G. Levai
Institute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI), P.O. Box 51, H–4001 Debrecen, Hungary e–mail: levai@atomki.hu
Recibido el 30 de enero de 2005
Aceptado el 15 de marzo de 2005
Abstract
]]> We apply the sextic oscillator as a 7–independent potential in the Bohr Hamiltonian and present exact analytic results for the energy eigenvalues and wavefunctions of the lowest few levels. Further properties, such as the flexible shape of the potential are also discussed. As illustration a potential reproducing the spectroscopic properties of the 134Ba nucleus, the first candidate for the E(5) symmetry is constructed. Fits to the energy spectrum of the 102Ru, 104Ru and 106Ru isotopes are also presented, and it is shown that in this region the potential undergoes changes characteristic for a transition from the spherical vibrator to the deformed 7–unstable domain. Possible generalizations of the model are also pointed out.Keywords: Nuclear shape; Quadrupole collectivity; Quasi–exactly solvable potentials.
Resumen
En este trabajo aplicamos el oscilador sextico como un potencial independiente de la variable 7 en el Hamiltoniano de Bohr y presentamos resultados analíticos para los valores propios y las funciones propias de los niveles de menor energía. Se discuten igualmente otras propiedades como la forma flexible del potencial. A manera de ilustración, se construye un potencial que reproduce las propiedades espectroscópicas del núcleo 134Ba, siendo esta el primer candidato de simetría E(5). Se presentan ajustes al espectro energético de los isótopos 102Ru, 104Ru y 106Ru y se muestra que en esta región el potencial sufre cambios característicos de la transición de vibrador esférico al dominio de 7 inestable. Se mencionan las posibles generalizaciones del modelo.
Descriptores: Forma del nucleo; colectividad cuadrupolar; potenciales con solucion cuasi–exacta.
PACS: 21.10.Re;03.65.Ge
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]]>Acknowledgments
This work was supported by the OTKA grant No. T37502 (Hungary). The author thanks J.M. Arias for the valuable discussions on the topic.
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