Research Group A02 Report (2008-2012)

Nuclear Physics Project
1 fm

10 fm

10 km

1.Hadron int. from LQCD
S. Aoki (Tsukuba)
K. Sasaki (Tsukuba)
N. Ishii (Tsukuba)
H. Nemura (Tsukuba)

2. Ab initio Few-Body Cal.
E. Hiyama (RIKEN)
K. Murano (RIKEN)

1.Hadron int. from LQCD
T. Hatsuda (RIKEN)
S. Ozaki (Tokyo)
Y. Ikeda (Tokyo/RIKEN)
S. Sasaki (Tokyo)

3. Ab initio Many-Body Cal. 5. Dense matter
T. Otsuka (Tokyo)
A. Nakamura (Hiroshima)
T. Abe (Tokyo)
K. Nagata (Hiroshima)
N. Shimizu (Tokyo)
M. Takano (Waseda)
S. Fujii (Tokyo)
T. Suzuki (Nihon)

4. Time dep. DFT
T. Nakatsukasa (RIKEN)
K. Sato (RIKEN)
K. Yabana (Tsukuba)

HPCI Field5 Subjects 1,2 (2011-2015)

Summary of A02 achievements

Progress of Theoretical and Experimental Physics, (2012) special volume“Computational Approaches in Particle, Nuclear and Astrophysics”
http://www.oxfordjournals.org/our_journals/ptep/special_issue_a.html
1. Lattice quantum chromodynamical approach to nuclear physics
HAL QCD Collaboration, Prog. Theor. Exp. Phys. (2012) 01A105.
2. Gaussian expansion method for few-body systems and its applications
to atomic and nuclear physics
E. Hiyama, Prog. Theor. Exp. Phys. (2012) 01A204
3. New-generation Monte Carlo shell model for the K computer era
N. Shimizu et al., Prog. Theor. Exp. Phys. (2012) 01A205
4. Density functional approaches to collective phenomena in nuclei:
Time-dependent density functional theory for perturbative andnon-perturbative nuclear dynamics
T. Nakatsukasa, Prog. Theor. Exp. Phys. (2012) 01A207.
5. Towards extremely dense matter on the lattice
XQCD-J Collaboration, Prog. Theor. Exp. Phys. (2012) 01A103.

Basic Strategy of research group A02
BG/L -> PACS-CS -> T2K -> BG/Q -> KEI(10TF -> 100TF -> 1PF -> 10PF)KEI Computer @ AICS (RIKEN)(10PFlops)

NN
NNNNuclei

Supernova explosion
Neutron star merger

YN,YY
YNN
YYN, YYY

J-PARC (KEK/JAEA)

Hypernuclei

Neutron star:
max mass, cooling etc

BB & BBB force
from lattice QCD“high precision”
NN interactions# ofparameters

CD Bonn38

AV1840EFT in N3LO

24

QCD has only four parameters :mu, md, ms, ΛQCD

HAL QCD method forhadron-hadron interactions

BB potentials (flavor SU(3) limit)

IHAL QCD Coll.
Phys. Rev. Lett. 106 (2011) 162002
Nucl. Phys. A881 (2012) 28

Repulsive core in NN channel

1S
3S

0 channel

3D channel–11Attractive core in H channel

Growing NN tensor force

NN phase shifts (flavor SU(3) limit)

NN
Attraction stonger in the deuteron channel

HAL QCD Coll.,
Phys. Rev. Lett. 106 (2011) 162002
Nucl. Phys. A881 (2012) 28

Highlights (2008-2012) in Lattice Nuclear Force・ basic concepts of the NN ineracition in LQCD
S. Aoki, T. Hatsuda & N. Ishii, PTP 123 (2010) 89
N. Ishii et al. [HAL QCD Coll.], Phys.Lett. B712 (2012) 437

・ central, tensor, LS forces Doi (Fri.), Ishii, Murano (poster)・ SU(3) BB force, H-dibaryon & N☆

 Inoue (Fri.)

T. Inoue et al. [HAL QCD Coll.], PRL 106 (2011) 162002
T. Inoue et al. [HAL QCD Coll.], Nucl.Phys. A881 (2012) 28

・ YN and YY forces

 K. Sasaki, Yamada, Nemura (poster)H. Nemura et al. [HAL QCD Coll.], Phys.Lett. B673 (2009) 136

・ NNN force and unified contraction algorithm
T. Doi et al. [HAL QCD Coll.], PTP 127 (2012) 723

