renormalized interactions with edf single-particle basis states and nushellx@msu alex brown, angelo...
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Renormalized Interactions with EDF Single-Particle Basis Statesand NuShellX@MSU
Alex Brown, Angelo Signoracci, Morten Hjorth-Jensen and Bill Rae
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Closed-shell vacuumfilled orbitals
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Closed-shell vacuumfilled orbitals
Skyrme phenomenology
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Closed-shell vacuumfilled orbitals
Skyrme phenomenology
NN potential with V_lowk
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Closed-shell vacuumfilled orbitals
Skyrme phenomenology
“tuned” valence two-body matrix elements
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Closed-shell vacuumfilled orbitals
“tuned” valence two-body matrix elements
A3 A2 A 1
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Typically one uses an harmonic-oscillator basis for the evaluation of the microscopic two-body matrix elements used in shell-model configuration mixing (N3LO + Vlowk+ core-polarization) .
Not realistic for the nuclei near the drip line.
No three-body interactions.
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Aspects of evaluating a microscopic two-body Hamiltonian (N3LO + Vlowk+ core-polarization) in a spherical EDF (energy-density functional) basis (i.e. Skyrme HF)
1)TBME (two-body matrix elements): Evaluate N3LO + Vlowk
with radial wave functions obtained with EDF.
2)TBME: Evaluate core-polarization with an underlying single-particle spectrum obtained from EDF.
3)TBME: Calculate monopole corrections from EDF that would implicitly include an effective three-body interaction of the valence nucleons with the core.
4)SPE: Use EDF single-particle energies – unless something better is known experimentally.
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Why use energy-density functionals (EDF)?
1)Parameters are global and can be extended to nuclear matter.
2)Large effort by several groups to improve the understanding and reliability (predictability) of EDF – in particular the UNEDF SciDAC project in the US.
3)This will involve new and extended functionals.
4)With a goal to connect the values of the EDF parameters to the NN and NNN interactions.
5)At this time we have a reasonably good start with some global parameters – for now I will use Skxtb (Skyrme with tensor) [BAB, T. Duguet, T. Otsuka, D. Abe and T. Suzuki, Phys. Rev. C 74, 061303(R) (2006)}.
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Calculations in a spherical basis with no correlations
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What do we get out of (spherical) EDF?
1)Binding energy for the closed shell
2)Radial wave functions in a finite-well (expanded in terms of harmonic oscillator).
3)ea = - [BE(A+1,a) – BE(A)] gives single-particle energies for the nucleons constrained to be in orbital (n l j)a where BE(A) is a doubly closed-shell nucleus.
4)M(a,b) = - [BE(A+2,a,b) – BE(A)] - ea - ea gives the monopole two-body matrix element for nucleons constrained to be in orbitals (n l j)a and (n l j)b
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TBME for the lowest proton (g7/2) and neutron (f7/2) orbitalsN3LO – Vlowk (lambda=2.2)
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TBME for the lowest proton (g7/2) and neutron (f7/2) orbitalsN3LO – Vlowk (lambda=2.2) - 4hw
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TBME for the lowest proton (g7/2) and neutron (f7/2) orbitalsN3LO – Vlowk (lambda=2.2) - 4hw
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TBME for the lowest proton (g7/2) and neutron (f7/2) orbitalsN3LO – Vlowk (lambda=2.2) - 4hw
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134Sn
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134Sb
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134Te
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136Te
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What do we get out of (spherical) EDF?
1)ea = - [BE(A+1,a) – BE(A)] gives single-particle energies for the nucleons constrained to be in orbital (n l j)a where BE(A) is a doubly closed-shell nucleus.
2)M(a,b) = -[BE(A+2,a,b) – BE(A)] - ea - ea gives the monopole two-body matrix element for nucleons constrained to be in orbitals (n l j)a and (n l j)b
3)[BE(146Gd) – BE(132Sn)] (MeV) theory: filled g7/2 and d5/2
101.585 experiment
117.232 using ea and M(a,b) from N3LO for all
98.573 Skxtb applied to 146Gd and 132Sn
97.925 using ea and M(a,b) from Skxtb
100.452 Skxtb + 2p-2h from N3LO
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134Te
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Experiment Skxtb134Sb
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Experiment “adjusted to exp”133Sb
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134Te
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Experiment Skxtb133Sn
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sdpn
fppn
jj44pn
jj44 means f5/2, p3/2, p1/2, g 9/2 orbits for protons and neutrons
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Recent results from Angelo Signoracci
SDPF-U: Nowacki and Poves, PRC79, 014310 (2009).
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Energy of first excited 2+ states
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What is NuShellX@MSU?
1)NuShellX - Nathan-type pn basis CI code implemented by Bill Rae (Garsington).
2)NuShellX@MSU - developments at MSU that includes wrapper code for input, Hamiltonians, output and comparison to data. Three parts:
3)Toi - connection with nuclear data base (175 MB)
4)Ham - connections with the codes of Morten Hjorth-Jensen together with EDF to generate new Hamiltonians.
5)Shell – implementations of NuShellX.
6)Windows version now – linux version being finished - maybe someday a Mac version.
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HamHamiltonian Input programs
Shell wrapper for NuShellX
ToiNuclear Data
*.sp *.int
library of tuned Hamiltonians*.int files (sps folder)
*.sp model space files*.int Hamiltonian files
*.eps
Outputs for energies *.lpt<|a+|> *.lsf<|a+ a|> *.obd<|a+ a+|> *.tna
postscrip (*.eps) (pdf) figures
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Shears Bands
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Energy of first excited 2+ states
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What might be possible to consider in the spherical CI basiswithin the next 5-10 years with M-basis dimensions up to 1014
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Test case for speed of NuShellX - 48Cr 0+ J-dim=41,355 M-dim=1,963,461 10 eigenstates to 1 keV precision
Chip RAM cpu speed time cost GB GHz sec $Intel i7 Quad (8GB) (2.8)x(4) = 11.2 23 (1,400)
Intel i7 2xQuad (48GB) (3.3)x(8) = 26.4 11 (10,000) How far can we go - number of cores and speed?
Now – transfer from ifort to Portland compilersNext – test replacement of OpenMP with MPITry out GPU