Nuclear structure studies of 20Ne and 24Mg in the variation-after-projection Hartree-Fock method

Cusson, R.Y.; Lee, H.C.

doi:10.1016/0375-9474(73)90435-1

Cited by 42 publications

(8 citation statements)

References 39 publications

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“…It is also rewarding that various other formulations of nuclear structure theory, both microscopic and macroscopic collective, are typically applied to sd shell nuclei. This makes it possible to study the re lative merits of a wide variety of different approaches (Harvey 1968, Ripka 1968, Cusson & Lee 1972, Malik & Scholz 1967.…”

Section: General Considerationsmentioning

confidence: 99%

Large-Scale Shell-Model Calculations

McGrory¹,

Wildenthal²

1980

Annu. Rev. Nucl. Part. Sci.

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Access provided by 44.224.250.200 on 05/10/21. For personal use only.1. choice of H l' the dominant central field;2. calculation of the one-particle eigenstates of HI and the selection, from this set, of the orbits of the model; 3. construction, for a given number of nucleons and the chosen model orbits, of the multinucleon eigenstates of HI; 4. specification of a residual two-body interaction of H 12; and 5. evaluation of the matrix elements of H 1 2 between the multinucleon eigenstates of HI and calculation of the eigenvalues and eigenvectors of this matrix.Many calculations assume that HI is a sum of a spherical harmonic oscillator potential, a spin-orbit (I• s) interaction, and a term proportional to 12. The single-particle eigenstates p(nlj) of a typical such interaction are shown in Figure 1 where the labels (n, i,j) specify the principal radial quantum number, the orbital angular momentum, and the total angular momentum. The simplest shell-model calculations, similar to those that first established the validity of the basic approximation (Mayer 1949), assume wave functions in which the nucleons fill the lowest available single particle orbits, where this availability is determined by the Pauli principle.Thus from Figure 1, the ground-state wave function of 170 would consist of the configuration (OSI/2)4, (Op3/2)8, (Opl/2)4, (Ods/2) 1 . The completely filled ("closed") shells are assumed to form an inert core with total angular

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Section: General Considerationsmentioning

confidence: 99%

Large-Scale Shell-Model Calculations

McGrory¹,

Wildenthal²

1980

Annu. Rev. Nucl. Part. Sci.

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“…With appropriate development of the required computational techniques, the Hamiltonian for the nucleus could then be diagonalised in a basis for this vector space to give the rotational states of the required algebraic many-nucleon version of the unified model. The construction of the rotational states of such a unified model corresponds closely to that of the angular-momentum projection methods of standard HF theory as outlined, for example, by Lee and Cusson [64,65]. The intrinsic beta and gamma vibrational excited states of this model are also defined by standard time-dependent mean-field, or equivalent RPA methods.…”

Section: An Algebraic Many-nucleon (Amn) Unified Modelmentioning

confidence: 95%

Nuclear shape coexistence from the perspective of an algebraic many-nucleon version of the Bohr-Mottelson unified model

Rowe

2019

Preprint

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A fully quantal algebraic version of the Bohr-Mottelson unified model is presented with the important property that its quantisation is defined by its irreducible unitary representations which span the many-nucleon Hilbert space of every nucleus. The model is uniquely defined by the requirement that its Lie algebra of observables includes the nuclear quadrupole moments and kinetic energy. It then follows that there can be no non-zero isoscalar E2 transitions between any states belonging to its different irreducible representations and, as a result, the states of the model are uniquely defined with the property that observed transitions between rotational states of nuclei are to be expressed in terms of mixtures of the model irreps. The algebraic version of the unified model parallels the Bohr-Mottelson model in most respects, including the possibility of including the effects of Coriolis and centrifugal forces as subsequent perturbations. However, it corrects its treatment of angular momentum quantisation and no longer uses an over-complete set of coordinates. These changes have significant implications for the dynamics of nuclear rotations which are hidden when its moments of inertia are considered as inertial masses in the standard expression of rotational kinetic energies. Thus, the developments put a new perspective on the phenomenon of shape coexistence.

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“…Many applications of these methods have recently been reviewed by Sun [118]. Here we briefly review, with some adjustment, the elegant approach of Lee and Cusson [119,120] as it applies to doubly even nuclei.…”

Section: B Angular-momentum Projectionmentioning

confidence: 99%

“…In standard mean-field theory, the state |Φ is the minimumenergy Slater determinant. More generally, it could be determined separately for each angular-momentum state by variation-after-projection methods [120]. Other possibilities, in which |Φ could be one of several optimally chosen intrinsic states for the irreps of a microscopic collective model, are discussed in Sections IX D and X C. Body-fixed axes, for an intrinsic state |Φ , are appropriately chosen to be principal axes of its quadrupole mass tensor.…”

Section: B Angular-momentum Projectionmentioning

confidence: 99%

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The evolving many-nucleon theory of nuclear rotations

Rowe

2017

Preprint

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The many approaches that have been pursued in seeking an understanding of nuclear rotational dynamics are reviewed and reassessed with a view to their development in the light of recent progress and the research tools that are now available. A motivation for this review is the widespread observation of nuclear shape coexistence and sequences of rotational states in all regions of the nuclear periodic table combined with the recognition that the study of the rotational dynamics of quantum fluids has led to significant advances in the quantum theory of many-boson systems. Recent experimental investigations of the rotational dynamics of a low-temperature 6 Li gas indicate that its slow rotational flows are likewise the irrotational flows of a superfluid. In this context, the dynamics of rotating nuclei are of fundamental interest because the nucleus is a unique zero-temperature finite many-fermion quantum system. A promising approach is provided by algebraic mean-field theory which, as its name suggests, is a combination of algebraic and mean-field methods. Static meanfield theories play a central role in many-body theory by defining optimal independent-particle and independent quasi-particle basis states for the quantum mechanics of many-fermion systems. Their time-dependent extensions also lead, in the small-amplitude random-phase approximation, to the quantisation of the classical normal-mode vibrations of many-fermion systems about their static equilibrium states. This review shows that mean-field methods become significantly more powerful when combined with algebraic methods and an appropriate coupling scheme for the nuclear shell model.

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Nuclear structure studies of 20Ne and 24Mg in the variation-after-projection Hartree-Fock method

Cited by 42 publications

References 39 publications

Large-Scale Shell-Model Calculations

Large-Scale Shell-Model Calculations

Nuclear shape coexistence from the perspective of an algebraic many-nucleon version of the Bohr-Mottelson unified model

The evolving many-nucleon theory of nuclear rotations

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