Analysis of 10Li and 11 low-energy transfer reactions · n9Li J ˇ= 1=2+;1=2 (w/o 9Li ... P3 (b) (c) d s /dE10 Li (mb/MeV) (a)P1I M.G.-R.,J.C.,A.M.M. 11Li and 10Li March 26, 2020

Analysis of 10Li and 11Li through intermediate-energy (p, pn) andlow-energy transfer reactions

M. Gómez-Ramos1, J. Casal2, A. M. Moro3

1 Institut für Kernphysik, Technische Universität Darmstadt,S2—14,Schlossgartenstrasse 9, 64289,Darmstadt

2 Dipartimento di Fisica e Astronomia “G. Galilei” and INFN-Sezione di Padova, Via Marzolo, 8,I-35131 Padova, Italy

3 Departamento de FAMN, Facultad de F́ısica, Universidad de Sevilla,Apdo. 1065, E-41080 Sevilla,Spain

March 26, 2020

M.G.-R.,J.C.,A.M.M. 11Li and 10Li March 26, 2020 1 / 34

Contents

1 Borromean nuclei. 11Li

2 p(11Li, d)10LiOverlap functionResults

3 p(11Li,pn)10LiTransfer to ContinuumResultsd-wave

49Li(d, p)10Li

Experimental dataResults

5 Conclusions


Borromean nuclei. 11Li

Contents




49Li(d, p)10Li


5 Conclusions



Borromean nuclei

n

1H 2H 3H 4H 5H 6H 7H

3He 4He 5He 6He 7He 8He 9He 10He

3Li 4Li 5Li 6Li 7Li 8Li 9Li 10Li 11Li 12Li 13Li

5Be 6Be 7Be 8Be 9Be 10Be 11Be 12Be 13Be 14Be 15Be 16Be

6B 7B 8B 9B 10B 11B 12B 13B 14B 15B 16B 17B 18B 19B 20B

8C 9C 10C 11C 12C 13C 14C 15C 16C 17C 18C 19C 20C 21C 22C

10N 11N 12N 13N 14N 15N 16N 17N 18N 19N 20N 21N 22N 23N

12O 13O 14O 15O 16O 17O 18O 19O 20O 21O 22O 23O 24O

14F 15F 16F 17F 18F 19F 20F 21F 22F 23F 24F 25F

16Ne 17Ne 18Ne 19Ne 20Ne 21Ne 22Ne 23Ne 24Ne 25Ne 26Ne

0 2 4 6 8 10 12 14 16

0

2

4

6

8

10

N

Z

p-rich

1p halo

2p halo

n-rich

1n halo

2n halo

stable

unbound

3-body system bound, but 2-body subsystems unbound

Close to neutron (proton) driplines

Halo structure



11Li,10Li

Halo structure

I. Tanihata et al, PRL 55, 2676 (1985)

Parity inversion

Unclear Structure

H.T. Fortune PLB 760, 577 (2016) E. Garrido et al NPA 700, 117 (2002)


p(11Li, d)10Li

Contents




49Li(d, p)10Li


5 Conclusions


p(11Li, d)10Li

p(11Li, d)10Li @ 5.7 MeV/A

Exp. data(A. Sanetullaev et alPLB 755, 481 (2016))

Participant-spectator model

DWBA formalism

Tif =〈χd10Liϕdφ10Li(E10Li)|Vpn|χp11Liφ11Li

〉Spectator model (10Li not modified byreaction)

Tif ∼〈χd10Liϕd|Vpn|χp11Liϕlj(E10Li)

〉ϕlj =< φ10Li(E10Li)|φ11Li >


p(11Li, d)10Li Overlap function

Overlap function < φ10Li(E10Li)|φ11Li >∣∣11Li〉Only ground state needed(B3b = 396keV)

3-body calculation (9Li+n+n)

Vn9Li, Vnn, Vnn9Li

Expansion in a transformedharmonic oscillator (THO) basiswith hyperspherical harmonicfunctions

Jπ = 0+ (w/o 9Li Spin)Jπ = 3/2− (w/ 9Li Spin)

