Renormalized Interactions with EDF Single-Particle Basis States
and NuShellX@MSU
Alex Brown, Angelo Signoracci, Morten Hjorth-Jensen and Bill Rae
Closed-shell vacuum
filled orbitals
Closed-shell vacuum
filled orbitals
Skyrme
phenomenology
Closed-shell vacuum
filled orbitals
NN potential with V_lowk
Skyrme
phenomenology
Closed-shell vacuum
filled orbitals
“tuned” valence
two-body matrix elements
Skyrme
phenomenology
Closed-shell vacuum
filled orbitals
“tuned” valence
two-body matrix elements
A3
A2
A
1
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+ corepolarization) .
Not realistic for the nuclei near the drip line.
No three-body interactions.
Aspects of evaluating a microscopic two-body Hamiltonian
(N3LO + Vlowk+ core-polarization) in a spherical EDF (energydensity 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.
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)}.
Calculations in a spherical basis with no correlations
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
TBME for the lowest proton (g7/2) and neutron (f7/2) orbitals
N3LO – Vlowk (lambda=2.2)
TBME for the lowest proton (g7/2) and neutron (f7/2) orbitals
N3LO – Vlowk (lambda=2.2) - 4hw
TBME for the lowest proton (g7/2) and neutron (f7/2) orbitals
N3LO – Vlowk (lambda=2.2) - 4hw
TBME for the lowest proton (g7/2) and neutron (f7/2) orbitals
N3LO – Vlowk (lambda=2.2) - 4hw
134Sn
134Sb
134Te
136Te
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
134Te
134Sb
Experiment
Skxtb
Experiment
133Sb
“adjusted to exp”
134Te
133Sn
Experiment
Skxtb
jj44pn
fppn
sdpn
jj44 means f5/2, p3/2, p1/2, g 9/2 orbits for protons and neutrons
Recent results from Angelo Signoracci
SDPF-U: Nowacki and Poves, PRC79, 014310 (2009).
Energy of first excited 2+ states
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.
Toi
Nuclear Data
*.sp model space files
*.int Hamiltonian files
Ham
Hamiltonian
Input programs
*.sp
*.int
library of
tuned Hamiltonians
*.int files (sps folder)
Shell
wrapper
for NuShellX
*.eps
Outputs for energies *.lpt
<|a+|> *.lsf
<|a+ a|> *.obd
<|a+ a+|> *.tna
postscrip (*.eps) (pdf)
figures
Shears Bands
Energy of first excited 2+ states
What might be possible to consider in the spherical CI basis
within the next 5-10 years with M-basis dimensions up to 1014
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
GB
GHz
Intel i7 Quad (8GB) (2.8)x(4) = 11.2
time
sec
23
Intel i7 2xQuad (48GB) (3.3)x(8) = 26.4
11
How far can we go - number of cores and speed?
Now – transfer from ifort to Portland compilers
Next – test replacement of OpenMP with MPI
Try out GPU
cost
$
(1,400)
(10,000)