April 17

DoE review 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 LaboratoryUCRL-PRES-235658

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+AXi) at energy Eprojectile

Computational Workflow

TargetA = (N,Z)

UNEDF:VNN, VNNN…

Veff forscattering

Structure ModelMethods: HF, DFT,

RPA, CI, CC, …

TransitionsCode

Ground state Excited states

Continuum states

FoldingCode

TransitionDensities

(r)

KEY:Code Modules

UNEDF Ab-initio InputUser Inputs/Outputs

Exchanged DataFuture research

Eprojectile

Transition Potentials V(r) (Later: density-dependent & non-local)

Coupled ChannelsCode: FRESCO

Fit Optical PotentialCode: IMAGO

Preequilibriumemission

PartialFusionTheory

Hauser-Feshbachdecay chains

Compoundemission

Residues (N’,Z’)

ElasticS-matrixelements

Inelasticproduction

Voptical

Global opticalpotentials

Compoundproduction

Prompt particleemissions

Delayedemissions

Deliverables

(other work)

(UNEDF work)

Reactionwork here

April 17DoE review

4

Coupled channels n+A*

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.

RPA:PH:

n+90Zrat 40 MeV

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.

April 17DoE 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 (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 SL or el() n+90Zr (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 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)