〈10Li

∣∣Unbound (all positive energiespossible)

E10Li = 0− 3 MeV consideredScattering states for Vn9Li

Jπ = 1/2+, 1/2− (w/o 9Li Spin)Jπ = 1−, 2−, 1+, 2+ (w/ 9Li Spin)

Er (MeV) a (fm) %p1/2 %s1/2 rmat (fm) rch (fm)1+ 2+ 1− 2−

P1I 0.37 0.61 – -37.9 31 67 3.2 2.41P2I 0.30 0.55 -1.1 -6.7 44 54 3.0 2.40

P3 0.50 -29.8 30 64 3.6 2.48P4 0.23 -16.2 67 26 3.3 2.43


p(11Li, d)10Li Results

10Li-energy distributions

0

100

200

300

With 9Li Spin

-1 0 1 2

E10Li

(MeV)

0

100

200

300

1+ (p

1/2)

2+ (p

1/2)

1- (s

1/2)

2- (s

1/2)

Total

Total folded

0

200

400p

1/2

s1/2

TotalTotal folded

w/o 9Li Spin

-1 0 1 2 3

E10Li

(MeV)

0

200

400P4P2I (d)

P3

(b)

(c)

dσ

/dE

10L

i (m

b/M

eV)

(a) P1I



Deuteron angular distribution



Deuteron angular distribution

Shape of distribution independent ofthe model

Data compatible with p-wavetransferred neutron

Data sensitive to weight of p-wavecomponent

Mostly insensitive to othercharacteristics of 11Li wf


p(11Li,pn)10Li

Contents




49Li(d, p)10Li


5 Conclusions


p(11Li,pn)10Li

(p, pN) reactions

A proton and a nucleus collide in such a way that a proton or neutron isremoved and the residual nucleus remains.

High energies (∼ 200-400 MeV) to increase mean free path of nucleon in nucleus.It is sometimes referred to as “quasifree” because the main interaction happensbetween the incoming proton and the extracted nucleon as if it was a freecollision.

This “quasifree” characteristic allows for the use of the participant-spectatormodel


p(11Li,pn)10Li Transfer to Continuum

Reaction formalism: Transfer to Continuum

Prior representation of the T-matrixfor the processp+A(B+N+N)→ p+N+C(B+N)(participant-spectator model)

T 3bif =〈

Ψ3b(−)f |VpN + UpC − UpA|ϕCAχ

(+)pA

〉p-N continuum states discretized inenergy binsDeuteron included for (p, pn)

φj,πn (kn, ~r′) =

√2

πN

∫ knkn−1

φj,πn (k, ~r′)dk

3-body final state wavefunctionexpanded in proton-nucleon states

Ψ3b(−)f ≈

∑n,j,π

φj,πn (kn, ~r′)χ

(−)n,j,π(

~Kpn′, ~R′)


p(11Li,pn)10Li Transfer to Continuum

p(11Li,pn)10Li @ 280 MeV/A

Y. Aksyutina et al, PLB 666, 430(2008)

Obtained through fitting

No prediction of absolute crosssection

Relative weight of s and p weightcannot be known

Distorsion of distribution due toreaction mechanism?


p(11Li,pn)10Li Results

Transfer to the Continuum calculations

No 9Li Spin model: P3



Transfer to the Continuum calculations

9Li Spin model: P1I



Results of calculation

The two potentials bestagreeing with p(11Li,d)10Liare presented

p(11Li,pn)10Li gives a betteragreement with P1I

Main difference is thesplitting of the virtual state

Experimental resolutionsmoothes out distribution,hiding features


p(11Li,pn)10Li d-wave

Low-energy d-wave?

11Li(p, pn)10Li

Y. Aksyutina et al, PLB 666, 430 (2008)

11Li(C,X)10Li

H. Simon et al, NPA 791, 267 (2007)

Is there a d-wave resonance at ∼1.5 MeV?



