Lawrence Livermore National Laboratory Physical Sciences Directorate - N Division Coupled Channel Calculations 06/25/2008 Gustavo P. A. Nobre Prepared by LLNL under Contract DE-AC52-07NA27344 Performance Measures x.x, x.x, and x.x

Target A = (N,Z) UNEDF: V NN, V NNN … V eff for scattering Structure Models Methods: HF, DFT, RPA, CI, CC, … Transition Density [Nobre] Ground state Excited states Continuum states Folding [Escher, Nobre] Transition Densities KEY: UNEDF Ab-initio Input User Inputs/Outputs Exchanged Data Related research E projectile Transition Potentials Coupled Channels or DWBA [Thompson, Summers] Optical Potential [Arbanas] Preequilibrium emission Partial Fusion Theory [Thompson] Hauser- Feshbach decay chains [Ormand] Compound emission Residues (N’,Z’) Elastic S-matrix elements Inelastic production V optical Global optical potentials Deliverables UNEDF Reaction Work Resonance Averaging [Arbanas] Neutron escape [Summers, Thompson] or Two-step Optical Potential

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

4 LLNL-PRES Pick-up Channel: Deuteron Formation Physical Sciences Directorate - N Division N. Keeley and R. S. Mackintosh * showed the importance of including pick-up channels in coupled reaction channel (CRC) calculations. 40 Ca(d,d) elastic scattering * Physical Review C 76, (2007) Physical Review C 77, (2008)  Large increase of σ R : closer to optical model!  Significant non- orthogonality effects

5 LLNL-PRES Non-Orthogonality and Fraction of σ R Physical Sciences Directorate - N Division Behaviour of non-orthogonality is sensitive to changes of the deuteron potential:  Coupling to 90 Zr(n,d,n) channel gives a large increment, approaching to the optical model calculation.  Non-Orthogonality has an additional effect. Better definition needed! Using Johnson-Soper * prescription: V d (R)=V n (r)+V p (R) α CC < α CC+CRC and α CC+CRC+NO Using the Daehnick et al. § potential for the deuteron. * Physical Review C 1, 976 (2008) § Physical Review C 21, 2253 (1980)

6 LLNL-PRES Coupling Between Excited States Physical Sciences Directorate - N Division  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” At not too low energies:

7 LLNL-PRES p + 90 Zr Physical Sciences Directorate - N Division Same overall results as obtained for n + 90 Zr:  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

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

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

10 LLNL-PRES Physical Sciences Directorate - N Division 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 spherical QRPA transition densities – now available from Chapel Hill  Use future deformed QRPA code (underway at Chapel Hill)