Bohr Hamiltonian for gamma=0 with Davidson Potential

Melek Gökbulut

Bohr Hamiltonian for gamma=0 with Davidson Potential

Melek Gökbulut

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Abstract

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.

Key takeaways

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The X(3)-D model utilizes Davidson potential in the β variable for analyzing nuclear phase transitions.
Energy eigenvalues and wave functions are derived using the Nikiforov-Uvarov analytical method.
BE(2) transition rates are calculated to examine structural properties of nuclei.
The study aims to identify the critical point between spherical and deformed nuclei.
The model shows good agreement with experimental data for various isotopes, indicating its applicability.

FAQ's

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What key findings support the effectiveness of the X(3)-D model using Davidson potential?add

The study finds that the X(3)-D model closely matches experimental data for isotopes like 104 Ru and 180 Os with adjusted minimum parameters around o β = 1.210 and 2.0, respectively.

How does the variational procedure enhance the X(3)-D model predictions?add

The variational procedure produces ground state band energies that align well with X(3)-D model outcomes, although discrepancies arise with the model's γ-rigid nature affecting close comparisons.

What method was employed to obtain energy eigenvalues for the X(3)-D model?add

The analytical method developed by Nikiforov and Uvarov was applied to transform the Schrödinger equation, resulting in specific energy eigenvalues determined through parametric polynomial definitions.

When do the X(3) and X(3)-D model predictions significantly differ?add

The X(3) model shows optimal agreement up to L=10 for isotopes like 104 Ru, while the X(3)-D model performs better with higher L values, specifically for isotopes near o β = 1.210.

What implications does the study present regarding shape-phase transitions in nuclei?add

The research indicates that the X(3)-D model effectively spans critical points between U(5) and SU(3) symmetries, corroborating alignment with isotopes like 156 Dy at o β = 1.905.

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