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Transcript of Lawrence Livermore National Laboratory 1 PLS Directorate, Physics Division – LLNL, Livermore, CA 2...
Lawrence Livermore National Laboratory
1PLS Directorate, Physics Division – LLNL, Livermore, CA2CEA, DAM, DIF, Arpajon, France
3University of North Carolina, Chapel Hill, NC
Accurate Reaction Cross-section Predictions
for Nucleon-Induced Reactions06/24/2010
G. P. A. Nobre1,*, I. J. Thompson1, J. E. Escher1, F. S. Dietrich1, M. Dupuis2, J. Terasaki3 and J. Engel3
Prepared by LLNL under Contract DE-AC52-07NA27344
Performance Measures x.x, x.x, and x.x
2LLNL-PRES-438113
PLS Directorate - Physics Division - NPS
3LLNL-PRES-438113
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-stepOpticalPotential
PLS Directorate - Physics Division - NPS
4LLNL-PRES-438113
Nuclear Excited States from Mean-field Models
Mean-field HFB calculations using SLy4 Skryme functional Use (Q)RPA to find all levels E*, with transition densities from the g.s.
Uncorrelatedparticle-hole states
Correlated p-h states in HO basis
Correlated p-h states in 15 fm box
Neutron separation energy is 9.5 MeV.Above this we have discretized continuum.
Collaboration withChapel Hill: Engel& Terasaki
PLS Directorate - Physics Division - NPS
6LLNL-PRES-438113
Diagonal Density
PLS Directorate - Physics Division - NPS
Example of diagonalDensity for 90Zr
Example of diagonalDensity for 90Zr
RPA
Folding of densities with n-n interaction Transition potentials
7LLNL-PRES-438113
Transition densities to Transition potentials
Diagonal folded potential Off-diagonal couplings
Natural parity states only: no spin-flip, so no spin-orbit forces generated.No energy or density dependence. Exchange contributions included implicitly.
All potentials real-valuedAll potentials real-valued
(So far)PLS Directorate - Physics Division - NPS
8LLNL-PRES-438113
PLS Directorate - Physics Division - NPS
Reaction Cross Sections with Inelastic Couplings
(Q)RPA Structure Calculations for n,p + 40,48Ca, 58Ni, 90Zr and 144 Sm Couple to all excited states, E* < 10, 20, 30, 40 MeV Find what fraction of σR corresponds to inelastic couplings
Not Converged yet! E* < 50, 60, 70, …?Not Converged yet! E* < 50, 60, 70, …?
9LLNL-PRES-438113
Inelastic Convergence
Coupling to more states gives larger effect
Convergence appears when all open channels are coupled
PLS Directorate - Physics Division - NPS
For reactions with protons as projectile, inelastic convergence is achieved with less couplings due to the Coulomb barrier
Protons as projectile
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Coupling Between Excited States
PLS Directorate - Physics Division - NPS
g.s.
At not too low energies:
Individual cross-sections change very little, except for some few states: up to 20%
Overall sum of reaction over states remains the same
Supports the concept of “doorway states”
At not too low energies:
Individual cross-sections change very little, except for some few states: up to 20%
Overall sum of reaction over states remains the same
Supports the concept of “doorway states”
Details in paper being prepared
for submission to PRC
Details in paper being prepared
for submission to PRC
11LLNL-PRES-438113
Pick-up Channel: Deuteron Formation
PLS Directorate - Physics Division - NPS
N. Keeley and R. S. Mackintosh* showed the importance of
including pick-up channels in coupled reaction channel (CRC)
calculations.
N. Keeley and R. S. Mackintosh* showed the importance of
including pick-up channels in coupled reaction channel (CRC)
calculations.
40Ca(d,d) elastic scattering
*Physical Review C 76, 024601 (2007) Physical Review C 77, 054603 (2008)
d
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Contribution of Transfer Channels
€
0hω
€
1hω
€
2hω
€
3hω
€
0s€
0p€
0d
€
1s
€
0 f
€
1p€
0g
€
0s1/2€
0p3/2
€
0p1/2
€
0d5/2
€
1s1/2
€
0d3/2
€
0 f7/2
€
1p3/2
€
0 f5/2
€
1p1/2
€
0g9/2
€
0g7 / 2
€
1d5/2
€
(2)€
(4)
€
(2)
€
(6)
€
(2)
€
(4)
€
(8)
€
(4)
€
(6)
€
(2)
€
(10)
€
Nhω
€
nL
€
nL j
€
2 j +1
€
2 j +1∑
€
2€
6
€
8
€
14
€
16
€
20
€
28
€
32
€
38
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40
€
50
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2
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50
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20
€
8
HarmonicOscillator
FiniteWellN=2n+L
With spin-orbit force nocc(j) Closedshells
Sum
Neutrons
Protons
There are many nucleons in the targetthat can be picked out to make a deuteron.
