M Pfeiffer et al Phys Rev Lett 92 (2004)

ANKE and COSY-11 The fit to the COSY-11 and ANKE data gave the value of the 3He-eta scattering length Those values implies the existence of a quasi-bound states very close to the reaction threshold MAMI difference between excitation curves for opening angles of 170- 180deg and 150-170deg in the center-of-mass frame revealed an enhancement just below the threshold of the g3He -gt3He-eta reaction which was interpreted as a possible signature of a 3He-eta bound state COSY-GEM Enhancement below h production threshold

MAMI zmierzylo potem z duza statystyka to uznali ze to nie jest prawdziwy sygnal tylko efekt od rezonansow ktore maja rozne krzywe wzbudzenia dla roznych katow i przy odjeciu (subtract) powstaje przypadkowo taka dziwna struktura Na pytanie czy taka struktura nie

uniemozliwi nam pomiaru Moze Pani odpowiedz ze z pomiarow ktore analizuje Wojciech Krzemien wszystkie krzywe wzbudzenia sa gladkie i nie ma zadnych struktur co moze wiazac sie z tym ze w rezonanse łatwiej sie wzbudzaja w oddziaływaniu elektromagnetycznym (czyli gamma 3He) niz w silnym proton-deuteron czy deutereon deuteron

ANKE

COSY-11 bull

that the result may be an artefact due to the strong influence of the resonances on the shape of the excitation function

Binding energy( -44 plusmn 42) MeV

Width (256 plusmn 61) MeV

7

) ) h pdpTpdnpdd spbsspsp

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

The quasi-free reaction mechanism GENERAL

8

d

[1] M Lacombe et al Phys Rev C21 861-873 (1980)

[2] R Machleidt Phys Rev C63 024001 (2001)

Two models describing momentum distribution of nucleons inside deuteron PARIS and CDBonn Description in my thesis and my notebook

9

npd

npd

mmm

mmm

) 222

Fpp pmEsp

Spectator assumption Proton is real particle on its mass shell

npnp mmmm

Assumption nnpp mmmm

sppdn EmE

beam deuteron n

n

pF

pF

pb

target deuteron

Explanation of the quasi free Reaction For fixed beam momentum we have distribution of neutron momentum given by Fermi motions=gtdistribution of invariant system mass

10

The quasi-free reaction mechanism IN DETAILS

Formation of -mesic Tritium might be realized by quasi-free reactions as already successfully used at COSY to study meson production in quasi free proton-neutron collisions [1 2] Measurements of such reactions is possible for the external COSY-TOF detector

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

1 Introduction

2 Model of the quasi-free

production of T-h bound state

3 Simulations of h-mesic T

production and decay

4 Summary

2

1 Wiadomości ogoacutelne-co to są BS i jaki jest warunek ich istnienia

2 Reakcje prod I rozp BS kinematyka omoacutewienie detektora TOF

3 Akceptancje geom Eff detektora TOF roacuteżne założenia- gamma i pf model spektatora

4 Podsumowanie

1 At the beginning short introduction what are bound states the conditions of their existence 2 Then I would like to tell about kinematical model of the quasi-free production of T-eta BS which I used in my simulations 3 Next Irsquod like to show the simulation results- acceptances of COSY-TOF detector for quasi-free dd reaction in which eta-T is produced and decays in considered channel assumptions which used for simulations 4 At the end short summary

3

STRONG INTERACTION

n

p p

p

p p

n n

n n

n

n n p

p

p

n

p

p p

p p

n n

n

n

n

n n p

p

p

snp BmNmZm

n

n

p h

n

n

p

h

sTbs Bmmm h

2mcBs

Atomic nucleus h-mesic nucleus

T-h Those new kind of exotic matter consists of Helium nucleus bound with eta meson via strong interaction (the mass of the bound system is less then the sum of He and eta masses because of binding energy-similarly like in case of atomic nucleus) The mesonic helium was postulated by Haider and Liu over 20 years ago however till now none of experiments confirmed empirically its existence

4

-gt Przyciąganie -gt Przyciąganiegtabsorpcja

Obecne teoretyczne przewidywania hadronowej i foto-produkcji ety In the 1980rsquos the ndashmesic nuclei were considered to exists for A 12 only due to the relatively small value of the N scattering length (a_ηN = (028 + i019) fm )

Green

fma d 30h

Attractive interaction between h and N R Bhalerao L C Liu Phys Lett B54 685 (1985)

possible existence of h-mesic bound state for Agt12

Q Haider L C Liu Phys Lett B172 257 (1986)

nucleusnucleus

nucleus

aa

a

hh

h

ImRe

0ReConditions for the existence

of eta-mesic nuclei

Dotychczas nie odkryto stanoacutew związanych ety z jądrami lekkimi choć teoretycznie zostały one przewidziane około 20 lat temu Na początku myślano że powinny istnieć duże jądra mezonowe ze względu na oddziaływanie silne (fals) Możliwe istnienie BS ze względu na odpowiedni zakres długości rozpraszania