11Li(p, pn)10Li∗: I9Li = 0 + d wave

Ep (MeV) a (fm) Ed (MeV) %p1/2 %s1/2 %d5/2 rmat (fm) rch (fm)P5 0.50 -29.8 1.5 35 39 23 3.2 2.42

0 0,5 1 1,5E

n9Li

(MeV)

0

25

50

75d

σ/d

En

9L

i (m

b/M

eV)

P5d wavep waves wave

0 0,5 1 1,5 2E

n9Li

(MeV)

0

25

50

75

dσ

/dE

n9L

i (m

b/M

eV)

Exp data

Before Exp. Res.

After Exp. Res.



11Li(p, pn)10Li∗: d-wave?

0

25

50

75

P1Is wavep wave

Exp. data

Before Exp. Res.

After Exp. Res.

0 0.5 1 1.5E

n9Li

(MeV)

0

25

50

75

P5d wavep waves wave

0 0.5 1 1.5 2E

n9Li

(MeV)

1+

2+1

-

2-

dσ

/dE

n9L

i (m

b/M

eV)



11Li(p, d)10Li∗: d-wave?

0 30 60 90 120θ

c.m. (deg)

0.1

1

10

100

1000

dσ

/dΩ

(m

b/s

r)Exp. data (Sanetullaev et al)

p1/2

P1I

p1/2

P2I

p1/2

P3

p1/2

P4

p1/2

P5

Are there other reactions to discern between these two models?


9Li(d, p)10Li

Contents




49Li(d, p)10Li


5 Conclusions


9Li(d, p)10Li Experimental data

9Li(d, p)10Li

The explored spectrum is no longer limited by , instead

d(9Li, p)10Li at 2.4 MeV/A

H.B. Jeppesen et al, PLB 642, 449 (2006)

d(9Li, p)10Li at 11 MeV/A

M. Cavallaro et al, PRL 118, 012701(2017)

Is there a virtual state in 10Li?

Why do the spectra look so different?


9Li(d, p)10Li Experimental data

Transfer to Continuum, slightly different

Prior representation of the T-matrixfor the process d+B → p+A(N +B)(participant-spectator model)

T 3bif =〈

Ψ3b(−)f |VNB + UpB − UdB |ϕABχ

(+)dB

〉N-B continuum states discretized inenergy bins and allowed to couple

φj,πn (kn, ~r′) =

√2

πN

∫ knkn−1

φj,πn (k, ~r′)dk

3-body final state wavefunctionexpanded in neutron-9Li states

Ψ3b(−)f ≈

∑n,j,π

φj,πn (kn, ~r′)χ

(−)n,j,π(

~KNB′, ~R′)


9Li(d, p)10Li Results

P3: warmup

0 0.5 1 1.5E

x (MeV)

0

10

20

30

dN

/dE

x (

cou

nts

per

10

0 k

eV)

0 1 2 3 4E

x (MeV)

0

1

2

3

4

5

dσ

/dE

x (

mb

/MeV

)

Datas

1/2

p1/2

Total

a) E=2.4 MeV/u (θc.m.

=98o-134

o)

b) E=11.1 MeV/u (θc.m.

=5.5o-16.5

o)

At 2.4 MeV/A, the maximum energy is too low to explore the spectrum over ∼1MeV, we will not get the d-wave resonance from there



P1I

0 0.5 1 1.5E

x (MeV)

0

10

20

30

dN

/dE

x (

cou

nts

per

10

0 k

eV)

0 1 2 3 4E

x (MeV)

0

1

2

3

4

5

dσ

/dE

x (

mb

/MeV

)

Data

s1/2

1-

s1/2

2-

p1/2

1+

p1/2

2+

Total

a) E=2.4 MeV/u (θc.m.

=98o-134

o) b) E=11.1 MeV/u (θ

c.m.=5.5

o-16.5

o)



Different spectra: Angular ranges

0 30 60 90 120 150

θc.m.

(deg)

0.1

1

10

100

dσ

/dΩ

(m

b/s

r)

0 30 60 90 120 150

θc.m.

(deg)

0.001

0.01

0.1

1

10

100

dσ

/dΩ

(m

b/s

r)

0 10 2010

-2

10-1

100

101

102s

1/2 1

-

s1/2

2-

p1/2

1+

p1/2

2+

Total

(Ex


P3 vs P5: Low-energy d-wave resonance?

