High momentum protons from 12 C fragmentation at intermediate energy

High momentum protons from 12C fragmentation at intermediate energy

B.M.Abramov, P.N.Alekseev,Yu.A.Borodin,S.A.Bulychjov, I.A.Dukhovskoy, A.B.Kaidalov,

A.I.Khanov, A.P.Krutenkova, V.V.Kulikov, M.A.Martemianov, M.A.Matsyuk, E.N.Turdakina,

Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia

Motivation for nuclear fragmentation study ITEP Heavy Ion Facility - TeraWatt Accumulator Experiment FRAGM: 12C + A F + X , T0 = 0.2- 3.2 GeV/n

Momentum and kinetic energy spectra of fragments x–distributions for 12C + Be p + X and QGS model Comparison with other experimental data Conclusion

Presented by A.P. Krutenkova

NPD RAS Conference, Moscow, ITEP, 21-25.11.2011

Apr 21, 2023 1A.P. Krutenkova, NPD RAS Session

Motivation for nuclear fragmentation study

1. Measurement of nuclear composition of secondary beams at ITEP heavy ion accelerator.

2. Precise measurement of high energy fragment spectra for a) search for cumulative effect in fragment production in heavy ion collisions,

b) test of theoretical models in the unstudied region of high momentum.

3. Now systematic data are needed as input to transport codes for radiotherapy with heavy ions, for shielding calculation for long-duration space missions and for RIB design


ITEP Heavy Ion Facility: TeraWatt Accumulator

Experiment FRAGM

Areas of slow extracted beams from U10 Ring

Target hall

Building for biological research and proton therapy

Areas of secondary beams from U10 Ring

Stand for radiation treatment of materials with high

intensity beams

Material irradiation zone 25 MeV proton LINAC

(I-2)

Area of fast extracted beam

Area of fast extracted beam from UK and U10 Rings

Area of fast extracted beam from UK Ring

10 m

Apr 21, 2023 3 A.P. Krutenkova, NPD RAS Session

Laser ion source

U-10 Ring

10 GeV PS. 8×1011 ppp4GeV IS. 4×108 12C/cycle

UK Ring

400 MeV IS2×109 ions/cycle

16m16m10m

Monitor

С-12

АВС

Scintillation counters

А 3(TOF+dE/dx) + H(20x10)B 2(TOF+dE/dx) Trigger = 1A ×1BC 14(TOF) 0.6 ×2.0 m×m

- thin foil internal target

- bending magnet

- quadrupole

Experiment FRAGM

θ


12C + Be p (d, t, 3He, 4He, 6He, 8He,… ) + X, θ = 3.5O T0 = 0.2, 0.3, 0.6, 0.95, 2.0 and 3.2 GeV/n

Relative yields of H and He isotopes at 3.5o from 12C fragmentation on Be target at 300 MeV

Rel

ativ

e yi

eld

Rigidity =plab /Z, GeV/c(Z is fragment charge)


Proton spectrum has non-Gaussian high momentum tail

t

Evaporation region tests

• In the rest frame of the nucleus,

momentum distribution of a fragment has Gaussian shape.

• Parabolic law for r.m.s. of momentum distributions:

σ2F= σ2

0AF(A – AF)/(A-1),

(A, AF are masses of nucleus, fragment;

σ is standard deviation) A.S. Goldhaber (1974)

• Limiting fragmentation hypothesis: fragmentation properties are independent of projectile energy and target mass.

Proton momentum spectrum in 12C rest frame (T0=300 MeV; fit with Gaussian from -0.2 to 0.1 GeV/c)

Invariant cross section (a.u.) vs proton longitudinal momentum (GeV/c)

Evaporation region σ=0.073±0.002 GeV/c

Preequilibrium region(“cumulative”)


Range of cross-section values covers eight orders of magnitude

PII, GeV/c

Kinematical limit for C+pp+X

Gaussian

Ts = 4.3±0.5 MeV

Forw. Backward


Triton spectrum is well described by Gaussian

Deuteron and triton momentum spectra (T0=300 MeV; fit with Gaussian )

χ 2 /ndf = 45.1/31

σ = .162±.003 GeV/c

Deuteron spectrum has sizeable high momentum non-Gaussian tail

σ = .121±.005 GeV/c

Apr 21, 2023 8

ALADIN GSI data Au+Au -> p+X at 1 GeV/n Hongfei Xi et al.(1997)

Statistical MultifragmentationModel

Other Measurements

A.P. Krutenkova, NPD RAS Session

Slope parameters from kinetic energy spectra (Ed3σ/d3p ~ Asexp(-T/Ts) + Acexp(-T/Tc); T0=300 MeV)

Ts = 4.3±0.5 MeV

Tc= 18.9±0.6 MeV

Forw. Backward


Invariant cross section (a.u.) vs rest frame kinetic energy T × sign (pII) (GeV)