 T. Doi (Fri.)・ meson-baryon interactions

 Charron, Ikeda, Ozaki (poster)T. Kawani and S. Sasaki, Phys. Rev. D82 (2010) 091501 )LQCD: 964 lattice, a=0.1fm, L=9.6fm, mπ=135MeV at K cmputerAb initio
nuclear few-body
calculations
Gaussian Expansion Method (GEM)
for N-body problems (N=3,4,5,…) by E. Hiyama
・ nuclei・ hypernuclei
・ cold atoms

Summary of progress（FY 2008-2012）i) Applying Gaussian Expansion Method to N-body problems N=5 became possible by nowii) Establishing the following frameworks
・ any interactions such as

central force, spin-orbit force, tensor force,momentum dependent force, quadratic spin-orbit force etc.
・ particle conversion interactions such as

ΛN－ΣN, ΛΛーΞN－ΣΣ etc.
・ bound states, resonant states and continuum states,

simultaneouslyWe succeeded ininterpreting thisevent as anobservation of theground state of ΛΛ11Be.
Also, we succeededin performing 5-bodyproblem.

New data at Jlab in 2012.

E. Hiyama et al., PRC 80,054321(2009).
E. Hiyama and Y. Yamamoto,Prog. Theor.
Phys., 128, 105, (2012).

Inconsistent with the datapαnAb initio
nuclear many-body
calculations
Monte Carlo Shell Model (MCSM) by T. Otsuka et al.
・a tool to go beyond the Lanczos
method・variational wave function +energy-variance extrapolation
・obtain a few lowest eigenstates・small I/O, good parallel computation

Intrinsic Density from ab initio calc.
8BeSummary of progress（FY 2008-2012）
N.B. SPIRE Field 5 launched since FY2011• Monte Carlo Shell Model– Methodology developments :Algorithm development (8 times accelerated)
Y. Utsuno et al., Comp. Phys. Comm. 184 102 (2013).

Energy-variance extrapolation for precise estimation of eigenenergies
N. Shimizu et al., Phys. Rev. C 82 061305R (2010), ibid 85 054301(2012).

– Applications：No-core calculations in light-mass nuclei
T. Abe et al., Phys. Rev. C 86 054301 (2012),
L. Liu et al., Phys. Rev. C 86 014302 (2012)

Shell-model calc. in medium-heavy nuclei

Abe (Fri.)
Tsunoda (Fri.)

Neutron-rich Ni, Cr isotopes and shell evolution (Y. Tsunoda et al. ),Xe, Ba isotopes and shape “phase” transition (N. Shimizu et al. ) For review: N. Shimizu, et al. Prog. Theor. Exp. Phys. 2012 01A205 (2012).

Developments of the Monte Carlo shell Model towards “K computer”
T. Otsuka, M. Honma, T. Mizusaki, N.
Shimizu, and Y. Utsuno, Prog. Part. Nucl.
Phys. 47, 319 (2001).

PC cluster
100CPU parallel

N. Shimizu, Y. Utsuno, T. Mizusaki, T. Otsuka, T. Abe,and M. Honma, Phys. Rev. C 82, 061305(R) (2010).

Precise estimation of energy eigenvalue
by variance extrapolation + reordering technique

Parallel efficiency
N. Shimizu et al., Phys. Rev. C 85054301(2012).

Improvement of the MCSM
by Conjugate Gradient method

Algorithm tuning
for computation
OpenMP+MPI hybrid parallel
N. Shimizu, et al. Prog. Theor. Exp. Phys.
2012 01A205 (2012).

100 CPUs

8 times fasterat maximum
Y. Utsuno, N. Shimizu, T. Otsuka, and T. Abe,Comp. Phys. Comm. 184 102 (2013).

SPARC64 VIIIfx 705,024 corestime (sec.)

Performance improvement of theMCSM code in a single processor@ Xeon 5430 2.2GHz
3.5 times speed up
10 times speed up for no-core shell model calc.
The performance improvement owes to the rewritten algorithm.

Time Dependent
Density Functional Theory
Time-dependent Kohn-Sham-Bogoliubov (TDKSB) eq.
by Nakatsukasa and Yabana

Nuclear dynamics in the density
functional theory (DFT)• Developments in new DFT computer codes– Static DFT• DFT with the iso-rotational invariance (pn mixing)– Linear response in TDDFT• Real-time approach to E1 response• Systematic calculation of photonuclear reactions
with the finite amplitude method– Beyond the linear regime• Shape fluctuation and shape transition with amicroscopically-derived collective Hamiltonian• Real-time description of fusion dynamics

TDDFT descriptionof microscopic nuclear dynamics
中務原子核理論研究室
Large amplitude shape dynamics

Ebata et al., PRC 82, 034306 (2010);
JPCS 312, 092023 (2011)

Hinohara et al., PRC 82, 064313(2010) ; PPC 84, 061302(R) (2011)
Sato et al, PRC 86, 024316 (2012)

Shape coexistence phenomena arebeing recognized as a kind ofuniversal feature in nuclei. Quantum
shape fluctuation and mixing aredescribed by the quantized collective
Hamiltonian obtained through theTDDFT.