5

Odpowiednie warunki na długość rozpraszania Teoretyczne zakresy dł rozpraszania-możliwe istnienie BS trytu helu a nawet deuteronu Wcześniej sądzono (lata80) że możliwe dla Agt12 (małe dł Rozpraszania) poacuteźniej model optyczny i Skyrma Wilkin eksperyment Green Teoria wielokrotnego rozpraszania Wycech Teoria wielokrotnego rozpraszania Optyczny potencjał Obecne teoretyczne przewidywania hadronowej i foto-produkcji ety In the 1980rsquos the ndashmesic nuclei were considered to exists for A 12 only due to the relatively small value of the N scattering length (a_ηN = (028 + i019) fm )

Green

fma d 30h

fmafm

fmafm

N

N

390Im190

051Re270

h

h

(4He-h)bs

(3He-h) bs

Recent theoretical investigations of hadronic- and photoproduction of h meson

Q Haider L C Liu Phys Lett C66 045208 (2002)

(T-h) bs

(d-h) bs

MeVB

MeV

s )155(

)407(

4He-eta z dł Rozpr 3He-eta wykluczony ale eksperymentalne sygnały obiecujące WASA measurement in 2010 with deuteron beam and target performed for beam momentum value varying continousely around eta meson production threshold analysis in PROGRESS (3He-eta) was searched in experiments at COSY ANKE and COSY-11

MOTYWACJA Możliwe badanie własności rezonansoacutew mezonu eta oraz jego oddziaływania z materią jądrową

6

bull ANKE and COSY-11 bull dp rarr 3Heη bull J Smyrski et al Phys Lett B 649 258 (2007)

bull T Mersmann et al Phys Rev Lett 98 242301

bull (2007)

bull TAPS at MAMI

bull γ3He rarr pπ X bull M Pfeiffer et al Phys Rev Lett 92 (2004)

ANKE and COSY-11 The fit to the COSY-11 and ANKE data gave the value of the 3He-eta scattering length Those values implies the existence of a quasi-bound states very close to the reaction threshold MAMI difference between excitation curves for opening angles of 170- 180deg and 150-170deg in the center-of-mass frame revealed an enhancement just below the threshold of the g3He -gt3He-eta reaction which was interpreted as a possible signature of a 3He-eta bound state COSY-GEM Enhancement below h production threshold

MAMI zmierzylo potem z duza statystyka to uznali ze to nie jest prawdziwy sygnal tylko efekt od rezonansow ktore maja rozne krzywe wzbudzenia dla roznych katow i przy odjeciu (subtract) powstaje przypadkowo taka dziwna struktura Na pytanie czy taka struktura nie

uniemozliwi nam pomiaru Moze Pani odpowiedz ze z pomiarow ktore analizuje Wojciech Krzemien wszystkie krzywe wzbudzenia sa gladkie i nie ma zadnych struktur co moze wiazac sie z tym ze w rezonanse łatwiej sie wzbudzaja w oddziaływaniu elektromagnetycznym (czyli gamma 3He) niz w silnym proton-deuteron czy deutereon deuteron

ANKE

COSY-11 bull

that the result may be an artefact due to the strong influence of the resonances on the shape of the excitation function

Binding energy( -44 plusmn 42) MeV

Width (256 plusmn 61) MeV

7

) ) h pdpTpdnpdd spbsspsp

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

The quasi-free reaction mechanism GENERAL

8

d

[1] M Lacombe et al Phys Rev C21 861-873 (1980)

[2] R Machleidt Phys Rev C63 024001 (2001)

Two models describing momentum distribution of nucleons inside deuteron PARIS and CDBonn Description in my thesis and my notebook

9

npd

npd

mmm

mmm

) 222

Fpp pmEsp

Spectator assumption Proton is real particle on its mass shell

npnp mmmm

Assumption nnpp mmmm

sppdn EmE

beam deuteron n

n

pF

pF

pb

target deuteron

Explanation of the quasi free Reaction For fixed beam momentum we have distribution of neutron momentum given by Fermi motions=gtdistribution of invariant system mass

10

The quasi-free reaction mechanism IN DETAILS

Formation of -mesic Tritium might be realized by quasi-free reactions as already successfully used at COSY to study meson production in quasi free proton-neutron collisions [1 2] Measurements of such reactions is possible for the external COSY-TOF detector

