STUDY OF THE TENSOR CORRELATION IN THE MEAN-FIELD-TYPE MODEL AND THE SHELL MODEL

2006 ◽  
Vol 21 (31n33) ◽  
pp. 2475-2482
Author(s):  
SATORU SUGIMOTO
Keyword(s):  
Shell Model ◽  
Single Particle ◽  
Mean Field ◽  
Tensor Force ◽  
Closed Shell ◽  
Wave Functions ◽  
Type Model ◽  
Tensor Correlation ◽  
Field Type ◽  
The Mean

We study the effect of the tensor correlation using a mean-field-type model and a shell model. To treat the tensor correlation in a mean-field-type model, we introduce single-particle states with the parity and charge mixing considering the pseudoscalar and isovector characters of the pion, which mediates the tensor force. We study closed-shell and sub-closed-shell oxygen isotopes and find that a sizable attractive energy from the tensor force is obtained by introducing the parity and charge mixing. We also perform a shell model calculation up to two-particle–two-hole configurations. A large attraction energy is obtained for 16 O when we introduce single-particle wave functions with narrow widths.

Gamow–Teller strength functions from scattering experiments

1987 ◽  
Vol 65 (6) ◽  
pp. 691-698 ◽  
Author(s):  
O. Häusser
Keyword(s):  
Shell Model ◽  
Cross Sections ◽  
Mean Field ◽  
Wave Functions ◽  
Structure Information ◽  
Model Wave ◽  
Spin Flip ◽  
Strength Functions ◽  
Gamow Teller ◽  
Good Agreement

We present here recent [Formula: see text] results from TRIUMF that are relevant to the determination of spin-flip isovector strength functions in nuclei. Distortion factors needed for the extraction of nuclear-structure information have been deduced from cross sections and analyzing powers in elastic scattering for several energies and targets. Nonrelativistic optical potentials obtained by folding effective nucleon (N)–nucleus interactions with nuclear densities are found to overpredict both elastic and reaction cross sections, whereas Dirac calculations that include Pauli blocking are in good agreement with the data. Spin observables (Snn and Ay) for the quasi-elastic region in 54Fe[Formula: see text] at 290 MeV provide some evidence for the reduction of the effective proton mass predicted in relativistic mean-field theories as a consequence of the attractive scalar field in the nuclear medium. The energy dependence of the effective N–nucleus interaction at small momentum transfers has been investigated using isoscalar and isovector 1+ states in 28Si as probe states. We find that the cross sections for the isovector transitions are in good agreement with predictions for the dominant Vστ part of the Franey–Love interaction. Gamow–Teller (GT) strength functions have been obtained in 24Mg and 54Fe from measurements of both cross sections and spin–flip probabilities Snn. The spin-flip cross sections σSnn are particularly useful in heavier nuclei to discriminate against a continuous background of ΔS = 0 excitations. In the (s, d) shell where full shell-model wave functions are available, the GT quenching factors [Formula: see text] are in good agreement with those from recent (p, n) and (n, p) experiments. We show that a state-by-state comparison of (p, p′) and (e, e′) results has the potential of identifying pionic current contributions in (e, e′). The GT quenching factors in 54Fe are smaller than in the (s, d) shell probably because of severely truncated shell-model wave functions, particularly those of the nuclear ground state.

scholarly journals Inverse mean field theories

2018 ◽  
Vol 20 (43) ◽  
pp. 27600-27610 ◽  
Author(s):  
Peter Schmitteckert
Keyword(s):  
Single Particle ◽  
Body Wave ◽  
Mean Field ◽  
Wave Functions ◽  
Field Theories ◽  
Many Body ◽  
Fermionic Systems ◽  
Mean Field Theories

In this work we discuss the extraction of mean field single particle Hamiltonians from many body wave functions of fermionic systems.

scholarly journals Explicit Characterization of Feedback Nash Equilibria for Indefinite, Linear-Quadratic, Mean-Field-Type Stochastic Zero-Sum Differential Games with Jump-Diffusion Models

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1669
Author(s):  
Jun Moon ◽  
Wonhee Kim
Keyword(s):  
Nash Equilibrium ◽  
Mean Field ◽  
Jump Diffusion ◽  
Linear Quadratic ◽  
Quadratic Mean ◽  
Field Type ◽  
The Mean ◽  
Zero Sum ◽  
Objective Functional

We consider the indefinite, linear-quadratic, mean-field-type stochastic zero-sum differential game for jump-diffusion models (I-LQ-MF-SZSDG-JD). Specifically, there are two players in the I-LQ-MF-SZSDG-JD, where Player 1 minimizes the objective functional, while Player 2 maximizes the same objective functional. In the I-LQ-MF-SZSDG-JD, the jump-diffusion-type state dynamics controlled by the two players and the objective functional include the mean-field variables, i.e., the expected values of state and control variables, and the parameters of the objective functional do not need to be (positive) definite matrices. These general settings of the I-LQ-MF-SZSDG-JD make the problem challenging, compared with the existing literature. By considering the interaction between two players and using the completion of the squares approach, we obtain the explicit feedback Nash equilibrium, which is linear in state and its expected value, and expressed as the coupled integro-Riccati differential equations (CIRDEs). Note that the interaction between the players is analyzed via a class of nonanticipative strategies and the “ordered interchangeability” property of multiple Nash equilibria in zero-sum games. We obtain explicit conditions to obtain the Nash equilibrium in terms of the CIRDEs. We also discuss the different solvability conditions of the CIRDEs, which lead to characterization of the Nash equilibrium for the I-LQ-MF-SZSDG-JD. Finally, our results are applied to the mean-field-type stochastic mean-variance differential game, for which the explicit Nash equilibrium is obtained and the simulation results are provided.

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