A new formula for rotational energies

Holmberg, P.; Lipas, P.O.

doi:10.1016/0375-9474(68)90830-0

Cited by 113 publications

(62 citation statements)

References 12 publications

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“…Another formula giving very good results for rotational spectra has been introduced by Holmberg and Lipas 213 , and rediscovered in 214 . In this case the energy levels are given by…”

Section: Generalized Deformed Su(2) Modelsmentioning

confidence: 99%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

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Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical tools (q-numbers, q-analysis, q-oscillators, q-algebras), the su q (2) rotator model and its extensions, the construction of deformed exactly soluble models (u(3)⊃so (3) model, Interacting Boson Model, Moszkowski model), the 3-dimensional q-deformed harmonic oscillator and its relation to the nuclear shell model, the use of deformed bosons in the description of pairing correlations, and the symmetries of the anisotropic quantum harmonic oscillator with rational ratios of frequencies, which underly the structure of superdeformed and hyperdeformed nuclei, are discussed in some detail. A brief description of similar applications to the structure of molecules and of atomic clusters, as well as an outlook are also given.

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“…Another formula giving very good results for rotational spectra has been introduced by Holmberg and Lipas 213 , and rediscovered in 214 . In this case the energy levels are given by…”

Section: Generalized Deformed Su(2) Modelsmentioning

confidence: 99%

Quantum groups and their applications in nuclear physics

Bonatsos

Daskaloyannis

1999

Progress in Particle and Nuclear Physics

198

203

View full text Add to dashboard Cite

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“…The measured transitions energies can be plotted against the spin of the parent state and fitted using a two parameter expression [27,28]:…”

mentioning

confidence: 99%

In-beam spectroscopy with intense ion beams: Evidence for a rotational structure in246Fm

Piot¹,

Gall²,

Dorvaux³

et al. 2012

Phys. Rev. C

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“…The occurence of SU(3) (with large boson numbers) in the X(5) framework is a new result, which has been proved by considering energy, intraband and interband B(E2), and quadrupole moment ratios, while the occurence of O(6) in the E(5) framework has essentially been observed earlier [8] and has been corroborated here by considering energy and intraband B(E2) ratios. 6) As a by-product, a derivation of the Holmberg-Lipas formula [26] has been achieved using Davidson potentials in the X(5) framework. 7) As another by-product, quadrupole moments for the X(5) model and the X(5)-β 2n models [14] for n = 1, 2, 3, 4 have been calculated.…”

Section: Discussionmentioning

confidence: 99%

“…In Section 2 the E(5) case is considered, while the X(5) case is examined in Section 3, in which a new derivation of the Holmberg-Lipas formula [26] for nuclear energy spectra, as well as quadrupole moments for the X(5) and related models are obtained as by-products. Finally, Section 4 contains a discussion of the present results and plans for further work.…”

Section: Introductionmentioning

confidence: 99%

E(5) and X(5) critical point symmetries obtained from Davidson potentials through a variational procedure

et al. 2004

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Davidson potentials of the form β 2 +β 4 0 /β 2 , when used in the E(5) framework (i.e., in the original Bohr Hamiltonian after separating variables as in the E(5) model, describing the critical point of the U(5) to O(6) shape phase transition) bridge the U(5) and O(6) symmetries, while they bridge the U(5) and SU(3) symmetries when used in the X(5) framework (i.e., in the original Bohr Hamiltonian after separating variables as in the X(5) model, corresponding to the critical point of the U(5) to SU(3) transition). Using a variational procedure, we determine for each value of angular momentum L the value of β 0 at which the rate of change of various physical quantities (energy ratios, intraband B(E2) ratios, quadrupole moment ratios) has a maximum, the collection of the values of the physical quantity formed in this way being a candidate for describing its behavior at the relevant critical point. Energy ratios lead to the E(5) and X(5) results (whice correspond to an infinite well potential in β), while intraband B(E2) ratios and quadrupole moments lead to the E(5)-β 4 and X(5)-β 4 results, which correspond to the use of a β 4 potential in the relevant framework. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product. (5) [2] models are supposed to describe shape phase transitions in atomic nuclei, the former being related to the transition from U(5) (vibrational) to O(6) (γ-unstable) nuclei, and the latter corresponding to the transition from U(5) to SU(3) (rotational) nuclei. In both cases the original Bohr collective Hamiltonian [3] is used, with an infinite well potential in the collective β-variable. Separation of variables is achieved in the E(5) case by assuming that the potential is independent of the collective γ-variable, while in the X(5) case the potential is assumed to be of the form u(β) + u(γ). We are going to refer to these two cases as "the E(5) framework" and "the X(5) framework" respectively. The selection of an infinite well potential in the β-variable in both cases is justified by the fact that the potential is expected to be flat around the point at which a shape phase transition occurs. Experimental evidence for the occurence of the E(5) and X(5) symmetries in some appropriate nuclei is growing ([4, 5] and [6,7] respectively).In the present work we examine if the choice of the infinite well potential is the optimum one for the description of shape phase transitions. For this purpose, we need one-parameter potentials which can span the U(5)-O(6) region in the E(5) framework, as well as the U(5)-SU(3) region in the X(5) framework. It turns out that the exactly soluble [8,9] Davidson potentials [10]

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A new formula for rotational energies

Cited by 113 publications

References 12 publications

Quantum groups and their applications in nuclear physics

Quantum groups and their applications in nuclear physics

In-beam spectroscopy with intense ion beams: Evidence for a rotational structure in246Fm

E(5) and X(5) critical point symmetries obtained from Davidson potentials through a variational procedure

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