Kinetic energy spectrum can be described by two exponents

Protons

Tc and Ts energy dependences for 12C (scaling value for pA is ~50 MeV)


Slope of preequilibrium (“cumulative”) part increases with T0 from 16 to 44 MeVTheoretical approaches connect “cumulative” effect with contribution of multiquark states in nuclei

Ts

Tc

T TC&TS, this experiment, C+Bep+X

TC, M.Anikina et al, C+Cp+X, JINR (1986) TC&TS,T.Odeh et al, Au+Aup+X, GSI (2000)

The production of cumulative particles in pA interaction was successfully considered in the framework of the QGSM. Assuming the existence of some coherent clusters in the nucleus and the asymptotic Regge behavior for their structure functions the distribution of quarks in the nucleus was derived and inclusive spectra of cumulative hadrons were analyzed.

Production of cumulative particles and Quark-Gluon String Model (QGSM)

A.V. Efremov, A.B. Kaidalov, G.I. Lykasov, N.V. Slavin, Phys. Atom. Nucl. 57 (1994) 932

Abstract


Cumulative protons in QGSM

Production of cumulative protons in fragmentation is considered as fragmentation into protons of clusters consisting of 3k valence quarks (k=1: (3q) - nucleon, k=2: (6q) – two-nucleon cluster, k=3: (9q) – three-nucleon cluster); wk is the probability to find

k-nucleon cluster in 12C

Fitted variables are: C’, W2 = w2/w1 , W3 = w3/w1 , , x


Ed3σ/d3p(x,pt2) =C’(w1g(x,pt

2)+w2b2(x,pt2)+w3b3(x,pt

2))

g(x,pt2)=G exp(-0.5 (1-x-)2 /x

2 ) exp(-0.5 pt2/p

2 )

b2(x,pt2)=B2 (x/2)3 (1-x/2)3exp(- pt

2), b2(x,pt2)=0 at x>2

b3(x,pt2)=B3 (x/3)3 (1-x/3)6exp(- pt

2), b3(x,pt2)=0 at x>3

where g, b2 , b3 are known fragmentation functions. G, B2 and B3 are known normalization constants. Transverse parameters andare from PRC 28 (1983) 1224

QGSM model fit of x=plab /p0 spectrum

Apr 21, 2023 13

3q

6q

9q


x=plab /p0 spectra at different energies

3q 3(3q)

Apr 21, 2023 14

6q

9q

3q


Probabilities of quark clusters existence

T0, GeV/n w1

(3q)w2

(6q)w3

(9q)

0.3 .87.87

0.13(3)0.13(2)

.0010(4).004(4)

0.6 .89 0.10(1) .005(2)

2.0 .91 0.09(2) .003(5)

3.2

12C(e,e’) atJ-LAB

.75

-

0.25(7)

0.19(4)

-

.006(2)

• Quantitative results on few nucleon clusters in nuclei could be obtained from fragmentation data.

• Wider range on x and wider projectile energy range are desirable


K.S. Egiyan et al (2006)

We used fitting procedure to get w2 and w3

Conclusion

• Light fragment momentum and kinetic energy spectra from reaction 9Be (12C, F)X were measured at T0 = 0.3-3.2 GeV/nucleon in evaporation and preequilibrium (“cumulative”) regions

• Momentum spectra in evaporation region are well described by Gaussians in accordance with SM.

• Proton kinetic energy spectrum in “cumulative” region has exponential shape with slope parameter Tc which increases with projectile energy from 16 to 44 MeV. It shows that scaling behaviour is not reached at studied energy range.

• Probabilities of existence of quark clusters in C-12 were estimated in QGSM. w2 ~10% and w3 <1% are in coincidence with those of two- and three-nucleon SRC measured at J-LAB


A.P. Krutenkova, NPD RAS Session Apr 21, 2023 17

Backup slides

Parameters of x spectra

T0, GeV/n

P0, GeV/c/n

Pt2 ,

(GeV/c)2

Xmax <x> x W2 W3 w w3x10 -3

0.2 0.67 .0016 1.35 - .152(6) - -

0.3 0.81 .0024 2.352.05

.086(6) .156(6).152(3)

.15(4)

.15(3).0015(4).004(4)

0.13(3)0.13(3)

10(4)4(4)

0.6 1.22 .0055 2.0 .108(3) .140(4) .11(1) .006(2) 0.10(1) 5(2)

-2.0

1.752.70

0.026

1.72.15

.127(1)-

-.186(10)

-.10(2)

-.0038(6)

0.09(2)

3(4)

3.2 4.03 .06 1.45 .122(7) .180(2) .31(9) - 0.25(7) -

3.6 4.63 2.1 .16(2) - - -


Run 11_04_03

Conclusion

• Light fragment momentum and kinetic energy spectra from reaction 9Be (12C, F)X were measured at T0 = 0.2-3.2 GeV/nucleon.