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

3

STRONG INTERACTION

n

p p

p

p p

n n

n n

n

n n p

p

p

n

p

p p

p p

n n

n

n

n

n n p

p

p

snp BmNmZm

n

n

p h

n

n

p

h

sTbs Bmmm h

2mcBs

Atomic nucleus h-mesic nucleus

T-h Those new kind of exotic matter consists of Helium nucleus bound with eta meson via strong interaction (the mass of the bound system is less then the sum of He and eta masses because of binding energy-similarly like in case of atomic nucleus) The mesonic helium was postulated by Haider and Liu over 20 years ago however till now none of experiments confirmed empirically its existence

4

-gt Przyciąganie -gt Przyciąganiegtabsorpcja

Obecne teoretyczne przewidywania hadronowej i foto-produkcji ety In the 1980rsquos the ndashmesic nuclei were considered to exists for A 12 only due to the relatively small value of the N scattering length (a_ηN = (028 + i019) fm )

Green

fma d 30h

Attractive interaction between h and N R Bhalerao L C Liu Phys Lett B54 685 (1985)

possible existence of h-mesic bound state for Agt12

Q Haider L C Liu Phys Lett B172 257 (1986)

nucleusnucleus

nucleus

aa

a

hh

h

ImRe

0ReConditions for the existence

of eta-mesic nuclei

Dotychczas nie odkryto stanoacutew związanych ety z jądrami lekkimi choć teoretycznie zostały one przewidziane około 20 lat temu Na początku myślano że powinny istnieć duże jądra mezonowe ze względu na oddziaływanie silne (fals) Możliwe istnienie BS ze względu na odpowiedni zakres długości rozpraszania

5

Odpowiednie warunki na długość rozpraszania Teoretyczne zakresy dł rozpraszania-możliwe istnienie BS trytu helu a nawet deuteronu Wcześniej sądzono (lata80) że możliwe dla Agt12 (małe dł Rozpraszania) poacuteźniej model optyczny i Skyrma Wilkin eksperyment Green Teoria wielokrotnego rozpraszania Wycech Teoria wielokrotnego rozpraszania Optyczny potencjał Obecne teoretyczne przewidywania hadronowej i foto-produkcji ety In the 1980rsquos the ndashmesic nuclei were considered to exists for A 12 only due to the relatively small value of the N scattering length (a_ηN = (028 + i019) fm )

Green

fma d 30h

fmafm

fmafm

N

N

390Im190

051Re270

h

h

(4He-h)bs

(3He-h) bs

Recent theoretical investigations of hadronic- and photoproduction of h meson

Q Haider L C Liu Phys Lett C66 045208 (2002)

(T-h) bs

(d-h) bs

MeVB

MeV

s )155(

)407(

4He-eta z dł Rozpr 3He-eta wykluczony ale eksperymentalne sygnały obiecujące WASA measurement in 2010 with deuteron beam and target performed for beam momentum value varying continousely around eta meson production threshold analysis in PROGRESS (3He-eta) was searched in experiments at COSY ANKE and COSY-11

MOTYWACJA Możliwe badanie własności rezonansoacutew mezonu eta oraz jego oddziaływania z materią jądrową

6

bull ANKE and COSY-11 bull dp rarr 3Heη bull J Smyrski et al Phys Lett B 649 258 (2007)

bull T Mersmann et al Phys Rev Lett 98 242301

bull (2007)

bull TAPS at MAMI

bull γ3He rarr pπ X bull M Pfeiffer et al Phys Rev Lett 92 (2004)

ANKE and COSY-11 The fit to the COSY-11 and ANKE data gave the value of the 3He-eta scattering length Those values implies the existence of a quasi-bound states very close to the reaction threshold MAMI difference between excitation curves for opening angles of 170- 180deg and 150-170deg in the center-of-mass frame revealed an enhancement just below the threshold of the g3He -gt3He-eta reaction which was interpreted as a possible signature of a 3He-eta bound state COSY-GEM Enhancement below h production threshold

MAMI zmierzylo potem z duza statystyka to uznali ze to nie jest prawdziwy sygnal tylko efekt od rezonansow ktore maja rozne krzywe wzbudzenia dla roznych katow i przy odjeciu (subtract) powstaje przypadkowo taka dziwna struktura Na pytanie czy taka struktura nie

uniemozliwi nam pomiaru Moze Pani odpowiedz ze z pomiarow ktore analizuje Wojciech Krzemien wszystkie krzywe wzbudzenia sa gladkie i nie ma zadnych struktur co moze wiazac sie z tym ze w rezonanse łatwiej sie wzbudzaja w oddziaływaniu elektromagnetycznym (czyli gamma 3He) niz w silnym proton-deuteron czy deutereon deuteron

ANKE

COSY-11 bull

that the result may be an artefact due to the strong influence of the resonances on the shape of the excitation function

