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Factorization and Universality
Or Hen β MIT
Quantitative Challenges in EMC and SRC Research, December 2nd 2016
Factorization and Universality Or Hen MIT Quantitative Challenges - - PowerPoint PPT Presentation
Factorization and Universality Or Hen MIT Quantitative Challenges - - PowerPoint PPT Presentation
Factorization and Universality Or Hen MIT Quantitative Challenges in EMC and SRC Research, December 2 nd 2016 Universal Nuclear Structure Effective Theories for Mean-Field Fermi Liquid E F Gas Drop Model Model Chiral Shell
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3
Shell Model Fermi Gas Model
EF
Liquid Drop Model Chiral Perturbation Theory Effective Theories for Mean-Field
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Whole is different from the sum of parts!
π"#(π&, π") β π#(π&) * π#(π") π"# π β
&, π
β
" β π# π
β
& * π#(π
β
")
Specifically, in coordinate space:
SRC: π"#(π β
&, π
β
") β 0 for |π
β
& β π
β
"| β π#
LRC: π"#(π β
&, π
β
") β 0 for |π
β
& β π
β
"| β π3
(Some) Interesting questions: Is there a way to factorize the two-body density? Can we separate the βmean-fieldβ and βSRCβ effects? Are the SRC effects universal?
4
Challenge of Correlations
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Hints from Many-Body (VMC) ?
- One body
momentum distribution scales above kF.
- Good scaling
relative to 4He NOT deuteron. => Importance of non-deuteron pairs? c.m. motion? Both?
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6
Hints from Many-Body (VMC) ?
Short-Range coordinate space density also scales (See talk by Joel Lyn)
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7
Jan Ryckebuschβs approach
Shift complexity from the wave-function to the
- perators:
β Start with a mean-field slater determinant. β Introduce SRCs using correlation operators (Central, Tensor, Spin-Isospin). β Act with the correlation operator only on 1S0 (3S0) mean-field pairs. Note: Correlation operators are universal! Main thing that is changing for different nuclei is the number of mean-field pairs!
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8
Jan Ryckebuschβs approach
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9
SRC Pair Counting
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10
One-Body Momentum Distribution
*Quantum numbers BEFORE action of correlation operators
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Two-Body Momentum Distribution
Two-Body density (integrated over c.m. momentum) not sensitive to pairs until VERY large relative momentum (See talk by Reynier)
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Alvioli and Ciofi
See talk by Alvioli
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Contact Approach
Generalized contact theory allows reproducing one-body densities using universality to 10-20% accuracy! (See talk by Ronen Weis) Nuclear contacts can be calculated AND extracted from experiment!
Wiess, Cruz-Torez, Barnea, Piasetzky, Hen
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