Proton momentum spectra cover evaporation and preequilibrium (“cumulative”) regions; eight orders of magnitude in cross section

• Momentum spectra in evaporation region are well described by Gaussians

• “Cumulative” region has exponential shape with slope parameter Tc increasing with initial energy from 16 to 44 MeV

• Estimated probabilities of existence of quark clusters w2 ~10% and w3 <1% are in agreement with those of two- and three-nucleon correlations in 12C nuclei measured at J-LAB


Mode of operation Accelerators Beam energy, MeV/n

Regime of beam extraction

Proton acceleration I-2

I-2/U-10

I-2/UK

25

up to 230

up to 3000

up to 9300 up to 3000

(9300)

up to 3000

pulse, 10 /s, 200 mA

medical extraction, 200 ns, 1011c-1

fast extraction, 800 ns, 5x1011c-1

internal target, 1s

slow extraction, 1s

fast and slow extraction, 0,5s

Ion acceleration, С, Al, Fe, Ag

(Mg,Si,Ti,V,Cr,Cu,Zn)

(Pb,Bi,U)

I-3/UK

I-3/UK/U-10

1,5 – 400

50 - 4000

fast extraction, 800 ns, С(2x109), Al(5x108), Fe(2.5x108), Ag(2x107) slow extraction, 0,5s

internal target, 1s, slow extraction, 1s

Nuclei accumulation,

С, Al, Fe,I-3/UK/U-10

200-300

700-1000fast extraction with compression to 150 ns, continue extraction of stacking beam

ITEP-TWAC Operation Parameters


Relative yield of H and He isotopes at 3.50 from 12C fragmentation on Be target at 600 MeV

Beam channel: rigidity P/Z=1.8 GeV/c/Z


Relative yield of H and He isotopes at 3.50 from 12C fragmentation on Be target

Rigidity =Plab /Z, GeV/c

Rel

ativ

e yi

eld


Relative yield of H/He isotopes at 3.50 from 12C fragmentation on Be target at 600 MeV


He-3 and He-4 momentum distributions

He-3 He-4

Ed3 σ

/d3 p

, re

lativ

e un

its

σ = .148±.003 GeV/cσ = .149±.003 GeV/c


Ed3 σ

/d3 p

, re

lativ

e un

its

He-6He-8

σ = .187±.007 GeV/cσ = .174±.009 GeV/c

He-6 and He-8 momentum distributions


Au+Au at 1000MeV/nfor protons.T.Odeh et al. PRL84,4557(2000)

Our data for C+Be at 300MeV/n -

Comparison with ALLADIN data


x=plab /p0 spectrum at 300 MeV

3q6q

9q


x=plab /p0 spectra at different energies

3q 3(3q)


6q

9q

3q

0.3 GeV/n 1.0 GeV/n this exp. Greiner et al. σ0

p 75.1±3.1 63±4 75.1±3.1 d 121.8±4.5 112±11 90.3±3.3 t 162.0±2.5 162±14 103.4±1.5 He-3 148.9±2.9 132±14 95.0±1.7 He-4 148.2±3.2 125±3 86.8±1.9 He-6 186.6±7.3 142±20 103.1±4.2 He-8 174.3±8.8 ------- 102.1±5.3

σF comparison with data and theoretical prediction

Data: D.E.Greiner et al. PRL35,152(1975) Theoretical prediction: A.S.Goldhaber, PL53B,306(1974)

(σF)2= (σ0)2F(Aproj. – F)/(Aproj,-1), where σ0 = 90 MeV/c


Test of Goldhaber parabolic law

This experiment – 0.3 GeV/n Greiner et al.- 1GeV/n

σ0 = 94±1 MeV/c χ2 /ndf =96/6

σ0 = 74±2 MeV/c χ2/ndf =20/5

σ0 = 90 MeV/c used by SM


Interpretation of “cumulative” events

• At high energies “cumulative” (x=plab /p0>1) production in pA was considered by Efremov, Kaidalov et al (1994) suggesting existence of multiquark clusters in nucleus and high energy behaviour of their structure functions in Quark-Gluon String Model (QGSM)

• Kaidalov proposed to use FRAGM data to estimate the values of probabilities wk to find k-nucleon clusters in 12C (k=1,2,3)

• Invariant cross-section was expressed as a sum of three terms:

Ed3σ/d3p(x,pt2)=C’(w1g(x,pt

2)+w2b2(x,pt2)+w3b3(x,pt

2))

where g, b2 , b3 are known fragmentation functions (fragmentation through nucleon component (3q), two- (6q) and three- (9q)

nucleon clusters, respectively; details at backup slide). w1+w2+w3=1


Documents

High momentum protons from 12 C fragmentation at intermediate energy