Furong Xu （许甫荣） Nuclear forces and applications to nuclear structure calculations Outline I. Nuclear forces II. N 3 LO (LQCD): MBPT, BHF, GSM (resonance + continuum) III. SM based on Gogny force SKLNPT ， School of Physics, Peking University 厦大,

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

In 1935, Yukawa discovered nuclear interaction by exchange meson, predicted π meson (Nobel prize in 1949) If the meson mass, it becomes electromagnetic interaction, exchanging photons Nuclear force has a finite range, mass range Electromagnetic force has an infinite range! Nuclear force is not a fundamental interaction, but an effective force! Its nature has not been well known.

From Machleidt4 Most general two-body potential under those symmetries (Okubo and Marshak, Ann. Phys. 4, 166 (1958)) with central tensor quadratic spin-orbit spin-orbit another tensor

Symmetries ： 1.parity 2.spin 3.isospin 1.Meson-exchange potential 2.QCD-based Chiral effective filed theory (Chiral EFT)

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

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)

8 2N forces 3N forces4N 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

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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

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 (N 3 LO), CD Bonn, AV18 … V low k, OLS, SRG, UCOM, G-Matrix, … Renormalization process to soften nuclear force to speed up convergence Ab initio calculation usually contains three steps

Our recent calculations: Starting with N3LO (LQCD) plus SRG or V low 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

NCSM S.K. Bogner et al., arXiv v2 (2007) Our MBPT calculations 4 He N 3 LO+SRG without 3NF

16 O Our MBPT: N 3 LO+SRG without 3NF

Our MBPT calculations with N 3 LO+SRG: convergence in radius

BHF calculations with N3LO

LQCD force provided by Sinya Aoki and Takashi Inoue, We renormalize it using V low-k Our MBPT calculations based on LQCD E expt = MeV

E expt = MeVE expt = MeV LQCD + MBPT

Ab-initio calculations for the resonance states of weakly bound nuclei: GSM using N 3 LO

MBPT for symmetric nuclear matter L. Coraggio et al., PRC 89, (2014) The importance of 3NF NCSM with chiral 2N and 3N forces By P. Navratil et al. 2N (N3LO) only 2N (N3LO) +3N (N2LO)

SM calculations with Gogny force in-medium (density-dependent) three-body force 3NF

TBMEs: Gogny vs. USDB 18 O 40 Ca

Gogny-force SM calculations for sd-shell nuclei In the existing Gogny force, taking: χ 0 =1 and α=1/3 Core ( 16 O) binding energy and single-particle energies can be calculated by the model itself.

Gogny-force SM calculations for spectroscopy: any excited states

Binding energy calculations

psd-shell calculations with much larger model space

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 N 3 LO (LQCD) i)Ab-initio MBPT and BHF ii)Ab-initio GSM to describe resonance and continuum iii)Shell model with Gogny force

An-initio nuclear structure at PKU Furong Xu Zhonghao Sun Baishan HuWeiguang Jiang Qiang WuMr. Sijie Dai

Thank you for your attention 30 厦大，