Kerman-Klein-Dönau-Frauendorf model for odd-odd nuclei: Formal theory

Abstract

The Kerman-Klein-Dönau-Frauendorf (KKDF) model is a linearized version of the non-linear Kerman-Klein (equations of motion) formulation of the nuclear many-body problem. In practice, it is a generalization of the standard core-particle coupling model that, like the latter, provides a description of the spectroscopy of odd nuclei in terms of the corresponding properties of neighboring even nuclei and of single-particle properties, that are the input parameters of the model. A divers sample of recent applications attest to the usefulness of the model. In this paper, we first present a concise general review of the fundamental equations and properties of the KKDF model. We then derive a corresponding formalism for odd-odd nuclei with proton-neutron number (Z, N ) that relates their properties to those of the four neighboring even nuclei (Z + 1, N + 1), (Z − 1, N + 1), (Z + 1, N − 1), and (Z − 1, N − 1), all of which are required if one is to include both multipole and pairing forces. * Email:aklein@dept.phys.upenn.edu † Email:pavlos@nscp.upenn.edu ‡ Email:Stanislaw-G.Rohozinski@fuw.edu.pl § Email:Starosta@nuclear.physics.sunsysb.edu 1We treat these equations in two ways. In the first, we make essential use of the solutions of the neighboring odd nucleus problem, as obtained by the KKDF method. In the second, we relate the properties of the odd-odd nucleus directly to those of the even nuclei. For both choices, we derive equations of motion, normalization conditions, and an expression for transition amplitudes. We also resolve the problem of choosing the subspace of physical solutions that arises in an equations of motion approach that includes pairing interactions.

Microscopic core-quasiparticle coupling model for spectroscopy of odd-mass nuclei

“…(34,35) of Ref. [33] because the signs of our definitions for pairing field ∆ and eigenvalue E αJ are opposite to those in Ref. [33].…”

“…In this work, our covariant EDF-based quadrupole collective Hamiltonian will be extended to describe the spectroscopy of odd-mass nuclei via the core-quasiparticle coupling (CQC) scheme. The CQC scheme has been extensively used with phenomenological inputs, e.g., a rotor or Bohr Hamiltonian for the core and a single particle in a phenomenological spherical potential [27][28][29][30][31][32][33][34], and microscopic inputs calculated from Hartree-Fock plus BCS [35][36][37].…”

Triaxiality explored by an odd quasi-particle

“…The resulting CQPC formalism was used in this paper (for a discussion of the DF approximation see Refs. [15,32]).…”

Exact general relativistic thick disks

“…This method was named by Synge as the g-method [30] in contrast to the t-method or direct method in which the source is given and the Einstein equations are solved. The t-method, has been used to generate disks by the Jena group [31,32,33,34,35,36,37]. Essentially, they are obtained by solving a Riemann-Hilbert problem.…”