April 17 DoE review 1 Reaction Theory in UNEDF Optical 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 UCRL-PRES 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

April 17DoE 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

 (n+A  X i ) at energy E projectile Computational Workflow Target A = (N,Z) UNEDF: V NN, V NNN … V eff for scattering Structure Model Methods: HF, DFT, RPA, CI, CC, … Transitions Code Ground state Excited states Continuum states Folding Code Transition Densities   (r) KEY: Code Modules UNEDF Ab-initio Input User Inputs/Outputs Exchanged Data Future research E projectile Transition Potentials V  (r) (Later: density-dependent & non-local) Coupled Channels Code: F RESCO Fit Optical Potential Code: I MAGO Preequilibrium emission Partial Fusion Theory Hauser-Feshbach decay chains Compound emission Residues (N’,Z’)  Elastic S-matrix elements Inelastic production V optical Global optical potentials Compound production Prompt particle emissions Delayed emissions Deliverables (other work) (UNEDF work) Reaction work here

April 17DoE review 4 Coupled channels n+A*  Spherical DFT calculations of 90 Zr 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. RPA:PH: n+ 90 Zr at 40 MeV  Consider n + 90 Zr at E lab (n)=40 MeV  Calculate Transition densities gs  E*(f)  Folding with effective V eff  V f0 (r; )  NO imaginary part in any input  Fresco Coupled Inelastic Channels  Try E* < 10, 20 or 30 MeV  Maximum 1277 partial waves.

April 17DoE review 5 Predicted Cross Sections  Reaction Cross Section (red line) is  R (L) =  (2L+1) [1–|S  | 2 ] / k 2 for each incoming wave L  Compare with  R (L) from fitted optical potential such as Becchetti- Greenlees (black line) 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 S L or  el (  ) n+ 90 Zr (RPA) at 40 MeV

April 17DoE 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

April 17DoE review 7 Improving the Accuracy  Feedback to UNEDF Structure Theorists!  Re-examine Effective Interaction V nn 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)