Two-Step Calculations of Nucleon-Nucleus Optical Potentials

1. Two-Step Calculations of Nucleon-Nucleus 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 LLNL-PRES-414025

2. Nucleon-nucleus Optical Potentials • UNEDF Deliverable: • Optical potentials for n-A scattering for energy En • Used for: • Compound-nucleus production – need reaction xsec sR(q,L) • Entrance/exit channels in direct reactions – need wfs ΨL(r) • Previous method: • Do coupled-channels calculation (CCh) with RPA excited states [Ti + Vb+ ei – En] Ψi (r) + ΣjN Vij(r) Ψj (r) = 0 • Use bare potential Vb = Vfold that is real. • Fit Vopt = Vb + VDPP by fitting elastic sCCh(q), after varying parameters of local Woods-Saxon form. • Requires ~150,000 RPA channels + ~100 transfer channels • Too difficult with present CCh methods (~5000 so far)

3. Counting RPA excited states (normal parity only) Levels in HO basis N=14 RPA levels inside r =16 fm RPA for 90Zr

4. How many Reaction Steps are Needed? • Gustavo Nobre’s work tells us we need: • All (Q)RPA excited states up to incident energy En • All possible intermediate deuteron channels • But not all couplings between the above states. • Jutta Escher’s work tells us we will need: • Exchange terms and other non-localities • Energy-dependence and/or effective mass and/or nonlocalities in the effective interaction for folding • SO, looks like we need only calculate two-step contributions • Couplings from gs to (and from) each excited state. • Exactly equivalent to CCh, but more favourable parallelisation Tried by Coulter & Satchler (1977), but only some inelastic states included

5. Two-Step Approximation • We need only calculate 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

6. Previous examples of Non-local Potentials • Coulter & Satchler NP A293 (1977) 269: Imaginary Part Real Part

7. JIVE: New Project at LLNL Parallel calculation of VDPP(r,r’,L,En) now underway • Produce full nonlocality, L- and E-dependence • No need for fitting WS parameters • Then calculate Vopt, elastic ΨL(r), • and then all nonelastic sj(q) for comparing with expt. Deliverables: • Consider delivering full VDPP(r,r’,L,En) ! • Look at averages over L, over r-r’, and at parameterising the En-dependence • Up to now, non-locality treated purely ad-hoc, and with several approximations that need to be tested. • Methods for non-locality already in the literature.

8. Reactions Workflow UNEDF Reaction Work Ground state Excited states Continuum states Target A = (N,Z) 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 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]