Single nucleon transfer between p-shell nuclei around 10 MeV/u

- for nuclear astrophysics

Livius TracheCyclotron Institute, Texas A&M University

ATLAS workshop 2009 User Group Meeting

Argonne, IL, Aug 8-9, 2009

Techniques used to determine (p,) reaction rates

• Work at TAMU on nuclear astrophysicsA) indirect methods (p- or n-transfer)B) RNBs or stable beams

• Lessons learned:1. Seek the relevant quantities (ex: SF vs ANC)2. Model or parameter independent3. Combination of methods is useful – availability

important4. Need more in terms of supportive information for

reliable calculations: theories, models (and codes), effective n-n interactions, systematics … → still need good stable beam data OMP

MARS group at Texas A&M University

Indirect methods for transfer reactions with stable and unstable beamsMajor accomplishments:

– ANC technique firmly established for transfer reactions• Proton transfer for 7Be(p, 11C(p,)12N, 12N(p, )13O, 13N(p,

)14O, 14N(p, )15O• neutron transfer and mirror symmetry for ANC

– (7Li,8Li) for (7Be,8B) → 7Be(p, )8B ( S17)– (22Ne,23Ne) for (22Mg,23Al) →22Mg(p,)23Al– (17O,18O) for (17F,18Ne) →17F(p, )18Ne

• Optical Model Potentials for nucleus-nucleus collisions from double-folding procedure using JLM eff inter. Needed in DWBA. Established with stable beams and tested for RNBs: 7Be, 8B, 11C, 12N, 13N, 17F, …

• Advances in Trojan-horse method (extrap to E=0 and electron screening effects)

Extracting spectroscopic factors or ANCs

Transfer reaction B+d→A+a peripheral (absorption)

• Transfer matrix element:

• Cross section in terms of the ANCs:

22 2

2( ) ( ) A A d d

A A

A

d

A d d

d

A dBp

DWl j l j

Bpl j apl jl j apl j bd b

C Cd

proton-nucleus also peripheral

( )2

, ( )ABpp C

ANC - independent on binding potential geometry!OMP knowledge crucial for reliable absolute values!

( ) ( )A df Bp ap iM I V I

I CW r

rBpA

r R

BpA l Bp Bp

Bp

Bp NA

, ( )12

2

Depend on geom (r0,a) of proton-binding potential < 20-40%

Depend on OMP* n Factors !!!

= studied at TAMU

Ne-Na cycleCNO, HCNO

12C 13C

13N 15N

15O

14N

17O

17F

16O

18F

18O14O

19Ne18Ne

13O

11C

12N

8B

7Be

9C 10C

10B

11N

11B9B

8Be

22Ne21Ne

9Be

23Na

17Ne

16F15F

22Na20Na

24Al23Al 25Al

24Mg23Mg22Mg21Mg20Mg

19Na

19F

20Ne

25Si24Si 26Si

15C14C

27Al26Al

28Si27Si 29Si

26Mg25Mg

27P26P 28P 30P29P 31P

28S27S 29S 31S30S 32S

32Ar31Ar 33Ar 35Ar34Ar 36Ar

31Cl30Cl 32Cl 34Cl33Cl 35Cl

34S33S

March 2009

etc.

= planned

12O

16Ne

22Al

23Si

25P

21Al

30Si

(p,n) possible

stable

used at TAMU

(p,2n) possible

21Na

also 38Ca, 46V, 57Cu, 62Ga, …

14F

Transfer r.

RNB

Cross sections for (p,) from p-transfer reactions with RNB from MARS

12 C

12 N

Melamine target

(Faraday Cup)

E - det . (PSSD)

Er - det .

12 C

12 N

Melamine target

(Faraday Cup)

E - det . (PSSD)

.

12C @23 MeV/uH2 cryotarget

12N @12 MeV/u99% pure, 4 mm diaMelamine target

Four telescopesystem (“the cross”):E – PSD 65, 110 m E – 500 m

Example 12N @12 MeV on N6C3H6 and C

• Primary beam: 12C @ 23 MeV/u 150 pnA• Secondary beam: 12N @12 MeV/u 2x105 pps

• Elastic cm =8-60 deg.• Fit OMP from folding JLM– no param adjust!• Transfer 14N(12N,13O)13C – fit w. DWBA extract ANC• 12N(p,)13O rate evaluated from ANC

A. Banu et al., PRC 79, 025805 (2009) C2p1/2

(13O g.s.)=2.53±0.30 fm-1

1/ 2

2pC

Details and problemsEnergy resolution (bad!)Beam res. 1-2% 2-4 MeV

angular resolution (limited!)Beam res. 0.8 – 2 deg!

Ang distr → ANC → astrophys S-factor → react rate

Wide systematics loosely bound stable p-shell nuclei

Semi-microscopic double folding potentialsfor nucleus-nucleus collisions

• HFB densities (to best match the surfaces)• tried various effective interactions (M3Y, DDM3Y, JLM, etc…)• Settled for JLM• Smearing w. range parameters tV=1.2 fm, tW=1. 75 fm• Renormalizations needed Nv, Nw

• JLM - uses eff inter of Jeukenne, Lejeune and Mahaux (PRC 16, 1977)• n-nucleus Bauge ea (PRC 58, 1998):

– energy and density dependent– independent geometry for real and imaginary potentials– normalization independent of partners– reproduces ELASTIC and TRANSFER data

• Checked for loosely bound p-shell nuclei stable beams ~ 10 MeV/u– Found Nv=0.37(2) Nw=1.0(1), tV=1.20 fm, tW=1. 75 fm

• Extended to RNB: 7Be, 8B, 11C, 12N, 13N, 17F on 12C, 14N targets

212121 ),,,()()()( rRrssEvrrrdrdRV eff

Double folding procedure:

( ) ( , ) ( , )VV W WU r V r i WtN rN t

Works for transfer reactionsJLM works for a range of energies E/A=15-50 MeV/u

JLM works for elastic & transfer

Works for RNBs

J. Blackmon ea, PRC 73, 034606 (2005)

G. Tabacaru ea, PRC 73, 025808

(2006)

7Be on melamine

A. Azhari ea,PRL 82, 3960 (1999)

12N on melamineTAMU exps @ 12 MeV/u

A. Banu ea,PRC 79, 025805 (2009)

Optical Model Potentials for Nucleus-Nucleus collisions

for RNBs ~ 10 MeV/u

Essential to make credible DWBA calc needed in transfer r.

Have established semi-microscopic double folding using JLM effective interaction:

• Established from exps with stable loosely bound p-shell nuclei: 6,7Li, 10B, 13C, 14N … @ 10 MeV/u

• Parameters: renormalization coeff. • Predicts well elastic scatt for RNBs:

•7Be, 8B, 11C, 12N, 13N, 17F• 7-10% uncertainty in DWBA calc

L. Trache ea, PRC 61 (2000)F Carstoiu ea PRC 70 (2004)OMP: need extension to sd-shell:

•Work on stable projectiles at TAMU

•RNB of good quality – ATLAS ?!

•Energy and angular resolution

Trojan-horse with RNB ?!

TECSA - simulations• Texas-Edinburgh-Catania Silicon Array• To work alone at MARS or coupled with MDM after upgrade (TRIBF?!)• “Flat” detector has better angular resolution, but less coverage.• “Lampshade” detector has more angular coverage but trickier angular resolution

(solid angle).

BT Roeder – MC simulations, Sep 2008

Future