New approach to superfluid nuclear systems
New TDDFT method with time-dependent
pairing dynamics was developed, which reduces
the computational cost by several orders ofmagnitude. This may allow a full microscopic
description of nuclear fission in future.

Pygmy dipole states and constraints on symmetry energy
Inakura et al., PRC 80, 044301 (2009); PRC 84, 021302(R) (2011)

Pygmy dipole states are one of typical modes of excitation in
exotic nuclei. We show that they may provide valuable
information on the neutron-skin thickness and density
dependence of the symmetry energy.
Proton-neutron-mixing density functional theory
14O(ground 0+)Tz=> K. Sato

(excited 0+; T=1)
14N

Tx

(Thurs.)(ground 0+)
14C

A computer program of a new nuclear DFT has beendeveloped based on a “iso-rotational” invariant energy
density functional. This will be further utilized in study theisoscalar (T=0) pairing and charge-exchange reaction.

Nuclear and SN EOS
Variational Method by Takano et al.
・ finite T・ asymmetric matterProgress of the Research (2008-2012)
Construction of a nuclear EOS for supernovae (SNe)with the cluster variational method (In progress)

MethodThe cluster variational method with AV18+UIX for uniform matter.
The Thomas-Fermi method for non-uniform matter.

Collaboration with A03-group Yamamuro, Nakazato, Suzuki(Tokyo Univ. Sci.)
Numerical calculations of the free energies for various densities,
temperature and proton fractions: ~ 107 points

Supported by A04-group Matsufuru(KEK)
A part of the energy is calculated with GPU: ~100 times faster!

The SN-EOS with the cluster variational method
 Togashi (Fri.)The free energy of hot asymmetric nuclear matter is calculatedwith the method by Schmidt and Pandharipande, toward a SN-EOS.
AM: A. Mukherjee, PRC79(2009)045811.

Variational method with the explicit energy functional
 Takano (poster)Pure Neutron Matter
Symmetric Nuclear Matter(Preliminary)
The v6’ potential
Reasonable energies are obtainedDense LQCD

Summary (2008-2012)• Lattice Study of Finite Density QCD– Wilson Fermions with improved Gauge and Fermion action• Fugacity Expansion Formula, 2010[PRD82,094027(2010)]– Fermion matrix size reduction (CPU time reduction)– Useful• in the Multi-Parameter Reweighting• to Lee-Yang zeros study• to calculate higher order Taylor coefficients

Summary continued• Imaginary Chemical Potential approach,
2011[PRD83,114507(2011)]– Continuation of the Imaginary chemical potential Phase
Boundary to Real chemical potential• Equation of State, 2012[JHEP1204,092,(2012) ]– Comparison of the Multi-Parameter Reweighting andTaylor Expansion• Lee-Yang Zeros and Canonical approach,
2012[PTEP01A103(2012)]• Towards Low Temperature and finite density,2012– To study Fermion Matrix behavior (eigenvalue behavior) ofthe reduction fermion matrix– To analyze how to take the limit towards Low temperature,
Finite density and Thermo-dynamical state

Highlights (2008-2012)• Lee-Yang Zero [PTEP01A103(2012)]– Zeros in Complex Fugacity plane– Reflects Phase Structure

At low T, two circles (baryon and anti-baryon)
At high T, they merge into one unit circle.

Nagata (Sat.) Summary of A02 achievements

Progress of Theoretical and Experimental Physics, (2012) special volume“Computational Approaches in Particle, Nuclear and Astrophysics”
http://www.oxfordjournals.org/our_journals/ptep/special_issue_a.html○ Lattice quantum chromodynamical approach to nuclear physics
HAL QCD Collaboration, Prog. Theor. Exp. Phys. (2012) 01A105.
○ Towards extremely dense matter on the lattice
XQCD-J Collaboration, Prog. Theor. Exp. Phys. (2012) 01A103.
○ Gaussian expansion method for few-body systems and its applications
to atomic and nuclear physics
E. Hiyama, Prog. Theor. Exp. Phys. (2012) 01A204○ New-generation Monte Carlo shell model for the K computer eraN. Shimizu et al., Prog. Theor. Exp. Phys. (2012) 01A205○ Density functional approaches to collective phenomena in nuclei:
Time-dependent density functional theory for perturbative andnon-perturbative nuclear dynamics
T. Nakatsukasa, Prog. Theor. Exp. Phys. (2012) 01A207.

