1. 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

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

3. 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 !

4. 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
. . .

5. 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:

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

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

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

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

10. Density
In second quantization with HO basis

11. 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.,

12. HF
2nd order
2nd order

13. Point-particle distribution radii:
Charge radius:

14. 4He NCSM S.K. Bogner et al., arXiv0708.3754v2 (2007)
N3LO+SRG without 3NF
Our MBPT
4He

15. MBPT: N3LO+SRG without 3NF

16. 4He
N3LO vs JISP16
equivalently

17. 16O
N3LO vs JISP16

18. Our MBPT calculations with N3LO+SRG: convergence in radius

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

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

21. 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

22. ii) Brueckner-Hartree-Fock calculations

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

24. Our BHF calculations with N3LO

27. 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 ……

28. 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)

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