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

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, g ) reaction rates.

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

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  1. 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

  2. Techniques used to determine (p,g) reaction rates • Work at TAMU on nuclear astrophysics • indirect methods (p- or n-transfer) • RNBs or stable beams • Lessons learned: • Seek the relevant quantities (ex: SF vs ANC) • Model or parameter independent • Combination of methods is useful – availability important • 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

  3. 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 7Be(p, g)8B, 11C(p,g)12N, 12N(p, g)13O, 13N(p, g)14O, 14N(p, g)15O • neutron transfer and mirror symmetry for ANC • (7Li,8Li) for (7Be,8B) → 7Be(p, g)8B ( S17) • (22Ne,23Ne) for (22Mg,23Al) →22Mg(p, g)23Al • (17O,18O) for (17F,18Ne) →17F(p, g)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)

  4. Depend on OMP * n Factors !!! Depend on geom (r0,a) of proton-binding potential < 20-40% Extracting spectroscopic factors or ANCs • Transfer reaction B+d→A+a peripheral (absorption) • Transfer matrix element: • Cross section in terms of the ANCs: ANC - independent on binding potential geometry! OMP knowledge crucial for reliable absolute values! proton-nucleus also peripheral

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

  6. (Faraday Cup) (Faraday Cup) Er - det . . 12 12 C C D D E E - - det det . (PSSD) . (PSSD) 12 12 N N Melamine target Melamine target Cross sections for (p,g) from p-transfer reactions with RNB from MARS 12N @12 MeV/u 99% pure, 4 mm dia Melamine target 12C @23 MeV/u H2 cryotarget Four telescope system (“the cross”): DE – PSD 65, 110 mm E – 500 mm

  7. 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 qcm =8-60 deg. • Fit OMP from folding JLM– no param adjust! • Transfer 14N(12N,13O)13C – fit w. DWBA extract ANC • 12N(p,g)13O rate evaluated from ANC A. Banu et al., PRC 79, 025805 (2009) C2p1/2(13O g.s.)=2.53±0.30 fm-1

  8. Details and problems angular resolution (limited!) Beam res. 0.8 – 2 deg! Energy resolution (bad!) Beam res. 1-2% 2-4 MeV Ang distr → ANC → astrophys S-factor → react rate

  9. Wide systematics loosely bound stable p-shell nuclei

  10. 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 Semi-microscopic double folding potentialsfor nucleus-nucleus collisions Double folding procedure:

  11. JLM works for elastic & transfer JLM works for a range of energies E/A=15-50 MeV/u Works for transfer reactions

  12. Works for RNBs 7Be on melamine A. Azhari ea, PRL 82, 3960 (1999) G. Tabacaru ea, PRC 73, 025808 (2006) J. Blackmon ea, PRC 73, 034606 (2005)

  13. TAMU exps @ 12 MeV/u 12N on melamine 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) A. Banu ea, PRC 79, 025805 (2009) • 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 ?!

  14. 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

  15. Future

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