Reaction Theory in UNEDF Optical Potentials from DFT models

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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
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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

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?(nA?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
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Coupled channels nA

• 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 lt 10, 20 or 30 MeV
• Maximum 1277 partial waves.

RPA
PH
n90Zr at 40 MeV
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Predicted Cross Sections

• Reaction Cross Section (red line) is ?R(L)
  ??(2L1) 1S??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 lt 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(?)

n90Zr (RPA) at 40 MeV
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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

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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)