Scientific Opportunities with In-flight Separated Beams

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Renormalized Interactions with EDF
Single-Particle Basis States and
NuShellX_at_MSU Alex Brown, Angelo Signoracci,
Morten Hjorth-Jensen and Bill Rae
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Closed-shell vacuum filled orbitals
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Closed-shell vacuum filled orbitals
Skyrme phenomenology
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Closed-shell vacuum filled orbitals
NN potential with V_lowk
Skyrme phenomenology
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Closed-shell vacuum filled orbitals
tuned valence two-body matrix elements
Skyrme phenomenology
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Closed-shell vacuum filled 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)
• TBME (two-body matrix elements) Evaluate N3LO
  Vlowk with radial wave functions obtained with
  EDF.
• TBME Evaluate core-polarization with an
  underlying single-particle spectrum obtained from
  EDF.
• TBME Calculate monopole corrections from EDF
  that would implicitly include an effective
  three-body interaction of the valence nucleons
  with the core.
• SPE Use EDF single-particle energies unless
  something better is known experimentally.

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• Why use energy-density functionals (EDF)?
• Parameters are global and can be extended to
  nuclear matter.
• Large effort by several groups to improve the
  understanding and reliability (predictability) of
  EDF in particular the UNEDF SciDAC project in
  the US.
• This will involve new and extended functionals.
• With a goal to connect the values of the EDF
  parameters to the NN and NNN interactions.
• 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?
• Binding energy for the closed shell
• Radial wave functions in a finite-well (expanded
  in terms of harmonic oscillator).
• ea - BE(A1,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.
• M(a,b) - BE(A2,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) orbitals N3LO Vlowk (lambda2.2)
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TBME for the lowest proton (g7/2) and neutron
(f7/2) orbitals N3LO Vlowk (lambda2.2) - 4hw
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TBME for the lowest proton (g7/2) and neutron
(f7/2) orbitals N3LO Vlowk (lambda2.2) - 4hw
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TBME for the lowest proton (g7/2) and neutron
(f7/2) orbitals N3LO Vlowk (lambda2.2) - 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?
• ea - BE(A1,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.
• M(a,b) -BE(A2,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
• 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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134Sb
Experiment Skxtb
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133Sb
Experiment adjusted to exp
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134Te
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133Sn
Experiment Skxtb
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jj44pn
fppn
sdpn
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_at_MSU?
• NuShellX - Nathan-type pn basis CI code
  implemented by Bill Rae (Garsington).
• NuShellX_at_MSU - developments at MSU that includes
  wrapper code for input, Hamiltonians, output and
  comparison to data. Three parts
• Toi - connection with nuclear data base (175 MB)
• Ham - connections with the codes of Morten
  Hjorth-Jensen together with EDF to generate new
  Hamiltonians.
• Shell implementations of NuShellX.
• Windows version now linux version being
  finished - maybe someday a Mac version.

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Toi Nuclear Data
.sp model space files .int Hamiltonian files
.sp .int
Ham Hamiltonian Input programs
Shell wrapper for NuShellX
.eps
Outputs for energies .lpt ltagt .lsf lta agt
.obd lta agt .tna postscrip (.eps) (pdf)
figures
library of tuned Hamiltonians .int files (sps
folder)
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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 basis within 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-dim41,355 M-dim1,963,461 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 compilers Next test replacement of
OpenMP with MPI Try out GPU