scidac reaction theory

Lawrence Livermore National Laboratory

SciDAC Reaction Theory

LLNL-PRES-436792

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

Ian Thompson

2LLNL-PRES-436792 UNEDF Meeting, June 2010


Part of the UNEDF Strategy

ExcitedStates

EffectiveInteraction

GroundState



1: UNEDF project: a national 5-year SciDAC collaboration

TargetA = (N,Z)

UNEDF:VNN, VNNN…

Veff forscattering

Structure ModelsMethods: HF, DFT,

RPA, CI, CC, …

TransitionDensity [Nobre]

Ground state Excited states

Continuum states

Folding[Escher, Nobre]

Transition Densities

KEY:UNEDF Ab-initio InputUser Inputs/Outputs

Exchanged DataRelated research

Eprojectile

Transition Potentials

Coupled Channels

[Thompson, Summers]

Optical Potentials[Arbanas]

Preequilibriumemission

PartialFusionTheory

[Thompson]

Hauser-Feshbach

decay chains[Ormand]

Compoundemission

Residues (N’,Z’)

ElasticS-matrixelements

Inelasticproduction

Voptical

Global opticalpotentials

Deliverables

UNEDF Reaction Work

ResonanceAveraging[Arbanas]

Neutron escape[Summers, Thompson]

or

Two-stepOptical

Potential



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,) 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

UCRL-PRES-436792

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

Ian Thompson



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

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 correctionTried by Coulter & Satchler (1977), but only some inelastic states includedTried by Coulter & Satchler (1977), but only some inelastic states included



Calculated Nonlocal Potentials V(r,r’) now

Real Imaginary

L=9

L=0



Low-energy Equivalents: Vlow-E(r) = ∫ V(r,r’) dr’

Real Imaginary

See strong L-dependence that is missing in empirical optical potentials.



Comparison of (complex) S-matrix elements

Comparisonof CRC+NONOresults 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

1. Compare coupled-channels cross sections with data

2. Reexamine treatment of low partial waves: improve fit?

3. Effect of different mean-field calculations from UNEDF.

4. Improve effective interactions:• Spin-orbit parts spin-orbit part of optical potential• Exchange terms in effective interaction small nonlocality.• Density dependence (improve central depth).

5. Examine effect of new optical potentials:• Are non-localities important?• Is L-dependence significant?

6. Use also ab-initio deuteron potential.

7. Do all this for deformed nuclei (Chapel Hill is developing a deformed-QRPA code)

scidac reaction theory

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