Why are deformed nuclei prolate?

Castel, B.; Rowe, D.J.; Zamick, Larry

doi:10.1016/0370-2693(90)90813-l

Cited by 17 publications

(14 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2) An almost pure harmonic oscillator potential (i.e., with f ls = f ll = ǫ 4 = 0 and weakened pairing) produces R p = 55%. This is an quantitative estimation of the tendency of prolate preference predicted by Castel et al [6] In summary, a strong interference is found between the effects of the spin-orbit and the l 2 terms of the Nilsson potential. The ratio of prolate nuclei among well-deformed even-even nuclei is more than 80% by using the standard strengths for the two terms.…”

supporting

confidence: 55%

“…[5], it is the spin-orbit potential which breaks this even situation by weakening the oblate-shape shell effect. A more general argument given by Castel et al [6] is that the summation of the single-particle energies of an isotropic harmonic oscillator is decreased by extending one axis and shrinking the other two axes under volume conservation condition neglecting detailed effects of the Pauli principle. (Their argument seems to apply only to the harmonic oscillator potential contrary to their insist.)…”

mentioning

confidence: 99%

See 1 more Smart Citation

Prolate dominance of nuclear shape caused by a strong interference between the effects of spin-orbit andl2terms of the Nilsson potential

Tajima¹,

Suzuki²

2001

Phys. Rev. C

View full text Add to dashboard Cite

The origin of the dominance of prolate shapes over oblate ones of the ground states of atomic nuclei is investigated with the Nilsson-Strutinsky method. The number of prolate nuclei among all the deformed even-even nuclei is calculated as a function of the strengths of the spin-orbit and the l 2 terms of the Nilsson potential. The latter simulates a square-well like radial profile of the mean potential. The ratio of prolate nuclei is 86% with the standard strengths corresponding to the actual atomic nuclei. By weakening the spin-orbit potential, the ratio oscillates strongly, having a local minimum value of 45% with a half of the standard strength and a local maximum value of 78% without the spin-orbit potential.

show abstract

supporting

confidence: 55%

mentioning

confidence: 99%

Prolate dominance of nuclear shape caused by a strong interference between the effects of spin-orbit andl2terms of the Nilsson potential

Tajima¹,

Suzuki²

2001

Phys. Rev. C

View full text Add to dashboard Cite

show abstract

“…Using the dynamical description through the time-dependent single-particle density matrix, they showed that the effective inertial parameter (collective mass) is also larger for the case of prolate deformation. Later, Castel, Rowe, and Zamick [22], using conditions of self-consistency [15], argued that estimates of kinetic energy are in fact sufficient to make similar conclusions concerning the total energy of the system. One can give arguments working in the same direction based on the semiclassical analysis of the single-particle level density [23], the simplest periodic orbits [24], and their bifurcations in a deformed cavity [25]; superdeformed nuclei are also expected to have prolate deformation.…”

Section: Predominance Of Prolate Deformationsmentioning

confidence: 96%

Random interactions explore the nuclear landscape: Predominance of prolate nuclear deformations

Horoi

Zelevinsky

2010

Phys. Rev. C

View full text Add to dashboard Cite

We use an ensemble of random but spin-and isospin-invariant interactions in a restricted orbital space as a tool for exploration of the shell-model parameter space to understand the source of collective effects. The mean field with the yrast state sequence 0 + − 2 + − 4 + , rotational energy ratio E(4 + )/E(2 + ), and rigid-rotor relation between the prolate quadrupole moment Q(2 + ) and the transition probability B(E2; 2 + → 0 + ) appears with a high probability as a result of mixing of single-particle orbitals split by deformation. For a given set of collective observables, we identify the responsible matrix elements of the effective forces. In this framework, we reanalyze an old problem of the predominance of prolate deformations among well-deformed nuclei.

show abstract

“…Such a self-consistency relationship has been used for other purposes; e.g., by Bohr and Mottelson [1,8] and Castel et al [61].…”

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

confidence: 99%

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

Rowe

2019

Preprint

View full text Add to dashboard Cite

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.

show abstract

Why are deformed nuclei prolate?

Cited by 17 publications

References 8 publications

Prolate dominance of nuclear shape caused by a strong interference between the effects of spin-orbit andl2terms of the Nilsson potential

Prolate dominance of nuclear shape caused by a strong interference between the effects of spin-orbit andl2terms of the Nilsson potential

Random interactions explore the nuclear landscape: Predominance of prolate nuclear deformations

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

Contact Info

Product

Resources

About