Advanced Institute for Computational Science (AICS), RIKEN
10 PFlops supercomputer KEI “京” (full operation started on Sep.28, 2012)
http://www.aics.riken.jp/en/

Five “strategic” programs (FY 2011-2015)
1. Life and Medicine
4. Engineering

2. New Materials
3. Environment
5. Particle, Nuclear and Astrophysics

Project 1: Lattice QCD
Project 3: Supernovae

Project 2: ab initio Nuclei
Project 4: First stars and galaxies

LQCD: 964 lattice, a=0.1fm, L=9.6fm, mπ=135MeV Yamazaki (fri.)Highlights of the MCSM studies
Energy-variance extrapolation

Benchmark calc. in light nuclei

Talk by T. Abe

Level scheme of 68Ni (a doubly magic nucleus)

Intrinsic Density from ab initio calc.
8Be

Talk by Y. Tsunoda

β ~ 0.0 β ~ -0.2 β ~ 0.4 (superdeformed)

List of related works（FY 2008-2012）•••••••••

Shape transition in exotic Si & S isotopes, Y. Utsuno, T. Otsuka, B. A. Brown, M. Honma,T. Mizusaki, and N. Shimizu, Phys.Rev. C86, 051301 (2012)
VMU in p-shell nuclei C. Yuan, T. Suzuki, T. Otsuka, F. Xu, and N. Tsunoda, Phys. Rev.
C85, 064324 (2012)
Beta decay for astrophysics T. Suzuki, T. Yoshida, T. Kajino, and T. Otsuka, Phys.Rev. C85,015802 (2012)
Renormalization persistency of tensor force in nuclei, N. Tsunoda, T. Otsuka, K.
Tsukiyama, and M. Hjorth-Jensen, Phys.Rev. C84, 044322 (2011)
Electron capture from astrophysical interest T. Suzuki, M. Honma, H. Mao, and T.
Otsuka, Phys.Rev. C83, 044619 (2011)
Novel features of nuclear forces and shell evolution in exotic nuclei, T. Otsuka, T. Suzuki,
M. Honma, Y. Utsuno, N. Tsunoda, K. Tsukiyama, and M. Hjorth-Jensen, Phys. Rev. Lett.
104 , 012501 (2010)
Three-body forces and the limit of oxygen isotopes, T. Otsuka, T. Suzuki, J. D. Holt, A.
Schwenk, and Y. Akaishi, Phys.Rev.Lett. 105, 032501 (2010)
Neutrino-induced reaction for stellar process T. Suzuki, M. Honma, K. Higashiyama, T.
Yoshida, T. Kajino, T. Otsuka, H. Umeda, and K. Nomoto, Phys.Rev. C79, 061603 (2009)
Exotic Magnetic Properties in 17C T. Suzuki, and T. Otsuka, Phys.Rev. C78, 061301 (2008)

Highlights of the MCSM studies I
Energy-variance extrapolation- precise estimate ofexact eigenvalues -Talk by T. Abe

Benchmark calc. in light nuclei- ready for systematic calcs. -Highlights of the MCSM studies II
Level scheme of 68Ni (a doubly magic nucleus)

Talk by Y. Tsunoda

Intrinsic Density from ab initio calc.
β ~ 0.0 β ~ -0.2 β ~ 0.4 (superdeformed)

three phases within 3 MeV

8Be

Highlights continued
Phase of Fermion Determinant-- The Origin of the Sign Problem
very sever just below Tc
not sever at low T and
At low temperature,
Fermion Determinants areinsensitive to the chemical
potential up toThis corresponds to(Silver-Blaze phenomena)This can be understood from Eigen Valuebehavior.

[PTEP01A103(2012)]

Variational Method with the Energy Functional
Uniform nuclear matter at zero temperature (M. Takano)
The central + tensor forces
Extension to the spin-orbit force
v8’ pot. + phenomenological TBF
Moderately constrained VM+All the three-body cluster terms

V6’ pot.

JPS2011

Two-body part: the tensor and spinorbit correlations are constrained.
Three-body part: tuned so as toreproduce the saturation point

Further refinement is in progress

NUFRA2011

Progress of the Research (A02: Takano)
Extension of the cluster variational method to Λ hyperon matter:
Collaboration with Hiyama (RIKEN: A02)
In progress2) Variational method with an explicit energy functional
Poster by Takano
Energy functional for nuclear matter with the v6’ potential
Explicit functional of two-body distribution functions
Full minimization
・Necessary conditions on structure functions are guaranteed.
・A main part of the higher-order cluster terms are included.
The results are reasonable as compared with thosewith other many-body calculations.
Extensions to the LS force and three-body force are in progress.