Transcript Challenges of Direct Reactions

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-235658
April 17
DoE review
This work was performed under the
auspices of the U.S. Department of Energy
by Lawrence Livermore National
Laboratory under Contract DE-AC5207NA27344, and under SciDAC Contract
DE-FC02-07ER41457
1
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
April 17
Eprojectile
(UNEDF work)
Target
A = (N,Z)
Ground state
Excited states
Continuum states
Structure Model
Methods: HF, DFT,
UNEDF:
VNN, VNNN…

RPA, CI, CC, …
Transitions
Code
Transition
Densities
(r)
Folding
Code
Veff for
scattering
Transition Potentials V(r)
(Later: density-dependent & non-local)
(other work)
Deliverables
Hauser-Feshbach
decay chains
Residues
(N’,Z’)
Compound
production
Partial
Fusion
Theory
Inelastic
production
Coupled Channels
Code: FRESCO
Delayed
emissions
Compound
emission
Preequilibrium
emission
Prompt particle
emissions
Elastic
S-matrix
elements
Voptical
Fit Optical Potential
Global optical
potentials
Code: IMAGO
KEY:
Code Modules
UNEDF Ab-initio Input
User Inputs/Outputs
Exchanged Data
Future research
(n+AXi) at energy Eprojectile
Computational Workflow
Reaction
work here
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.



Consider n + 90Zr at Elab(n)=40 MeV
Calculate Transition densities gs  E*(f)
Folding with effective Veff  Vf0(r;)


Fresco Coupled Inelastic Channels


PH:
NO imaginary part in any input
Try E* < 10, 20 or 30 MeV
Maximum 1277 partial waves.
RPA:
n+90Zr
at
40 MeV
DoE review
April 17
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 BecchettiGreenlees (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
DoE review
April 17
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
April 17
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
April 17