Coupled Channel Calculations 06/25/2008

1. Performance Measures x.x, x.x, and x.x Coupled Channel Calculations06/25/2008 Gustavo P. A. Nobre nobre1@llnl.gov Physical Sciences Directorate - N Division Prepared by LLNL under Contract DE-AC52-07NA27344

2. 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 or DWBA[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 or Resonance Averaging [Arbanas] Neutron escape [Summers, Thompson] Preequilibrium emission Voptical Global optical potentials Optical Potential [Arbanas]

3. Starting Point • RPA Structure Calculations for 90Zr • n + 90Zr scattering for different values of Elab • CC to RPA states, E* < 10, 20, 30, 40 MeV • Find what fraction of σR corresponds to inelastic couplings Not Converged yet!  E* < 50, 60, 70, …? Physical Sciences Directorate - N Division

4. 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) • Large increase of σR: closer to optical model! • Significant non-orthogonality effects Physical Sciences Directorate - N Division

5. 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 (2008) §Physical Review C 21, 2253 (1980) Physical Sciences Directorate - N Division

6. 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” Physical Sciences Directorate - N Division

7. p + 90Zr Same overall results as obtained for n + 90Zr: • CC has not converged yet with states up to 40 MeV • CC+ CRC + non-orthogonality give most of reaction cross-sections • Deuteron Optical Potential needs extra attention Physical Sciences Directorate - N Division

8. Comparison with Experimental Data Good description of experimental data! However… • There is still possibility for improvements. Physical Sciences Directorate - N Division

9. Effect of the Binding Energies on σR We reduced the binding energies of neutron levels of 90Zr close to Fermi level. We can qualitatively identify a dependence of the slope of the reaction cross-section on the binding energies of the target. Physical Sciences Directorate - N Division

10. Future Work - Next Steps • Couple to even higher states to achieve convergence • Solve consistency issues about deuteron potential, break-up, triton coupling • Two-step approach  Ian Thompson’s talk • Analyze reactions involving other nuclei from UNEDF collaboration • Investigate density dependence of interaction (J. Escher) • Use sphericalQRPA transition densities – now available from Chapel Hill • Use future deformed QRPA code (underway at Chapel Hill) Physical Sciences Directorate - N Division