Eigenfunctions for calculating electronic vibrational intensities

Davidson, P. M.

doi:10.1098/rspa.1932.0045

Cited by 105 publications

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“…The calculations reported here are carried out with a simple Davidson interaction potential [9]. This interaction preserves a higher, symplectic model, symmetry which makes calculations in a very large multi-shell space possible.…”

Section: Introductionmentioning

confidence: 99%

SU(3) quasi-dynamical symmetry as an organizational mechanism for generating nuclear rotational motions

Bahri

Rowe

2000

Nuclear Physics A

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The phenomenological symplectic model with a Davidson potential is used to construct rotational states for a rare-earth nucleus with microscopic wave functions. The energy levels and E2 transitions obtained are in remarkably close agreement (to within a few percent) with those of the rotor model with vibrational shape fluctations that are adiabaticallly decoupled from the rotational degrees of freedom. An analysis of the states in terms of their SU(3) content shows that SU(3) is a very poor dynamical symmetry but an excellent quasi-dynamical symmetry for the model. It is argued that such quasi-dynamical symmetry can be expected for any Hamiltonian that reproduces the observed low-energy properties of a well-deformed nucleus, whenever the latter are well-described by the nuclear rotor model. 03.65.Fd, 05.70.Fh, 21.60.Fw, 21.60.Ev

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Section: Introductionmentioning

confidence: 99%

SU(3) quasi-dynamical symmetry as an organizational mechanism for generating nuclear rotational motions

Bahri

Rowe

2000

Nuclear Physics A

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“…where β 0 represents the position of the minimum of the potential. According to the specific form of the potential (20), we choose the deformation function in the following special form f (β) = 1 + aβ 2 , a << 1.…”

Section: Z(4)-ddm-d Solution For β Part Of the Hamiltonianmentioning

confidence: 99%

“…However, here one has to notice that such a new model parameter should not be regarded as a simple additional one for fitting experimental data, but as a model's structural one as it has been shown in [19]. In the present work, we intend to apply Davydov-Chaban Hamiltonian in the framework of DDMF with the Davidson [20] potential for β-vibrations. We will proceed to a systematic comparison of the obtained results, by the presently elaborated model being called Z(4)-DDM-D, for energy spectra and electromagnetic transition probabilities of even-even Pd, Xe, Ce and Pt isotopes, with the available experimental data and some theoretical models.…”

Section: Introductionmentioning

confidence: 99%

Davydov–Chaban Hamiltonian with deformation-dependent mass term for γ= 30∘

Buganu¹,

Chabab

Batoul

et al. 2018

Nuclear Physics A

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Motivation : Several theoretical comparisons with experimental data have recently pointed out that the mass tensor of the collective Bohr Hamiltonian cannot be considered as a constant and should be taken as a function of the collective coordinates.Method : The Davydov-Chaban Hamiltonian, describing the collective motion of γ-rigid atomic nuclei, is modified by allowing the mass to depend on the nuclear deformation. Moreover, the eigenvalue problem for this Hamiltonian is solved for Davidson potential and γ = 30 • involving an Asymptotic Iteration Method (AIM). The present model is conventionally called Z(4)-DDM-D (Deformation Dependent Mass with Davidson potential), in respect to the so called Z(4) model.Results : Exact analytical expressions are derived for energy spectra and normalized wave functions, for the present model. The obtained results show an overall agreement with the experimental data for 108−116 Pd, 128−132 Xe, 136, Pt and an important improvement in respect to other models. Prediction of a new candidate nucleus for triaxial symmetry is made.Conclusion : The dependence of the mass on the deformation reduces the increase rate of the moment of inertia with deformation, removing a main drawback of the model and leading to an improved agreement with the corresponding experimental data.

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“…The sequence of potentials studied in [18,19] give the opportunity to approach the E (5) and X(5) symmetries starting from U (5). Davidson type potentials [20], having a minimum at 0   , are good candidates for approaching the E(5) and X(5) symmetries starting respectively from the O(6) and SU(3) limiting structures. This gives rise to exact solutions which cover all the way from U(5) to O(6) and from U(5) to SU(3).…”

Section: Introductionmentioning

confidence: 99%

“…In the present study a version of the X(3) model is introduced by using the Davidson potential [20] in the  -part of the Schrödinger equation. This solution is going to be called the X(3)-D model.…”

Section: Introductionmentioning

confidence: 99%

Bohr Hamiltonian for $\gamma = 0^{\circ}$ γ = 0 ∘ with Davidson potential

Yigitoglu

Gökbulut

2017

Eur. Phys. J. Plus

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A  -rigid solution of the Bohr Hamiltonian is derived for 0   utilizing the Davidson potential in the  variable. This solution is going to be called X(3)-D. The energy eigenvalues and wave functions are obtained by using an analytic method which has been developed by Nikiforov and Uvarov. BE(2) transition rates are calculated. A variational procedure is applied to energy ratios to determine whether or not the X(3) model is located at the critical point between spherical and deformed nuclei.

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Eigenfunctions for calculating electronic vibrational intensities

Cited by 105 publications

References 0 publications

SU(3) quasi-dynamical symmetry as an organizational mechanism for generating nuclear rotational motions

SU(3) quasi-dynamical symmetry as an organizational mechanism for generating nuclear rotational motions

Davydov–Chaban Hamiltonian with deformation-dependent mass term for γ= 30∘

Bohr Hamiltonian for $\gamma = 0^{\circ}$ γ = 0 ∘ with Davidson potential

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