RelativisticRmatrix and continuum shell model

Abstract

Background:The R matrix formalism of Lane and Thomas has proven to be a convenient reaction theory for solving many-coupled channel systems. The theory provides solutions to bound states, scattering states, and resonances for microscopic models in one formalism. Purpose: The first purpose is to extend this formalism to the relativistic case so that the many-coupled channels problem may be solved for systems in which binary breakup channels satisfy a relative Dirac equation. The second purpose is to employ this formalism in a relativistic continuum shell model. Methods: Expressions for the collision matrix and the scattering amplitude, from which observables may be calculated, are derived. The formalism is applied to the 1p-1h relativistic continuum shell model with an interaction extracted from relativistic mean field theory. Results:The simplest of the σ + ω + ρ exchange interactions produces a reasonable description of proton scattering from 15 N, and, therefore, provides a simple, relatively self-consist, physically justifiable model for use in knockout reactions. 24.10.Eq, 24.10.Jv, 25.40.Cm

Quantum phase transitions in the noncommutative Dirac oscillator

“…(47) and is again the same as that of Eqs. (24) which shows that the role of the angular momentum quantum number is once again reversed and now it is identical to that of case 1. The excited levels (n r ≥ 1) are then derived from the second order equations c.f.…”

“…We only mention here that in Eqs (47). the sign of the angular momentum operator is changed relative to Eqs (24). which anticipates that in the right phase the role of the angular momentum quantum number is reversed.…”

Probing resonances in the Dirac equation with quadrupole-deformed potentials with the complex momentum representation method

“…This method has avoided all the defects in the CSM, and has been used to explore the bound states [30,31] and resonant states [32,33] in the nonrelativistic case, and used as the so-called "Berggren representation" in the shellmodel calculations [34,35]. Considering that the relativistic resonances are widely concerned, almost all the methods for resonances have been extended to the relativistic framework [36][37][38][39][40][41][42], including the relativistic CSM [22,27] and relativistic complex scaled Green's function method [25]. Recently, we applied the CMR method to the relativistic mean-field (RMF) framework and established the RMF-CMR method for the resonances in the spherical case [43], in which both bound states and resonant states have been treated on the same footing.…”

Re-entrant phase transitions in non-commutative quantum mechanics

“…In mathematical physics the Dirac oscillator has become a paradigm for the realization of covariant quantum models and it has found applications both in nuclear [23][24][25] and subnuclear [26,27] physics as well as in quantum optics [28][29][30]. Very recently a one dimensional version of the Dirac oscillator has been realised experimentally [31] for the first time with realistic prospects to realise in the near future the two dimensional version of the Dirac oscillator which may be feasible using networks of microwave coaxial cables [32][33][34].…”