0 1 2 3 4E

x (MeV)

0

2

4

6

8

10d

σ/d

Ex (

mb/M

eV)

TRIUMF datas

1/2

p1/2

d5/2

Sum

0 1 2 3 4E

x (MeV)

0

2

4

6

8

10

dσ

/dE

x (

mb/M

eV)

P3 P5

Strong coupling to d-wave states, this rules out a defined low-energy resonance(it could be fragmented)



P1I: Ambiguities in the l = 2 contribution

0 1 2 3 4E

x (MeV)

0

1

2

3

4

5

6

dσ

/dE

x (

mb

/MeV

)

E4

-= 6 MeV

0 1 2 3 4E

x (MeV)

0

1

2

3

4

5

6

dσ

/dE

x (

mb

/MeV

)

TRIUMF data

s1/2

1-

s1/2

2-

p1/2

1+

p1/2

2+

d5/2

(1-,2

-,3

-,4

-)

Sum

E4

-=3.9 MeV

(1−, 2−, 3−, 4−) multiplet, too many free parameters to adjustphenomenologically, and too few data.



NFT calculations

d(9Li, p)10Li at 2.4 MeV/A d(9Li, p)10Li at 11 MeV/A

F. Barranco et al, PRC 101, 031305(R) (2020)


Conclusions

Contents




49Li(d, p)10Li


5 Conclusions


Conclusions

Conclusions

A method to obtain < C +N |C +N +N > overlaps for Borromean nuclei from3-body structure calculations has been developed and applied to 11Li.

These overlaps can be used for various reactions, as long as they verify theparticipant-spectator model for the components of the Borromean nucleus

The method has been applied for the reactions p(11Li, d)10Li at 5.7 MeV/A,p(11Li,pn)10Li at 280 MeV/A, and 9Li(d, p)10Li at 2.4 and 11.1 MeV/Aobtaining remarkable agreement for all reactions, using the same n-9Liinteraction.

The (p, d) transfer reaction is found to be sensitive to the angular momentumand spectroscopic factor of the transferred nucleon mostly.

The (p, pn) nucleon removal reaction seems to favour a description including thespin of 9Li and splitting of the virtual state and resonance or the inclusion oflow-energy d-wave resonance

The 9Li(d, p)10Li transfer rejects low-energy d-wave resonance, but the d-wavespectrum is still not well understood (10Li always laughs last).


Conclusions

14Be(p, pn)13Be∗, A. Corsi et al, PLB 797, 134843 (2019)

0 1 2 3 4ε

n-12

Be (MeV)

0

5

10

15

20

25

30

35

dσ

/dε

n-1

2B

e (m

b/M

eV)

present data

1/2+ [s1/2 ⊗ 0

+]

1/2- [p1/2 ⊗ 0

+]

5/2+ [d5/2 ⊗ 0

+]

5/2+ [s1/2 ⊗ 2

+]

total TC

Fig. from Y. Aksyutina et al, PRC 87,064316 (2013)

-300 -200 -100 0 100 2000.0

0.2

0.4

0.6

0.8

1.0

dN

/dp

x (

arb. unit

s)

s wavep wave

d wave

0 - 0.2 MeV

-300 -200 -100 0 100 200 300p

x (MeV/c)

0.4 - 0.6 MeV

-200 -100 0 100 200 300

1.8 - 2.2 MeV

χ2/N = 3.6 χ

2/N = 4.5 χ

2/N = 7.47


Borromean nuclei. 11Lip(11Li,d)10LiOverlap functionResults

p(11Li,pn)10LiTransfer to ContinuumResultsd-wave

9Li(d,p)10LiExperimental dataResults

Conclusions

Documents

Analysis of 10Li and 11 low-energy transfer reactions · n9Li J ˇ= 1=2+;1=2 (w/o 9Li ... P3 (b) (c) d s /dE10 Li (mb/MeV) (a)P1I M.G.-R.,J.C.,A.M.M. 11Li and 10Li March 26, 2020