Accurate Reaction Cross-section Predictions for Nucleon-Induced Reactions 06/24/2010

1. Performance Measures x.x, x.x, and x.x Accurate Reaction Cross-section Predictions for Nucleon-Induced Reactions06/24/2010 G. P. A. Nobre1,*, I. J. Thompson1, J. E. Escher1, F. S. Dietrich1, M. Dupuis2, J. Terasaki3 and J. Engel3 1PLS Directorate, Physics Division – LLNL, Livermore, CA 2CEA, DAM, DIF, Arpajon, France 3University of North Carolina, Chapel Hill, NC *nobre1@llnl.gov Prepared by LLNL under Contract DE-AC52-07NA27344

2. PLS Directorate - Physics Division - NPS

3. 1: UNEDF project: a national 5-year SciDAC collaboration Target A = (N,Z) Ground state Excited states Continuum states Structure ModelsMethods: HF, DFT, RPA, CI, CC, … Transition Density [Nobre] KEY: UNEDF Ab-initio Input User Inputs/Outputs Exchanged Data Related research UNEDF: VNN, VNNN… Transition Densities Veff for scattering UNEDF Reaction Work Folding [Escher, Nobre] Eprojectile Transition Potentials Deliverables Coupled Channels[Thompson, Summers] Hauser- Feshbach decay chains [Ormand] Partial Fusion Theory [Thompson] Residues (N’,Z’) Inelastic production Compound emission Two-step Optical Potential Elastic S-matrix elements Resonance Averaging [Arbanas] or Neutron escape [Summers, Thompson] Preequilibrium emission Voptical Global optical potentials Optical Potentials [Arbanas] PLS Directorate - Physics Division - NPS

4. Nuclear Excited States from Mean-field Models Collaboration with Chapel Hill: Engel & Terasaki • Mean-field HFB calculations using SLy4 Skryme functional • Use (Q)RPA to find all levels E*, with transition densities from the g.s. Uncorrelated particle-hole states Correlated p-h states in HO basis Correlated p-h states in 15 fm box Neutron separation energy is 9.5 MeV. Above this we have discretized continuum. PLS Directorate - Physics Division - NPS

5. Diagonal Density Example of diagonal Density for 90Zr RPA Folding of densities with n-n interaction  Transition potentials PLS Directorate - Physics Division - NPS

6. Transition densities to Transition potentials Diagonal folded potential Off-diagonal couplings All potentials real-valued Natural parity states only: no spin-flip, so no spin-orbit forces generated. No energy or density dependence. Exchange contributions included implicitly. (So far) PLS Directorate - Physics Division - NPS

7. Reaction Cross Sections with Inelastic Couplings • (Q)RPA Structure Calculations for n,p + 40,48Ca, 58Ni, 90Zr and 144 Sm • Couple to all excited states, E* < 10, 20, 30, 40 MeV • Find what fraction of σR corresponds to inelastic couplings Not Converged yet!  E* < 50, 60, 70, …? PLS Directorate - Physics Division - NPS

8. Inelastic Convergence • Coupling to more states gives larger effect • Convergence appears when all open channels are coupled Protons as projectile For reactions with protons as projectile, inelastic convergence is achieved with less couplings due to the Coulomb barrier PLS Directorate - Physics Division - NPS

9. Coupling Between Excited States • At not too low energies: • Individual cross-sections change very little, except for some few states: up to 20% • Overall sum of reaction over states remains the same • Supports the concept of “doorway states” g.s. Details in paper being prepared for submission to PRC PLS Directorate - Physics Division - NPS

10. Pick-up Channel: Deuteron Formation 40Ca(d,d) elastic scattering N. Keeley and R. S. Mackintosh*showed the importance of including pick-up channels in coupled reaction channel (CRC) calculations. *Physical Review C 76, 024601 (2007) Physical Review C 77, 054603 (2008) d PLS Directorate - Physics Division - NPS

11. Contribution of Transfer Channels • Large contribution to σR: closer to OM! • Significant non-orthogonality effects There are many nucleons in the target that can be picked out to make a deuteron. HarmonicOscillator Finite Well N=2n+L With spin-orbit force nocc(j) Sum Closedshells Effect depends on binding energy and size of bound state wave functions: Given by the mean-field model Neutrons Protons

12. Non-Orthogonality and Fraction of σR Behaviour of non-orthogonality is sensitive to changes of the deuteron potential: Better definition needed! Using Johnson-Soper* prescription: Using the Daehnick et al.§ potential for the deuteron. Vd(R)=Vn(r)+Vp(R) • Coupling to 90Zr(n,d,n) channel gives a large increment, approaching to the optical model calculation. • Non-Orthogonality has an additional effect. αCC < αCC+CRC and αCC+CRC+NO *Physical Review C 1, 976 (1970) §Physical Review C 21, 2253 (1980) PLS Directorate - Physics Division - NPS

13. Comparison with Experimental Data Good description of experimental data! There is still possibility for improvements. Inelastic convergence when coupling up to all open channels PLS Directorate - Physics Division - NPS

14. Comparison with Experimental Data Good description of experimental data! Inelastic and pick-up channels account for all reaction cross sections arXiv:1006.0267 Submitted to PRL PLS Directorate - Physics Division - NPS

15. Summary of Results at Elab = 30 MeV Targets Inelastic + Transfer with non-orthogonality 40Ca, 48Ca, 58Ni, 90Zr, 144Sm Inelastic couplings only Inelastic + Transfer Phenomenological Optical Model With all couplings, calculations agree with experimental data arXiv:1006.0267 - Submitted to PRL PLS Directorate - Physics Division - NPS

16. Elastic Angular Distributions Results will be shown in paper being prepared for submission to PRC • Provide complementary information on reaction mechanisms • Are sensitive to the effective interaction used Our approach predicts a variety of reaction observables. Data provides constraints on the ingredients. • Density-dependent effective interaction: • Resulting coupling potentials improve large-angle behavior, still need improvements for small angles. • Work in progress to treat and then test UNEDF Skyrme functionals. PLS Directorate - Physics Division - NPS

17. Conclusions • Inelastic (Q)RPA couplings account for a fraction of reaction cross-section • To achieve convergence, couplings to (at least) all open channels is necessary • Coupling to pick-up channel is very important • Deuteron potential • Non-orthogonality • Concept of “doorway states” is a good approximation: simplifies the problem, saves computational time • Coupling to inelastic and deuteron channels accounts for (almost) all reaction cross sections • Angular distributions are sensitive to the effective interaction arXiv:1006.0267 - Submitted to PRL PLS Directorate - Physics Division - NPS

18. Future Work - Next Steps • Incorporate UNEDF functionals into folding potentials and examine effects, in particular density-dependence (Jutta Escher) • Use densities from deformed QRPA code (Terasaki & Engel, Chapel Hill, NC)* • Analyze reactions on a range of nuclei, using spherical and deformed QRPA transition densities and functionals from UNEDF* • Two-step approach (Ian Thompson) • Couple to even higher states to achieve convergence* • Solve consistency issues about deuteron potential, break-up, triton coupling • Draw conclusions about the most important ingredients for a predictive reaction calculation. • Future Publications: • Detailed paper to be submitted to PRC • Proceeding for INPC2010, Vancouver *Computational Challenges PLS Directorate - Physics Division - NPS