Binding energy( -44 plusmn 42) MeV

Width (256 plusmn 61) MeV

7

) ) h pdpTpdnpdd spbsspsp

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

The quasi-free reaction mechanism GENERAL

8

d

[1] M Lacombe et al Phys Rev C21 861-873 (1980)

[2] R Machleidt Phys Rev C63 024001 (2001)

Two models describing momentum distribution of nucleons inside deuteron PARIS and CDBonn Description in my thesis and my notebook

9

npd

npd

mmm

mmm

) 222

Fpp pmEsp

Spectator assumption Proton is real particle on its mass shell

npnp mmmm

Assumption nnpp mmmm

sppdn EmE

beam deuteron n

n

pF

pF

pb

target deuteron

Explanation of the quasi free Reaction For fixed beam momentum we have distribution of neutron momentum given by Fermi motions=gtdistribution of invariant system mass

10

The quasi-free reaction mechanism IN DETAILS

Formation of -mesic Tritium might be realized by quasi-free reactions as already successfully used at COSY to study meson production in quasi free proton-neutron collisions [1 2] Measurements of such reactions is possible for the external COSY-TOF detector

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

4

-gt Przyciąganie -gt Przyciąganiegtabsorpcja

Obecne teoretyczne przewidywania hadronowej i foto-produkcji ety In the 1980rsquos the ndashmesic nuclei were considered to exists for A 12 only due to the relatively small value of the N scattering length (a_ηN = (028 + i019) fm )

Green

fma d 30h

Attractive interaction between h and N R Bhalerao L C Liu Phys Lett B54 685 (1985)

possible existence of h-mesic bound state for Agt12

Q Haider L C Liu Phys Lett B172 257 (1986)

nucleusnucleus

nucleus

aa

a

hh

h

ImRe

0ReConditions for the existence

of eta-mesic nuclei

Dotychczas nie odkryto stanoacutew związanych ety z jądrami lekkimi choć teoretycznie zostały one przewidziane około 20 lat temu Na początku myślano że powinny istnieć duże jądra mezonowe ze względu na oddziaływanie silne (fals) Możliwe istnienie BS ze względu na odpowiedni zakres długości rozpraszania

5

Odpowiednie warunki na długość rozpraszania Teoretyczne zakresy dł rozpraszania-możliwe istnienie BS trytu helu a nawet deuteronu Wcześniej sądzono (lata80) że możliwe dla Agt12 (małe dł Rozpraszania) poacuteźniej model optyczny i Skyrma Wilkin eksperyment Green Teoria wielokrotnego rozpraszania Wycech Teoria wielokrotnego rozpraszania Optyczny potencjał Obecne teoretyczne przewidywania hadronowej i foto-produkcji ety In the 1980rsquos the ndashmesic nuclei were considered to exists for A 12 only due to the relatively small value of the N scattering length (a_ηN = (028 + i019) fm )

Green

fma d 30h

fmafm

fmafm

N

N

390Im190

051Re270

h

h

(4He-h)bs

(3He-h) bs

Recent theoretical investigations of hadronic- and photoproduction of h meson

Q Haider L C Liu Phys Lett C66 045208 (2002)

(T-h) bs

(d-h) bs

MeVB

MeV

s )155(

)407(

4He-eta z dł Rozpr 3He-eta wykluczony ale eksperymentalne sygnały obiecujące WASA measurement in 2010 with deuteron beam and target performed for beam momentum value varying continousely around eta meson production threshold analysis in PROGRESS (3He-eta) was searched in experiments at COSY ANKE and COSY-11

MOTYWACJA Możliwe badanie własności rezonansoacutew mezonu eta oraz jego oddziaływania z materią jądrową

6

bull ANKE and COSY-11 bull dp rarr 3Heη bull J Smyrski et al Phys Lett B 649 258 (2007)

bull T Mersmann et al Phys Rev Lett 98 242301

bull (2007)

bull TAPS at MAMI

bull γ3He rarr pπ X bull M Pfeiffer et al Phys Rev Lett 92 (2004)

ANKE and COSY-11 The fit to the COSY-11 and ANKE data gave the value of the 3He-eta scattering length Those values implies the existence of a quasi-bound states very close to the reaction threshold MAMI difference between excitation curves for opening angles of 170- 180deg and 150-170deg in the center-of-mass frame revealed an enhancement just below the threshold of the g3He -gt3He-eta reaction which was interpreted as a possible signature of a 3He-eta bound state COSY-GEM Enhancement below h production threshold

