Reaction Theory in UNEDF Optical Potentials from DFT models

1. Reaction Theory in UNEDFOptical Potentials from DFT models Ian Thompson*, J. Escher (LLNL) T. Kawano, M. Dupuis (LANL) G. Arbanas (ORNL) * Nuclear Theory and Modeling Group, Lawrence Livermore National Laboratory This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and under SciDAC Contract DE-FC02-07ER41457 UCRL-PRES-235658 DoE review

2. The Optical Potential • Crucial for Low-energy Neutron-Nucleus Scattering • The Optical Potential: • Contains real and imaginary components • Fits elastic scattering in 1-channel case • Summary of all fast higher-order effects • Imaginary part: gives production of compound-nucleus states • Essential to Hauser-Feshbach decay models. • When resonances: • Gives Energy-averaged Scattering Amplitudes. • A Deliverable from UNEDF Project DoE review

3. (n+AXi) at energy Eprojectile Computational Workflow Eprojectile (UNEDF work) Target A = (N,Z) Ground state Excited states Continuum states TransitionDensities(r) Structure ModelMethods: HF, DFT, RPA, CI, CC, … Transitions Code UNEDF: VNN, VNNN…  Folding Code Veff for scattering Transition Potentials V(r) (Later: density-dependent & non-local) (other work) Deliverables Inelastic production Compound production Coupled ChannelsCode: FRESCO Partial Fusion Theory Hauser-Feshbach decay chains Residues (N’,Z’) Delayed emissions Compound emission Elastic S-matrix elements Voptical Preequilibrium emission Prompt particle emissions Fit Optical Potential Code: IMAGO Global optical potentials KEY: Code Modules UNEDF Ab-initio Input User Inputs/Outputs Exchanged Data Future research Reaction work here

4. Spherical DFT calculations of 90Zr from UNEDF RPA calculation of excitation spectrum (removing spurious 1– state that is cm motion) RPA moves 1– strength (to GDR), and enhances collective 2+, 3– Extract super-positions of particle-hole amplitudes for each state. Consider n + 90Zr at Elab(n)=40 MeV Calculate Transition densities gs  E*(f) Folding with effective Veff  Vf0(r;) NO imaginary part in any input Fresco Coupled Inelastic Channels Try E* < 10, 20 or 30 MeV Maximum 1277 partial waves. Coupled channels n+A* PH: RPA: n+90Zr at 40 MeV DoE review

5. Predicted Cross Sections • Reaction Cross Section (red line) is R(L) = (2L+1) [1–|S|2] / k2 for each incoming wave L • Compare with R(L) from fitted optical potential such as Becchetti-Greenlees (blackline)And from 50% of imaginary part: (blue line) • Result: with E* < 30 MeV of RPA, we obtain about half of ‘observed’ reaction cross section. • Optical Potentials can be obtained by fitting to elastic SL or el() n+90Zr (RPA) at 40 MeV DoE review

6. Conclusions • We can now Begin to: • Use Structure Models for Doorway States, to • Give Transition Densities, to • Find Transition Potentials, to • Do large Coupled Channels Calculations, to • Extract Reaction Cross Sections & Optical Potentials • Other Work in Progress: • Direct and Semi-direct in (n,) Capture Reactions • Pre-equilibrium Knockout Reactions on Actinides (2-step, so far) • Still Need: • More detailed effective interaction for scattering (density dependence, all spin terms, etc) • Transfer Reactions • (Starting to) Unify Direct Reaction and Statistical Methods DoE review

7. Improving the Accuracy • Feedback to UNEDF Structure Theorists! • Re-examine Effective Interaction Vnn • Especially its Density-Dependence • We should couple between RPA states • (Known to have big effect in breakup reactions) • Damping of RPA states to 2nd-RPA states. • RPA states are ‘doorway states’. • Pickup reactions in second order: (n,d)(d,n) DoE review