Many-Body Perturbation Theory Calculations (Baishan Hu) Supervisor: - - PowerPoint PPT Presentation
FRIB-Theory Alliance workshop Many-Body Perturbation Theory Calculations (Baishan Hu) Supervisor: (Furong Xu) E-mail: hubsh@pku.edu.cn Peking University, Beijing, China June 21, 2018 @
北京大学物理学院（Peking University, Beijing, China） June 21, 2018 @ East Lansing, MI
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a) MBPT for closed-shell nuclei b) MBPT (Q-box + folded diagrams) for open-shell nuclei c) MBPT for nuclear reaction (RGM)
As Prof. F.R. Xu’s talk
takes us from a simple, exactly solvable (unperturbed) problem to a corresponding real (perturbed) problem The key formulas in perturbation theory are In MBPT the ambition is to include in H0 as much “physics” as possible, so that V represents a “small” perturbation
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Key tool from 1950’s to 1970’s Great depression in 1980’s Today MBPT is coming back ...
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Faster convergence Some perturbation diagrams are cancelled out In HO basis, calculations could be ħω dependent, while much less in HF basis
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Harmoni nic Oscillat ator
Hartree e Fock
16 16O
Energy up to 3rd order Wave function up to 2nd order (One-body density)
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E(2) E(3)
E=E(0)+E(1) +E(2)+E(3) + … ψ(1) ψ(2) Ψ =ΦHF+ ψ(1) + ψ(2)+ …
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Point-proton rms radius
B.S. Hu, F.R. Xu, et al., PRC 94, 014303 (2017)
Binding energy HF-RSPT calculations for 16O with N3LO-SRG, Nshell=13, ħω=35 MeV 3NF important !
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Normal ordering with HF reference state
𝑰HF
Discard residual 3B part: NO2B approximation
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NO2B
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NO2B approximation:
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NN-only N3LO-SRG Bare JISP16
Nshell=7, ħω=30 MeV
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Charge radius Binding energy HF-RSPT calculations with NO2B N2LOsat, Nshell=13, ħω=22 MeV
B.S. Hu, T. Li, F.R. Xu, in preparation (2018)
PRL114, 212502 (2015) 6Li 15
Bound, resonant and scattering states may be strongly coupled. Need nuclear theory including the continuum.
Many-body dynamics Input NN+3NFs,
Open channels
isotopes
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𝑾𝒎𝒑𝒙−𝒍, SRG, OLS, … Bare forces: Strong repulsion， tensor force , slow convergence Valence-space effective interactions Complex shell model code
(Jacobi-Davidson, N. Michel)
HO/HF; Gamow-Berggren basis (a,b): WS/GHF pp,nn: pn: Extended Kuo-Krenciglowa method (EKK)
Realistic Gamow shell model Workflow
Up to third ird order rder
As Prof. F.R. Xu’s talk
Faster convergence Some perturbation diagrams are cancelled out In HO basis, calculations could be ħω dependent, while much less in HF basis
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18 18O
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The pictures are taken from M. Hjorth-Jensen, et al., Physics Reports 261 (1995) 125.
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Step ❸: Obtain the radial wave function u(r)/r in complex-k plane Outgoing solution at large distance Exterior complex scaling Step ❶: Solve the Hartree-Fock equations in HO representation using Hint,
Step ❷: Extract the non-local HF potential ʋ(r,r’)
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MeV
sp energies sp resonance
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Bare NNLOopt ħω=20 MeV Nshell=12 SPEs Q-box
22O core, sd-shell
Q-box
Q-box folded diagrams
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d3/2 channel
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…… 40 20 8
…… 40 20 14
22O
Model Space
Resonance
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Kondo, et al, (2016): ~0.110 MeVLunderberg, et al, (2012): ~0.005 MeV Kohley et al, (2013): 4.5+11
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Long-lived 41
+ isomer, T1/2=2.2(1) ms,
Lepailleur, et al., PRL110, 082502 (2013)
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COSM
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force corrections.
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interactions with the nuclear reaction theory (GSM-RGM)
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Collaborators:
Furong Xu (Peking University) Qiang Wu (Peking University) Tong Li (Michigan State University) Zhonghao Sun (Oak Ridge National Laboratory) Jianguo Li (Peking University) Nicolas Michel (Michigan State University)
Gratitude:
Junchen Pei (Peking University) Simin Wang (Michigan State University) Thomas Papenbrock (Oak Ridge National Laboratory) Gustav R. Jansen (Oak Ridge National Laboratory) Luigi Coraggio (INFN-Naples) James P. Vary (Iowa State University) Ruprecht Machleidt (University of Idaho) Marek Ploszajczak (GANIL) Our group: Yuanzhuo Ma, Bo Dai, Sijie Dai, Yifang Geng, …
北京大学物理学院粒子物理与原子核物理专业 2015年11月25日
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From Bound States to the Continuum, Jun 21, 2018 31
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