MAMI zmierzylo potem z duza statystyka to uznali ze to nie jest prawdziwy sygnal tylko efekt od rezonansow ktore maja rozne krzywe wzbudzenia dla roznych katow i przy odjeciu (subtract) powstaje przypadkowo taka dziwna struktura Na pytanie czy taka struktura nie

uniemozliwi nam pomiaru Moze Pani odpowiedz ze z pomiarow ktore analizuje Wojciech Krzemien wszystkie krzywe wzbudzenia sa gladkie i nie ma zadnych struktur co moze wiazac sie z tym ze w rezonanse łatwiej sie wzbudzaja w oddziaływaniu elektromagnetycznym (czyli gamma 3He) niz w silnym proton-deuteron czy deutereon deuteron

ANKE

COSY-11 bull

that the result may be an artefact due to the strong influence of the resonances on the shape of the excitation function

Binding energy( -44 plusmn 42) MeV

Width (256 plusmn 61) MeV

7

) ) h pdpTpdnpdd spbsspsp

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

The quasi-free reaction mechanism GENERAL

8

d

[1] M Lacombe et al Phys Rev C21 861-873 (1980)

[2] R Machleidt Phys Rev C63 024001 (2001)

Two models describing momentum distribution of nucleons inside deuteron PARIS and CDBonn Description in my thesis and my notebook

9

npd

npd

mmm

mmm

) 222

Fpp pmEsp

Spectator assumption Proton is real particle on its mass shell

npnp mmmm

Assumption nnpp mmmm

sppdn EmE

beam deuteron n

n

pF

pF

pb

target deuteron

Explanation of the quasi free Reaction For fixed beam momentum we have distribution of neutron momentum given by Fermi motions=gtdistribution of invariant system mass

10

The quasi-free reaction mechanism IN DETAILS

Formation of -mesic Tritium might be realized by quasi-free reactions as already successfully used at COSY to study meson production in quasi free proton-neutron collisions [1 2] Measurements of such reactions is possible for the external COSY-TOF detector

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

5

Odpowiednie warunki na długość rozpraszania Teoretyczne zakresy dł rozpraszania-możliwe istnienie BS trytu helu a nawet deuteronu Wcześniej sądzono (lata80) że możliwe dla Agt12 (małe dł Rozpraszania) poacuteźniej model optyczny i Skyrma Wilkin eksperyment Green Teoria wielokrotnego rozpraszania Wycech Teoria wielokrotnego rozpraszania Optyczny potencjał Obecne teoretyczne przewidywania hadronowej i foto-produkcji ety In the 1980rsquos the ndashmesic nuclei were considered to exists for A 12 only due to the relatively small value of the N scattering length (a_ηN = (028 + i019) fm )

Green

fma d 30h

fmafm

fmafm

N

N

390Im190

051Re270

h

h

(4He-h)bs

(3He-h) bs

Recent theoretical investigations of hadronic- and photoproduction of h meson

Q Haider L C Liu Phys Lett C66 045208 (2002)

(T-h) bs

(d-h) bs

MeVB

MeV

s )155(

)407(

4He-eta z dł Rozpr 3He-eta wykluczony ale eksperymentalne sygnały obiecujące WASA measurement in 2010 with deuteron beam and target performed for beam momentum value varying continousely around eta meson production threshold analysis in PROGRESS (3He-eta) was searched in experiments at COSY ANKE and COSY-11

MOTYWACJA Możliwe badanie własności rezonansoacutew mezonu eta oraz jego oddziaływania z materią jądrową

6

bull ANKE and COSY-11 bull dp rarr 3Heη bull J Smyrski et al Phys Lett B 649 258 (2007)

bull T Mersmann et al Phys Rev Lett 98 242301

bull (2007)

bull TAPS at MAMI

bull γ3He rarr pπ X bull M Pfeiffer et al Phys Rev Lett 92 (2004)

ANKE and COSY-11 The fit to the COSY-11 and ANKE data gave the value of the 3He-eta scattering length Those values implies the existence of a quasi-bound states very close to the reaction threshold MAMI difference between excitation curves for opening angles of 170- 180deg and 150-170deg in the center-of-mass frame revealed an enhancement just below the threshold of the g3He -gt3He-eta reaction which was interpreted as a possible signature of a 3He-eta bound state COSY-GEM Enhancement below h production threshold

MAMI zmierzylo potem z duza statystyka to uznali ze to nie jest prawdziwy sygnal tylko efekt od rezonansow ktore maja rozne krzywe wzbudzenia dla roznych katow i przy odjeciu (subtract) powstaje przypadkowo taka dziwna struktura Na pytanie czy taka struktura nie

uniemozliwi nam pomiaru Moze Pani odpowiedz ze z pomiarow ktore analizuje Wojciech Krzemien wszystkie krzywe wzbudzenia sa gladkie i nie ma zadnych struktur co moze wiazac sie z tym ze w rezonanse łatwiej sie wzbudzaja w oddziaływaniu elektromagnetycznym (czyli gamma 3He) niz w silnym proton-deuteron czy deutereon deuteron

