29 research outputs found
New features of the triaxial nuclei described with a coherent state model
Supplementing the Liquid Drop Model (LDM) Hamiltonian, written in the
intrinsic reference frame, with a sextic oscillator plus a centrifugal term in
the variable and a potential in with a minimum in
, the Sch\"{o}dinger equation is separated for the two variables
which results in having a new description for the triaxial nuclei, called
Sextic and Mathieu Approach (SMA). SMA is applied for two non-axial nuclei,
Hf and W and results are compared with those yielded by the
Coherent State Model (CSM). As the main result of this paper we derive
analytically the equations characterizing SMA from a semi-classical treatment
of the CSM Hamiltonian. In this manner the potentials in and
variables respectively, show up in a quite natural way which contrasts their
ad-hoc choice when SMA emerges from LDM.Comment: 13 figures, 13 page
Application of the sextic oscillator potential together with Mathieu and spheroidal functions for triaxial and X(5) type nuclei
The Bohr-Mottelson Hamiltonian is amended with a potential which depends on both β and γ deformation variables and which allows us to separate the β variable from the other variables. The equation for the β variable is quasi-exactly solved for a sextic oscillator with centrifugal barrier potential. Concerning the γ equation, its solutions are the angular spheroidal and Mathieu functions for X(5) type and triaxial nuclei, respectively. The models developed in this way are conventionally called the Sextic and Spheroidal Approach (SSA) and the Sextic and Mathieu Approach (SMA). SSA and SMA was successfully applied for several nuclei, details being presented below
Application of the sextic oscillator potential together with Mathieu and spheroidal functions for triaxial and X(5) type nuclei
The Bohr-Mottelson Hamiltonian is amended with a potential which depends on both β and γ deformation variables and which allows us to separate the β variable from the other variables. The equation for the β variable is quasi-exactly solved for a sextic oscillator with centrifugal barrier potential. Concerning the γ equation, its solutions are the angular spheroidal and Mathieu functions for X(5) type and triaxial nuclei, respectively. The models developed in this way are conventionally called the Sextic and Spheroidal Approach (SSA) and the Sextic and Mathieu Approach (SMA). SSA and SMA was successfully applied for several nuclei, details being presented below