Application of the Kerman-Klein Method to the Solution of a Spherical Shell Model for a Deformed Rare-Earth Nucleus

Protopapas, Pavlos; Klein, Abraham

doi:10.1103/physrevlett.78.4347

Cited by 2 publications

(1 citation statement)

References 16 publications

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“…As such it generalizes phenomenological core-particle coupling models, to which it can be shown to reduce in various limits [12]. The past decade has witnessed further development of the theory and additional applications [13][14][15][16][17][18][19][20][21] including, for example, a suggested solution of the Coriolis attenuation problem [17,18]. A review of this more recent work is in preparation [22].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2004

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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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2004

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Foundations of self-consistent particle-rotor models and of self-consistent cranking models

Klein

2000

Phys. Rev. C

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The Kerman-Klein formulation of the equations of motion for a nuclear shell model and its associated variational principle are reviewed briefly. It is then applied to the derivation of the self-consistent particle-rotor model and of the self-consistent cranking model, for both axially symmetric and triaxial nuclei. Two derivations of the particle-rotor model are given. One of these is of a form that lends itself to an expansion of the result in powers of the ratio of single-particle angular momentum to collective angular momentum, which is essential to reach the cranking limit. The derivation of the latter also requires a distinct, angular-momentum violating step. The structure of the result implies the possibility of tilted-axis cranking for the axial case and full three-dimensional cranking for the triaxial one. The final equations remain number conserving.

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Application of the Kerman-Klein Method to the Solution of a Spherical Shell Model for a Deformed Rare-Earth Nucleus

Cited by 2 publications

References 16 publications

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

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

Foundations of self-consistent particle-rotor models and of self-consistent cranking models

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