ANKE

COSY-11 bull

that the result may be an artefact due to the strong influence of the resonances on the shape of the excitation function

Binding energy( -44 plusmn 42) MeV

Width (256 plusmn 61) MeV

7

) ) h pdpTpdnpdd spbsspsp

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

The quasi-free reaction mechanism GENERAL

8

d

[1] M Lacombe et al Phys Rev C21 861-873 (1980)

[2] R Machleidt Phys Rev C63 024001 (2001)

Two models describing momentum distribution of nucleons inside deuteron PARIS and CDBonn Description in my thesis and my notebook

9

npd

npd

mmm

mmm

) 222

Fpp pmEsp

Spectator assumption Proton is real particle on its mass shell

npnp mmmm

Assumption nnpp mmmm

sppdn EmE

beam deuteron n

n

pF

pF

pb

target deuteron

Explanation of the quasi free Reaction For fixed beam momentum we have distribution of neutron momentum given by Fermi motions=gtdistribution of invariant system mass

10

The quasi-free reaction mechanism IN DETAILS

Formation of -mesic Tritium might be realized by quasi-free reactions as already successfully used at COSY to study meson production in quasi free proton-neutron collisions [1 2] Measurements of such reactions is possible for the external COSY-TOF detector

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

6

bull ANKE and COSY-11 bull dp rarr 3Heη bull J Smyrski et al Phys Lett B 649 258 (2007)

bull T Mersmann et al Phys Rev Lett 98 242301

bull (2007)

bull TAPS at MAMI

bull γ3He rarr pπ X bull M Pfeiffer et al Phys Rev Lett 92 (2004)

ANKE and COSY-11 The fit to the COSY-11 and ANKE data gave the value of the 3He-eta scattering length Those values implies the existence of a quasi-bound states very close to the reaction threshold MAMI difference between excitation curves for opening angles of 170- 180deg and 150-170deg in the center-of-mass frame revealed an enhancement just below the threshold of the g3He -gt3He-eta reaction which was interpreted as a possible signature of a 3He-eta bound state COSY-GEM Enhancement below h production threshold

MAMI zmierzylo potem z duza statystyka to uznali ze to nie jest prawdziwy sygnal tylko efekt od rezonansow ktore maja rozne krzywe wzbudzenia dla roznych katow i przy odjeciu (subtract) powstaje przypadkowo taka dziwna struktura Na pytanie czy taka struktura nie

uniemozliwi nam pomiaru Moze Pani odpowiedz ze z pomiarow ktore analizuje Wojciech Krzemien wszystkie krzywe wzbudzenia sa gladkie i nie ma zadnych struktur co moze wiazac sie z tym ze w rezonanse łatwiej sie wzbudzaja w oddziaływaniu elektromagnetycznym (czyli gamma 3He) niz w silnym proton-deuteron czy deutereon deuteron

ANKE

COSY-11 bull

that the result may be an artefact due to the strong influence of the resonances on the shape of the excitation function

Binding energy( -44 plusmn 42) MeV

Width (256 plusmn 61) MeV

7

) ) h pdpTpdnpdd spbsspsp

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

The quasi-free reaction mechanism GENERAL

8

d

[1] M Lacombe et al Phys Rev C21 861-873 (1980)

[2] R Machleidt Phys Rev C63 024001 (2001)

Two models describing momentum distribution of nucleons inside deuteron PARIS and CDBonn Description in my thesis and my notebook

9

npd

npd

mmm

mmm

) 222

Fpp pmEsp

Spectator assumption Proton is real particle on its mass shell

npnp mmmm

Assumption nnpp mmmm

sppdn EmE

beam deuteron n

n

pF

pF

pb

target deuteron

Explanation of the quasi free Reaction For fixed beam momentum we have distribution of neutron momentum given by Fermi motions=gtdistribution of invariant system mass

10

The quasi-free reaction mechanism IN DETAILS

Formation of -mesic Tritium might be realized by quasi-free reactions as already successfully used at COSY to study meson production in quasi free proton-neutron collisions [1 2] Measurements of such reactions is possible for the external COSY-TOF detector

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

7

) ) h pdpTpdnpdd spbsspsp

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

The quasi-free reaction mechanism GENERAL

8

d

[1] M Lacombe et al Phys Rev C21 861-873 (1980)

[2] R Machleidt Phys Rev C63 024001 (2001)

Two models describing momentum distribution of nucleons inside deuteron PARIS and CDBonn Description in my thesis and my notebook