Effect depends on binding energy and size of bound state wave functions: Given by the mean-field model
Large contribution to σR: closer to OM!
Significant non-orthogonality effects
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Non-Orthogonality and Fraction of σR
PLS Directorate - Physics Division - NPS
Behaviour of non-orthogonality is sensitive to changes of the deuteron potential:
Coupling to 90Zr(n,d,n) channel gives a large increment, approaching to the optical model calculation.
Non-Orthogonality has an additional effect.
Better definition needed!
Using Johnson-Soper* prescription:
Vd(R)=Vn(r)+Vp(R) Vd(R)=Vn(r)+Vp(R)
αCC < αCC+CRC and αCC+CRC+NOαCC < αCC+CRC and αCC+CRC+NO
Using the Daehnick et al.§ potential for the deuteron.
*Physical Review C 1, 976 (1970)§Physical Review C 21, 2253 (1980)
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Comparison with Experimental Data
PLS Directorate - Physics Division - NPS
Good description of experimental data!
Good description of experimental data!
There is still possibility for improvements.
Inelastic convergence when coupling up to all
open channels
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Comparison with Experimental Data
PLS Directorate - Physics Division - NPS
Good description of experimental data!
Good description of experimental data!
Inelastic and pick-up channels account for all reaction cross sections
arXiv:1006.0267Submitted to PRLarXiv:1006.0267
Submitted to PRL
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Summary of Results at Elab = 30 MeV
PLS Directorate - Physics Division - NPS
Inelastic + Transfer with non-orthogonality
Inelastic couplings only
Inelastic + Transfer
Phenomenological Optical Model
Targets
40Ca, 48Ca, 58Ni, 90Zr, 144Sm
With all couplings, calculations agree with experimental data
arXiv:1006.0267 - Submitted to PRLarXiv:1006.0267 - Submitted to PRL
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Elastic Angular Distributions
PLS Directorate - Physics Division - NPS
• Provide complementary information on reaction mechanisms• Are sensitive to the effective interaction used
Density-dependent effective interaction:
•Resulting coupling potentials improve large-angle behavior, still need improvements for small angles.•Work in progress to treat and then test UNEDF Skyrme functionals.
Our approach predicts a variety of reaction observables.
Data provides constraints on the ingredients.
Our approach predicts a variety of reaction observables.
Data provides constraints on the ingredients.
Results will be shown in paper being prepared for
submission to PRC
Results will be shown in paper being prepared for
submission to PRC
18LLNL-PRES-438113
Conclusions
Inelastic (Q)RPA couplings account for a fraction of reaction cross-section
To achieve convergence, couplings to (at least) all open channels is necessary
Coupling to pick-up channel is very important• Deuteron potential• Non-orthogonality
Concept of “doorway states” is a good approximation: simplifies the problem, saves computational time
Coupling to inelastic and deuteron channels accounts for (almost) all reaction cross sections
Angular distributions are sensitive to the effective interaction
PLS Directorate - Physics Division - NPS
arXiv:1006.0267 - Submitted to PRLarXiv:1006.0267 - Submitted to PRL
19LLNL-PRES-438113
PLS Directorate - Physics Division - NPS
Future Work - Next Steps
Incorporate UNEDF functionals into folding potentials and examine effects, in particular density-dependence (Jutta Escher)
Use densities from deformed QRPA code (Terasaki & Engel, Chapel Hill, NC)*
Analyze reactions on a range of nuclei, using spherical and deformed QRPA transition densities and functionals from UNEDF*
Two-step approach (Ian Thompson)
Couple to even higher states to achieve convergence*
Solve consistency issues about deuteron potential, break-up, triton coupling
Draw conclusions about the most important ingredients for a predictive reaction calculation.
*Computational Challenges
Future Publications:
• Detailed paper to be submitted to PRC• Proceeding for INPC2010, Vancouver