Lawrence Livermore National Laboratory SciDAC Reaction Theory LLNL-PRES Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, CA This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 Ian Thompson

2 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Part of the UNEDF Strategy Excited States Effective Interaction Ground State

3 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory 1: UNEDF project: a national 5-year SciDAC collaboration 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 [Thompson, Summers] Optical Potentials [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

4 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Promised Year-4 Deliverables  Fold QRPA transition densities, with exchange terms, for systematic neutron-nucleus scattering.  Derive optical potentials using parallel coupled-channel reaction code capable of handling 10 5 linear equations  Use CCh channel wave functions for direct and semi- direct (n,  ) capture processes.  Consistently include multi-step transfer contributions via deuteron channels and implement and benchmark the two-step method to generate non-local optical potentials.  Extend and apply KKM model to scattering with doorway states.

5 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Three Talks on Reaction Theory Gustavo Nobre  Accurate reaction cross-section predictions for nucleon- induced reactions Goran Arbanas  Local Equivalent Potentials  Statistical Nuclear Reactions Ian Thompson  Generating and Using Microscopic Non-local Optical Potentials

Lawrence Livermore National Laboratory Generating and Using Microscopic Non-local Optical Potentials UCRL-PRES Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, CA This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 Ian Thompson

7 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Optical Potentials Define: The one-channel effective interaction to generate all the previous reaction cross sections  Needed for direct reactions: use to give elastic wave function Hauser-Feshbach: use to generate reaction cross sections = Compound Nucleus production cross sec.  In general, the ‘exact optical potential’ is Energy-dependent L-dependent, parity-dependent Non-local  Empirical: local, L-independent, slow E-dependence fitted to experimental elastic data

8 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Two-Step Approximation We found we need only two-step contributions These simply add for all j=1,N inelastic & transfer states: V DPP = Σ j N V 0j G j V j0. G j = [E n - e j – H j ] -1 : channel-j Green’s function V j0 = V 0j : coupling form elastic channel to excited state j Gives V DPP (r,r’,L,E n ): nonlocal, L- and E-dependent. In detail: V DPP (r,r’,L,E n ) = Σ j N V 0j (r) G jL (r,r’) V j0 (r’) = V + i W Quadratic in the effective interactions in the couplings V ij Can be generalised to non-local V ij (r,r’) more easily than CCh. Treat any higher-order couplings as a perturbative correction We found we need only two-step contributions These simply add for all j=1,N inelastic & transfer states: V DPP = Σ j N V 0j G j V j0. G j = [E n - e j – H j ] -1 : channel-j Green’s function V j0 = V 0j : coupling form elastic channel to excited state j Gives V DPP (r,r’,L,E n ): nonlocal, L- and E-dependent. In detail: V DPP (r,r’,L,E n ) = Σ j N V 0j (r) G jL (r,r’) V j0 (r’) = V + i W Quadratic in the effective interactions in the couplings V ij Can be generalised to non-local V ij (r,r’) more easily than CCh. Treat any higher-order couplings as a perturbative correction Tried by Coulter & Satchler (1977), but only some inelastic states included

9 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Previous examples of Non-local Potentials  Coulter & Satchler NP A293 (1977) 269: Imaginary Part Real Part

10 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Calculated Nonlocal Potentials V(r,r’) now Real Imaginary L=9 L=0

11 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Low-energy Equivalents: V low-E (r) = ∫ V(r,r’) dr’ Real Imaginary See strong L-dependence that is missing in empirical optical potentials.

12 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Comparison of (complex) S-matrix elements Comparison of CRC+NONO results with Empirical optical potls (central part). See more rotation (phase shift). Room for improvements! Labeled by partial wave L

13 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Exact equivalents: fitted to S-matrix elements Fit real and imaginary shapes of an optical potential to the S-matrix elements. Again: too much attraction at short distances

14 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Perey Effect: of Non-locality on Wavefunctions WF(NL) = WF(local) * Perey-factor If regular and irregular solutions have the same Perey factor, then we have a simple derivation: Since local wfs have unit Wronskian: Wr(R,I) = [ R’ I – I’ R ] / k We have: PF= sqrt(Wr(Reg NL,Irreg NL )) We see large R- and L-dependent deviations from unity! Significant for direct reactions: inelastic, transfer, captures.

15 LLNL-PRES UNEDF Meeting, June 2010 Lawrence Livermore National Laboratory Further Research on Optical Potentials 1.Compare coupled-channels cross sections with data 2.Reexamine treatment of low partial waves: improve fit? 3.Effect of different mean-field calculations from UNEDF. 4.Improve effective interactions: Spin-orbit parts  spin-orbit part of optical potential Exchange terms in effective interaction  small nonlocality. Density dependence (improve central depth). 5.Examine effect of new optical potentials: Are non-localities important? Is L-dependence significant? 6.Use also ab-initio deuteron potential. 7.Do all this for deformed nuclei (Chapel Hill is developing a deformed-QRPA code)