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Furong Xu (许甫荣)
Many-body calculations
with realistic and phenomenological nuclear forces
Outline
I. Nuclear forces
II. N3LO (LQCD): MBPT, BHF, GSM (resonance + continuum)
III. SM based on Gogny force
SKLNPT , School of Physics, Peking University
JCNP2015, Osaka, Nov. 7-12, 2015
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In nuclear structure calculations (starting from realistic forces ) ,
there are three key problems
1. Nuclear forces
2. Renormalization (softening) of nuclear forces
3. Many-body methods
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In 1935, Yukawa discovered nuclear interaction by exchange meson,
predicted π meson (Nobel prize in 1949)
2
( )4
m cr
g eV r
r
p
p
-
=-h
If the meson mass , it becomes electromagnetic interaction, exchanging photons
0m®
1( )V r
r:
Nuclear force has a finite range, mass range Electromagnetic force has an infinite range!
0m=
Nuclear force is not a fundamental interaction, but an effective force!
Its nature has not been well known.
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From Machleidt 4
Most general two-body potential under those symmetries (Okubo and Marshak, Ann. Phys. 4, 166 (1958))
with
NNV central
tensorquadratic spin-orbit
spin-orbit
another tensor
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Symmetries :1. parity
2. spin
3. isospin
1. Meson-exchange potential
2. QCD-based Chiral effective filed
theory (Chiral EFT)
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Van der Waals force
+-
+-
The effective interaction between
neutral atoms: the residual force
of electromagnetic interaction
outside atom.
Nuclear force
Residual force of the QCD strong interaction outside the nucleon
What is the nature of nuclear force?
Quarks and gluons are confined into colorless hadrons
Analogy
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Weinberg (1990’s)
Chiral EFT=nucleons+pions (symmetries: spin, isospin, parity, chiral symmetry broken spontaneously)
At low energy, the effective degrees of freedom are nucleon and pion, rather than quark and gluon!
QCD=quarks + gluons (symmetries: spin, isospin, parity, chiral symmetry broken spontaneously)
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8
2N forces 3N forces 4N forces
Leading Order
Next-to-Next-to Leading Order
Next-to-Next-to-Next-to Leading Order
Next-to Leading Order
Chiral EFT
Power counting :Q (π mass ) soft scale;
Λ (heavier mesons), hard scale
/Q L
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-9-
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1) Start from realistic nuclear force !
Reproduce experimental NN scattering phase shifts .
2) A “good enough” theoretical method solves the many-body problem of nucleus
What is ab-initio calculations?
The calculation is from the beginning of physics principles
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No Core Shell Model (NCSM)
Coupled Cluster (CC)
Many-Body Perturbation Theory (MBPT)
Greens Function
Bruckner-Hartree-Fock
Gamow Shell model
Lattice Nuclear Chiral EFT, . . .
Realistic nuclear forces:
Ab-initio many-body methods
Chiral EFT (N3LO), CD Bonn, AV18 …
Vlow k , OLS, SRG, UCOM, G-Matrix, …
Renormalization process to soften nuclear force to speed up convergence
Ab initio calculation usually contains three steps
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Our recent calculations:
Starting with N3LO (LQCD) plus SRG or Vlow k
1. Many-body perturbation theory
2. Brueckner Hartee Fock
3. Gamow Shell Model (for weakly bound nuclei,
to describe resonance and continuum)
4. Shell Model based on Gogny force
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NCSM S.K. Bogner et al., arXiv0708.3754v2 (2007) Our MBPT calculations
4He
N3LO+SRG without 3NF
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16O
Our MBPT: N3LO+SRG without 3NF
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Our MBPT calculations with N3LO+SRG: convergence in radius
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BHF calculations with N3LO
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LQCD force provided by Sinya Aoki and Takashi Inoue,
We renormalize it using V low-k
Our MBPT calculations based on LQCD
Eexpt = -28.3 MeV
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Eexpt = -127.6 MeV Eexpt = -342.0 MeV
LQCD + MBPT
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Ab-initio calculations for the resonance states of weakly bound nuclei: GSM using N3LO
0.1 1
0.120.13
0.1
GSM USDB Exp.
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MBPT for symmetric nuclear matter
L. Coraggio et al., PRC 89, 044321 (2014)
The importance of 3NF
NCSM with chiral 2N and 3N forces
By P. Navratil et al.
2N (N3LO) only
2N (N3LO)
+3N (N2LO)
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SM calculations with Gogny force
in-medium (density-dependent) three-body force
3NF
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TBMEs: Gogny vs. USDB
18O 40Ca
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Gogny-force SM calculations for sd-shell nuclei
In the existing Gogny force,
taking: χ0=1 and α=1/3
Core (16O) binding energy and
single-particle energies can be
calculated by the model itself.
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Density iteration
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.05
0.1
0.15
0.2
0.25
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.05
0.1
0.15
0.2
0.25
H.O. density distribution Iterated density distribution
r(fm)r(fm)
Single-particle energies in the spherical H.O. basis :
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Core energy (i.e., 16O for sd shell):
Close-shell kinetic energy:
Close-shell interaction energy:
Center-of-mass energy:
Binding Energy calculations:
is calculated by diagonalizing all configurations within in valence shell space.
The two-body Coulomb energy:
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Gogny-force SM calculations for spectroscopy: any excited states
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Binding energy calculations
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psd-shell calculations with much larger model space
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Automatically smooth cutoff2 21 2|k | /4i ke m- -v v
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Advantages of ab-initio calculations:
i) To understand the nature of nuclear forces;
Summary
• Nuclear force is still a big issue in nuclear physics
• Many-body methods need to be developed
ii) To understand many-body correlations;
Our recent works:
Starting from N3LO (LQCD)
i) Ab-initio MBPT and BHF
ii) Ab-initio GSM to describe resonance and continuum
iii) Shell model with Gogny force
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An-initio nuclear structure at PKU
Furong Xu
Zhonghao Sun Baishan Hu Weiguang Jiang Qiang Wu Mr. Sijie Dai
http://www.phy.pku.edu.cn/~frxu
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Thank you for your attention
34
JCNP2015, Osaka, Nov. 7-12, 2015