Single nucleon transfer between p- shell nuclei around 10 MeV/u - for nuclear astrophysics Livius Trache Cyclotron 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 astrophysics A)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 independent 3.Combination of methods is useful – availability important 4.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 beams Major accomplishments: –ANC technique firmly established for transfer reactions Proton transfer for 7 Be(p,    11 C(p,  ) 12 N, 12 N(p,  ) 13 O, 13 N(p,  ) 14 O, 14 N(p,  ) 15 O neutron transfer and mirror symmetry for ANC –( 7 Li, 8 Li) for ( 7 Be, 8 B) → 7 Be(p,  ) 8 B ( S 17 ) –( 22 Ne, 23 Ne) for ( 22 Mg, 23 Al) → 22 Mg(p,  ) 23 Al –( 17 O, 18 O) for ( 17 F, 18 Ne) → 17 F(p,  ) 18 Ne 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: 7 Be, 8 B, 11 C, 12 N, 13 N, 17 F, … 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: proton-nucleus also peripheral ANC - independent on binding potential geometry! OMP knowledge crucial for reliable absolute values! Depend on geom (r 0,a) of proton-binding potential < 20-40% Depend on OMP * n Factors !!!

= studied at TAMU Ne-Na cycle CNO, HCNO 12 C 13 C 13 N 15 N 15 O 14 N 17 O 17 F 16 O 18 F 18 O 14 O 19 Ne 18 Ne 13 O 11 C 12 N 8B8B 7 Be 9C9C 10 C 10 B 11 N 11 B 9B9B 8 Be 22 Ne 21 Ne 9 Be 23 Na 17 Ne 16 F 15 F 22 Na 20 Na 24 Al 23 Al 25 Al 24 Mg 23 Mg 22 Mg 21 Mg 20 Mg 19 Na 19 F 20 Ne 25 Si 24 Si 26 Si 15 C 14 C 27 Al 26 Al 28 Si 27 Si 29 Si 26 Mg 25 Mg 27 P 26 P 28 P 30 P 29 P 31 P 28 S 27 S 29 S 31 S 30 S 32 S 32 Ar 31 Ar 33 Ar 35 Ar 34 Ar 36 Ar 31 Cl 30 Cl 32 Cl 34 Cl 33 Cl 35 Cl 34 S 33 S March 2009 etc. = planned 12 O 16 Ne 22 Al 23 Si 25 P 21 Al 30 Si (p,n) possible stable used at TAMU (p,2n) possible 21 Na also 38 Ca, 46 V, 57 Cu, 62 Ga, … 14 F Transfer r. RNB

Cross sections for (p,  ) from p-transfer reactions with RNB from MARS 12 C N Melamine target (Faraday Cup)  E-det. (PSSD) Er-det. 12 C N Melamine target (Faraday Cup)  E-det. (PSSD). 12 MeV/u H 2 cryotarget 12 MeV/u 99% pure, 4 mm dia Melamine target Four telescope system (“the cross”):  E – PSD 65, 110  m E – 500  m

Example 12 MeV on N 6 C 3 H 6 and C Primary beam: MeV/u 150 pnA Secondary beam: 12 MeV/u 2x10 5 pps Elastic  cm =8-60 deg. Fit OMP from folding JLM– no param adjust! Transfer 14 N( 12 N, 13 O) 13 C – fit w. DWBA extract ANC 12 N(p,  ) 13 O rate evaluated from ANC A. Banu et al., PRC 79, (2009) C 2 p1/2 ( 13 O g.s.)=2.53±0.30 fm -1

Details and problems Energy 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 potentials for 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 t V =1.2 fm, t W =1. 75 fm Renormalizations needed N v, N w 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 N v =0.37(2) N w =1.0(1), t V =1.20 fm, t W =1. 75 fm Extended to RNB: 7 Be, 8 B, 11 C, 12 N, 13 N, 17 F on 12 C, 14 N targets Double folding procedure:

Works for transfer reactions JLM 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, (2005) G. Tabacaru ea, PRC 73, (2006) 7 Be on melamine A. Azhari ea, PRL 82, 3960 (1999)

12 N on melamine TAMU 12 MeV/u A. Banu ea, PRC 79, (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: 6,7 Li, 10 B, 13 C, 14 N 10 MeV/u Parameters: renormalization coeff. Predicts well elastic scatt for RNBs: 7 Be, 8 B, 11 C, 12 N, 13 N, 17 F 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