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

Klein, Abraham

doi:10.1103/physrevc.63.014316

Cited by 15 publications

(9 citation statements)

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“…The quantitative description of magnetic bands was achieved by the Tilted-Axis-Cranking (TAC) model proposed by Frauendorf [1,28,85], the two quasiparticle rotor model [86,87,88,89,91,92], and the particle-core coupling model [37,93,94,95].…”

Section: Schematic Calculationsmentioning

confidence: 99%

Specific features and symmetries for magnetic and chiral bands in nuclei

Râduţâ

2016

Progress in Particle and Nuclear Physics

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Magnetic and chiral bands have been a hot subject for more than twenty years. Therefore, quite large volumes of experimental data as well as theoretical descriptions have been accumulated. Although some of the formalisms are not so easy to handle, the results agree impressively well with the data. The objective of this paper is to review the actual status of both experimental and theoretical investigations. Aiming at making this material accessible to a large variety of readers, including young students and researchers, I gave some details on the schematic models which are able to unveil the main features of chirality in nuclei. Also, since most formalisms use a rigid triaxial rotor for the nuclear system's core, I devoted some space to the semi-classical description of the rigid triaxial as well as of the tilted triaxial rotor. In order to answer the question whether the chiral phenomenon is spread over the whole nuclear chart and whether it is specific only to a certain type of nuclei, odd-odd, odd-even or even-even, the current results in the mass regions of $A\sim 60,80,100,130,180,200$ are briefly described for all kinds of odd/even-odd/even systems. The chiral geometry is a sufficient condition for a system of proton-particle, neutron-hole and a triaxial rotor to have the electromagnetic properties of chiral bands. In order to prove that such geometry is not unique for generating magnetic bands with chiral features, I presented a mechanism for a new type of chiral bands. One tries to underline the fact that this rapidly developing field is very successful in pushing forward nuclear structure studies.Comment: 80 pages, 22 figure

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Section: Schematic Calculationsmentioning

confidence: 99%

Specific features and symmetries for magnetic and chiral bands in nuclei

Râduţâ

2016

Progress in Particle and Nuclear Physics

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Quan

Liu

et al. 2017

Phys. Rev. C

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Background Predictions of the spectroscopic properties of low-lying states are critical for nuclear structure studies, but are problematic for nuclei with an odd nucleon due to the interplay of the unpaired single particle with nuclear collective degrees of freedom.Purpose To predict the spectroscopic properties of odd-mass medium-heavy and heavy nuclei with a model that treats single-particle and collective degrees of freedom within the same microscopic framework.Method A microscopic core-quasiparticle coupling (CQC) model based on the covariant density functional theory is developed that contains the collective excitations of even-mass cores and spherical single-particle states of the odd nucleon as calculated from a quadrupole collective Hamiltonian combined with a constrained triaxial relativistic Hartree-Bogoliubov model. ResultsPredictions of the new model for excitation energies, kinematic and dynamic moments of inertia, and transition rates are shown to be in good agreement with results of low-lying spectroscopy measurements of the axially deformed odd-proton nucleus 159 Tb and the oddneutron nucleus 157 Gd.Conclusions A microscopic CQC model based on covariant density functional theory is developed for odd-mass nuclei and shown to give predictions that agree with measurements of two medium-heavy nuclei. Future studies with additional nuclei are planned. Figure 7 displays the core and single-particle contributions to the intraband B(E2; J → J − 1), B(E2; J → J − 2), and B(M1; J → J − 1) in the ground state bands of 159 Tb and 157 Gd. It is found that the B(E2) transitions are dominated by the core component and present monotonically increasing B(E2; J → J − 2) and monotonically decreasing B(E2; J → J − 1) as functions of spin. This is because the core has the majority of the

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

Cited by 15 publications

References 59 publications

Specific features and symmetries for magnetic and chiral bands in nuclei

Specific features and symmetries for magnetic and chiral bands in nuclei

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

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

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