9

npd

npd

mmm

mmm

) 222

Fpp pmEsp

Spectator assumption Proton is real particle on its mass shell

npnp mmmm

Assumption nnpp mmmm

sppdn EmE

beam deuteron n

n

pF

pF

pb

target deuteron

Explanation of the quasi free Reaction For fixed beam momentum we have distribution of neutron momentum given by Fermi motions=gtdistribution of invariant system mass

10

The quasi-free reaction mechanism IN DETAILS

Formation of -mesic Tritium might be realized by quasi-free reactions as already successfully used at COSY to study meson production in quasi free proton-neutron collisions [1 2] Measurements of such reactions is possible for the external COSY-TOF detector

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

8

d

[1] M Lacombe et al Phys Rev C21 861-873 (1980)

[2] R Machleidt Phys Rev C63 024001 (2001)

Two models describing momentum distribution of nucleons inside deuteron PARIS and CDBonn Description in my thesis and my notebook

9

npd

npd

mmm

mmm

) 222

Fpp pmEsp

Spectator assumption Proton is real particle on its mass shell

npnp mmmm

Assumption nnpp mmmm

sppdn EmE

beam deuteron n

n

pF

pF

pb

target deuteron

Explanation of the quasi free Reaction For fixed beam momentum we have distribution of neutron momentum given by Fermi motions=gtdistribution of invariant system mass

10

The quasi-free reaction mechanism IN DETAILS

Formation of -mesic Tritium might be realized by quasi-free reactions as already successfully used at COSY to study meson production in quasi free proton-neutron collisions [1 2] Measurements of such reactions is possible for the external COSY-TOF detector

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

9

npd

npd

mmm

mmm

) 222

Fpp pmEsp

Spectator assumption Proton is real particle on its mass shell

npnp mmmm

Assumption nnpp mmmm

sppdn EmE

beam deuteron n

n

pF

pF

pb

target deuteron

Explanation of the quasi free Reaction For fixed beam momentum we have distribution of neutron momentum given by Fermi motions=gtdistribution of invariant system mass

10

The quasi-free reaction mechanism IN DETAILS

Formation of -mesic Tritium might be realized by quasi-free reactions as already successfully used at COSY to study meson production in quasi free proton-neutron collisions [1 2] Measurements of such reactions is possible for the external COSY-TOF detector

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

10

The quasi-free reaction mechanism IN DETAILS

Formation of -mesic Tritium might be realized by quasi-free reactions as already successfully used at COSY to study meson production in quasi free proton-neutron collisions [1 2] Measurements of such reactions is possible for the external COSY-TOF detector

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

11

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34ordm to 74ordm

STOP 07ordm to 767ordm

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

The angle range for proton spectator is small

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

12

Angle between p i in the

NCM frame 0180

NCM

Resonant structure below h meson production threshold

) h pdTnd bs

The systematic uncertainties in establishing the shape of the excitation functions are signicantly reduced when using this method In case of quasi-free reaction the energy scan (in the range of about 100 MeV) around the meson production threshold can be achieved from the Fermi motion of the nucleons inside the deuteron beam at a fixed value of the beam momentum

where the search for -mesic Tritium can be carried out by the measurement of the excitation function of the nd (3H-)bs dp1048576 reaction using a deuteron beam and tagging the nd reactions by measuring the spectator protons (psp) from the dd pspnd psp(3H-)bs pspdp1048576 reaction The signal from (3H-)bs is expected below the threshold of the nd -gthellip reaction threshold

) ) h pdpTpdnpdd spbsspsp

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

13

Resonant structure of the eta-mesic bound

state given by Breit-Wigner distribution

(with assumed width and binding energy)

Nucleon momenta in atomic nuclei

described by Fermi distributions

Spectator model

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

Assumed and Bs

14

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s )155(

)407(

MeVB

MeV

MeV

MeV

s 10

40

25

10

3

2

1

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

15

Omoacutewić poszczegoacutelne rozkłady roacuteżnice miedzy nimi

T

[3] Yu S Kalashnikova I M Narodetskii and V P Yurov Preprint ITEP-88-12 Moscow (1988)

[4] A Nogga Phys Rev C67 064004 (2003)

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

n

n

deuteron beam

deuteron target

before the reaction

n p n

h

proton spectator

T-h bound state

after the reaction

proton spectator

n

deuteron spectator

pion

proton

) ) h pdpTpdnpdd spspbsspsp

16

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

17

1 REACTION KINEMATIC

2 ASSUMPTIONS

3 DETECTOR GEOMETRY

ACCEPTANCE

) ) h pdpTpdnpdd spbsspsp

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

1 Omoacutewić to gdzie lecą cząstki z tej

reakcji

Proton_sp th=(010)st max_th=3st

Deuteron th=(030)st max_th=8st

Proton th=(0130)st max_th=40st

Pion th=(0180)st max_th=50st

Można sprawdzić na

c11ikpe1106ikpkfa-juelichde

target

18

psp

d

p

4 detector installed at an external beamline of the COSY synchrotron

START 34st to 74st

STOP 07st to 767st

) ) h pdpTpdnpdd spbsspsp

beam

at a fixed value of the beam momentum

START 34ordm to 74ordm

STOP 07ordm to 767ordm

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

Geometrical acceptance of the detector

19

) ) h pdpTpdnpdd spbsspsp

pdpspIn START and STOP detector

The acceptance of the reaction for each excess energy value is calculated as number of events accepted by detector divided by number of generated events An event is accepted when all outgoing particles being reaction products can be registered in the detector In simulations I assume that the outgoing particles are registered in START and STOP detectors

