Odd nuclei in the skyrme hfb theory standard fits of

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Odd Nuclei in the Skyrme HFB Theory Standard fits of Skyrme functionals do not probe time-odd part: How well do existing interactions ? How much of a leverage do the time- odd part give us ? Odd particle described as a one quasi-particle excitation on a fully- paired vacuum = blocking approximation Equal Filling Approximation (EFA): Average over blocking time- reversal partners: “ EFA ⟩ = ⌈ + ⌈ Conserves time-reversal symmetry Time-odd part of the functional becomes active in odd nuclei Practical issues: Dependent on the quality of the pairing interaction used (density-dependent delta-pairing here) Blocked state is not known beforehand: warm-start from even-even core Broken time-reversal symmetry + many configurations to consider = computationally VERY demanding 3 1. Quality of the EFA approximation 2. Impact of time-odd fields Theory (2/3)
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Symmetries and Blocking 4 Theory (3/3) Skyrme functional (any functional based on 2-body interaction) gives time-odd fields They break T-symmetry Definition of the blocked state: Criterion: quasi-particle of largest overlap with “some” single- particle state identified by a set of quantum numbers Quantum numbers are related to symmetry operators: Time-odd fields depend on choice of quantization axis – Example: Symmetry operator chosen to identify s.p. states must commute with the projection of the spin operator onto the quantization axis
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DFT Solver: HFODD 5 Solves the HFB problem in the anisotropic cartesian harmonic oscillator basis Most general, symmetry-unrestricted code Recent upgrades include: Broyden Method, shell correction, interface with HFBTHO (Schunck) Isospin projection (Satuła) Exact Coulomb exchange (Dobaczewski) Finite temperature (Sheik) Truncation scheme: dependence of results on N shell , ħ , deformation of the basis (see NCSM, CC, SM, etc.) Reference provided by HFB-AX Error estimate for given model space give theoretical error bars Codes (1/2)
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Terascale Computing in DFT Applications 6 Codes (2/2)
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  • Fall '19
  • density functional theory

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