SciDAC Reaction Theory Ian Thompson Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, CA 94551 This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 LLNL-PRES-436792
Part of the UNEDF Strategy Ground State Effective Interaction Excited States
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]
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 105 linear equations • Use CCh channel wave functions for direct and semi-direct (n,g) 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.
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
Generating and UsingMicroscopic Non-local Optical Potentials Ian Thompson Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, CA 94551 This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 UCRL-PRES-436792
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
Two-Step Approximation We found we need only two-step contributions • These simply add for all j=1,N inelastic & transfer states: VDPP = ΣjN V0j Gj Vj0. Gj = [En - ej – Hj]-1: channel-j Green’s function Vj0 = V0j : coupling form elastic channel to excited state j • Gives VDPP(r,r’,L,En): nonlocal, L- and E-dependent. In detail: VDPP(r,r’,L,En) = ΣjN V0j(r) GjL(r,r’) Vj0(r’) = V + iW • Quadratic in the effective interactions in the couplings Vij • Can be generalised to non-local Vij(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
Calculated Nonlocal Potentials V(r,r’) now Real Imaginary L=0 L=9
Low-energy Equivalents: Vlow-E(r) = ∫ V(r,r’) dr’ Imaginary Real See strong L-dependence that is missing in empirical optical potentials.
Comparison of (complex) S-matrix elements Comparisonof CRC+NONO results with Empiricaloptical potls(central part). See more rotation(phase shift). Room for improvements! Labeled by partial wave L
Exact equivalents: fitted to S-matrix elements Fit real and imaginary shapes of an optical potentialto the S-matrix elements. Again: too much attraction at short distances
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(RegNL,IrregNL)) We see large R- and L-dependent deviations from unity! Significant for direct reactions: inelastic, transfer, captures.
Further Research on Optical Potentials • Compare coupled-channels cross sections with data • Reexamine treatment of low partial waves: improve fit? • Effect of different mean-field calculations from UNEDF. • Improve effective interactions: • Spin-orbit parts spin-orbit part of optical potential • Exchange terms in effective interaction small nonlocality. • Density dependence (improve central depth). • Examine effect of new optical potentials: • Are non-localities important? • Is L-dependence significant? • Use also ab-initio deuteron potential. • Do all this for deformed nuclei (Chapel Hill is developing a deformed-QRPA code)