Ab-initio nuclear structure calculations with MBPT and BHF 北京大学 Peking University Furong Xu Ab-initio nuclear structure calculations with MBPT and BHF

Outline I. Introduction II. Our ab-initio calculations Many-Body Perturbation Theory (MBPT ) + SRG Brueckner-Hartree-Fock (BHF) Based on: N3LO, JISP16 III. Summary

Ab-initio calculation I. Introduction Ab-initio calculation 1) Realistic nuclear force ! Hamiltonian可能包含的对称性：I, T, parity? In Chiral EFT （手征有效场理论），由于pion的质量不为零，所以手征对称性是破缺的,正像QCD中，由于u和d夸克的质量不为零，所以QCD强相互作用的手征对称性是破缺的。 理论方法要好。 第二项公式的第一项是质心系动能，但（p_i-p_j)不是相对动量，如果两个物体质量相同，则相对动量是(p_i-p_j)/2，具体推导见笔记。 Reproduce experimental two-body NN scattering data. 2) “Good enough” approximations to solve the Hamiltonian !

Realistic nuclear forces: Chiral EFT (e.g., N3LO), CD Bonn, AV18, JISP16 (bare) … Renormalization methods G-Matrix, UCOM, Vlow-k , Okubo-Lee-Suzuki (OLS), SRG ab-initio methods In coordinate space: Greens Function Monte Carlo (GFMC) In basis space: No Core Shell Model (NCSM) No Core Full Configurations (NCFC) Coupled Cluster (CC) Many-Body Perturbation Theory (MBPT) Lattice Nuclear Chiral EFT . . .

II. Our ab-initio calculations with MBPT ; , First we did HF calculations (in HO basis); The HF state is chosen as a reference state. In the HF basis, we make MBPT corrections up to 3rd order:

Perturbation (MBPT) For the ground state: Rayleigh-Schrodinger method resolvent [re,solvent] Rayleigh-Schrodinger method

HF energy φ0就是HF wave function, 给出HF energy, i.e., E(0)+E(1) HF

E(0)+E(1) E(2) E(3) Anti-Symmetrized Goldstone (ASG) diagram expansion HF energy E(3) Vertex [və:’teks] 2p4h =

ASG diagrams for wave functions ψ(1) ψ(2)

Density In second quantization with HO basis

For the ground state, the 2nd order correction to density is only from the 4th and 5th ASG diagrams of the 2nd-order wave function, others belong to higher-order corrections, i.e.,

HF 2nd order 2nd order

Point-particle distribution radii: Charge radius:

4He NCSM S.K. Bogner et al., arXiv0708.3754v2 (2007) N3LO+SRG without 3NF Our MBPT 4He

MBPT: N3LO+SRG without 3NF

4He N3LO vs JISP16 equivalently

16O N3LO vs JISP16

Our MBPT calculations with N3LO+SRG: convergence in radius

R. Roth et al. (2006) PRC 73, 044312 AV18, UCOM, corrections to 3rd order in energy, 2nd order in radius

for symmetric nuclear matter MBPT calculations for symmetric nuclear matter L. Coraggio et al., PRC 89, 044321 (2014)

NCSM calculation by P. Navratil et al. Calculating the properties of light nuclei using chiral 2N and 3N forces NCSM calculation by P. Navratil et al. 3NF is crucial 2N (N3LO) +3N (N2LO) 2N (N3LO) only From R. Machleidt

ii) Brueckner-Hartree-Fock calculations

With N3LO (no 3NF) , we determine ω by reproducing the NCSM calculations in 4He preliminary

Our BHF calculations with N3LO

III. Summary Ab-initio calculation provides a good playground We have done ab-initio calculations with MBPT based on realistic forces N3LO and JISP16 We have improved BHF +N3LO for finite nuclei (self-consistently in the HF basis) Reasonable results have been obtained, but 3NF would be needed for further improvements. Ab-initio calculation provides a good playground i) To understand the nature of nuclear forces; ii) To develop theories with less assumptions or approximations ……

Collaborators B.S. Hu and Z.H. Sun (PhD students at PKU) CUSTIPEN collaborations (China-U.S. Theory Institute for Physics with Exotic Nuclei) J. Vary (JISP16) R. Machleidt (N3LO)

Thank you for your attention NN2015 Catania, June 21-25, 2015 Peking University Campus 29