Trzeba jeszcze wytlumaczyc roznice miedzy A(Q) i A

ACCEPTANCE calculated for ten of beam momentum

values for the range of pb=26 GeVc to 35 GeVc

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

20

threshold

The excess energy distribution for nd -gt(T-h)bs reactions determined by the Fermi momentum distribution of neutron inside deuteron is presented in this figure for p_beam equal to 26 GeVc 31 GeVc and 35 GeVc For each case the number of nd -gt(T- h)bs generated events as a function of the excess energy Q is represented by solid line while the excess energy distribution for accepted events is shown by dashed line P_thr= 31 GeVc for the case if the Fermi momentum in the beam deuteron is equal to 0

Tu powinna Pani zwrocic uwage ze wraz ze zmiana pedu wiazki zmienia sie rozklad Q a w szczegolnosci wraz z rosnacym pedem wiazki cale widmo Q przesuwa sie ku wiekszym wartosciom

The excess energy distribution for nd -gt(T-h)bs reaction

thr

ndnd ssQ )(

)()(

QN

QNQA

gen

accN

QAA

Q

)(

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

21

EFFECTIVE ACCEPTANCE

gen

effN

NAA

)2060(

A-average acceptance

Ngen-number of generated

events

N(-6020)-number of generated

events for Q (-6020) MeV

In order to determine the effective acceptance for registering the quasi-free reaction in the near to threshold Q range from -60 MeV to 20 MeV when using the TOF detector the following formula is used

Ta formula głoacutewnie uwzględnia to że najbardziej interesujący dla nas jest obszar Q od -60 do 20 wiec zdarzenia z poza tego obszaru nie beda sie liczyly To dobrze sobie usmyslowic na slajdzie 20 dla widma dla p=35 gdzie wiekszosc zdarezn jest dla Q gt 20 i chociaz duzo sie będzie rejestrowac to wiekszosc bedzie w nieinteresujacym obszarze

) ) h pdpTpdnpdd spbsspsp

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

Assumed and Bs

22

N2

N

ndshTm hmmT sB

) )

sTT

Tnd

nd

Bmmm

ms

sN

hh

h

4

2

12

2

)bsTdd h

MeVB

MeV

s 10

101

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

23

EFFECTIVE ACCEPTANCE

BW

gen

BWBW

effN

NAA

)2060(

A-average acceptance

NBWgen-number of generated events

accepted with prob calculated acc

BW distr

NBW(-6020)-number of generated

events for Q (-6020) MeV accepted

with prob calculated acc BW distr

31GeVc

From the dependence shown in above figure it results that the highest probability for the registration of considered quasi-free dd -gt psp(T-h)bs -gt pspdpi-reaction is for the beam momentum pbeam=31 GeVc corresponding to the dd-gt p_sp(pf=0)(T-h)bs -gtpspdppi- reaction threshold whereas for the beam momentum above and below the threshold the effective acceptance decreases Above considerations were carried out for the Paris model of nucleon Fermi momentum distribution inside deuteron 1=10 MeV bound state width and analitic formula describing nucleon Fermi momentum distribution inside T The calculations are consistent with the one for CDBonn model of nucleon momentum distribution inside deuteron with an accurancy better than 4 and are independent of models of nucleon Fermi momentum distribution inside tritium

In the simulations of this quasi-free reaction it is assumed that the square of invariant mass of T- nuclei is given by Breit-Wigner distribution In this case an effective acceptance for the registration of the bound state decay products is calculated by formula

) ) h pdpTpdnpdd spbsspsp

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

For the quasi-free

acceptance is dependent on the beam momentum

value

The highest value of A (the most efficient

measurement) for pb=31GeVc corresponding to the

reaction threshold (pF=0)

24

) ) h pdpTpdnpdd spbsspsp

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund

INTERNATIONAL PHD PROJECTS IN APPLIED NUCLEAR PHYSICS AND INNOVATIVE TECHNOLOGIES This project is supported by the Foundation for Polish Science ndash MPD program co-financed by the European Union within the European

Regional Development Fund