One plus two-body random matrix ensembles with parity: Density of states and parity ratios

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PHYSREVC.83.064301· OSTI ID:21502761

Vyas, Manan; Srivastava, P C ^[1]; Kota, V K. B. ^[1]

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1. Physical Research Laboratory, Ahmedabad 380 009 (India)

One plus two-body embedded Gaussian orthogonal ensemble of random matrices with parity [EGOE(1+2)-{pi}] generated by a random two-body interaction (modeled by GOE in two-particle spaces) in the presence of a mean field for spinless identical fermion systems is defined, generalizing the two-body ensemble with parity analyzed by Papenbrock and Weidenmueller [Phys. Rev. C 78, 054305 (2008)], in terms of two mixing parameters and a gap between the positive ({pi}=+) and negative ({pi}=-) parity single-particle (sp) states. Numerical calculations are used to demonstrate, using realistic values of the mixing parameters appropriate for some nuclei, that the EGOE(1+2)-{pi} ensemble generates Gaussian form (with corrections) for fixed parity eigenvalue densities (i.e., state densities). The random matrix model also generates many features in parity ratios of state densities that are similar to those predicted by a method based on the Fermi-gas model for nuclei. We have also obtained, by applying the formulation due to Chang et al. [Ann. Phys. (NY) 66, 137 (1971)], a simple formula for the spectral variances defined over fixed-(m{sub 1},m{sub 2}) spaces, where m{sub 1} is the number of fermions in the positive parity sp states and m{sub 2} is the number of fermions in the negative parity sp states. Similarly, using the binary correlation approximation, in the dilute limit, we have derived expressions for the lowest two-shape parameters. The smoothed densities generated by the sum of fixed-(m{sub 1},m{sub 2}) Gaussians with lowest two-shape corrections describe the numerical results in many situations. The model also generates preponderance of positive parity ground states for small values of the mixing parameters, and this is a feature seen in nuclear shell-model results.

• OSTI ID: 21502761
• Journal Information: Physical Review. C, Nuclear Physics, Vol. 83, Issue 6; Other Information: DOI: 10.1103/PhysRevC.83.064301; (c) 2011 American Institute of Physics; ISSN 0556-2813
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
97 MATHEMATICAL METHODS AND COMPUTING
APPROXIMATIONS
COMPUTERIZED SIMULATION
CORRELATIONS
DENSITY
EIGENVALUES
FERMI GAS MODEL
FERMIONS
GROUND STATES
INTERACTIONS
MATHEMATICAL MODELS
MEAN-FIELD THEORY
MIXING
NUCLEI
PARITY
RANDOMNESS
SHELL MODELS
TWO-BODY PROBLEM
CALCULATION METHODS
ENERGY LEVELS
MANY-BODY PROBLEM
NUCLEAR MODELS
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
SIMULATION