249 research outputs found
Simplified approach to the application of the geometric collective model
The predictions of the geometric collective model (GCM) for different sets of
Hamiltonian parameter values are related by analytic scaling relations. For the
quartic truncated form of the GCM -- which describes harmonic oscillator,
rotor, deformed gamma-soft, and intermediate transitional structures -- these
relations are applied to reduce the effective number of model parameters from
four to two. Analytic estimates of the dependence of the model predictions upon
these parameters are derived. Numerical predictions over the entire parameter
space are compactly summarized in two-dimensional contour plots. The results
considerably simplify the application of the GCM, allowing the parameters
relevant to a given nucleus to be deduced essentially by inspection. A
precomputed mesh of calculations covering this parameter space and an
associated computer code for extracting observable values are made available
through the Electronic Physics Auxiliary Publication Service. For illustration,
the nucleus 102Pd is considered.Comment: RevTeX 4, 15 pages, to be published in Phys. Rev.
Solvable models for the gamma deformation having X(5) as limiting symmetry. Removing some drawbacks of the existent descriptions
Two solvable Hamiltonians for describing the dynamic gamma deformation, are
proposed. The limiting case of each of them is the X(5) Hamiltonian. Analytical
solutions for both energies and wave functions, which are periodic in ,
are presented in terms of spheroidal and Mathieu functions, respectively.
Moreover, the gamma depending factors of the transition operator can be
treated.Comment: four two column pages, 1 figur
Description of even-even triaxial Nuclei within the Coherent State and the Triaxial Rotation-Vibration Models
The coherent state model (CSM) and the triaxial rotation-vibration model
(TRVM) are alternatively used to describe the ground, gamma and beta bands of
228Th. CSM is also applied to the nuclei 126Xe and 130Ba, which were recently
considered in TRVM. The two models are compared with respect to both their
underlying assumptions and to their predicted results for energy levels and E2
branching ratios. Both models describe energies and quadrupole transitions of
228Th equally well and in good agreement with experiment, if the 0 level
at 1120 keV is interpreted as the head of the beta band. The other two 0
levels at 832 and 939 keV are most likely not of a pure quadrupole vibration
nature as has already been pointed out in the literature.Comment: 31 pages, RevTeX, 6 figure
Construction of SO(5)>SO(3) spherical harmonics and Clebsch-Gordan coefficients
The SO(5)>SO(3) spherical harmonics form a natural basis for expansion of
nuclear collective model angular wave functions. They underlie the
recently-proposed algebraic method for diagonalization of the nuclear
collective model Hamiltonian in an SU(1,1)xSO(5) basis. We present a computer
code for explicit construction of the SO(5)>SO(3) spherical harmonics and use
them to compute the Clebsch-Gordan coefficients needed for collective model
calculations in an SO(3)-coupled basis. With these Clebsch-Gordan coefficients
it becomes possible to compute the matrix elements of collective model
observables by purely algebraic methods.Comment: LaTeX (RevTeX), 15 pages; to be published in Computer Phys. Comm
Effective theory for deformed nuclei
Techniques from effective field theory are applied to nuclear rotation. This
approach exploits the spontaneous breaking of rotational symmetry and the
separation of scale between low-energy Nambu-Goldstone rotational modes and
high-energy vibrational and nucleonic degrees of freedom. A power counting is
established and the Hamiltonian is constructed at next-to-leading order
Collective quadrupole excitations in the 50<Z,N<82 nuclei with the generalized Bohr Hamiltonian
The generalized Bohr Hamiltonian is applied to a description of low-lying
collective excitations in even-even isotopes of Te, Xe, Ba, Ce, Nd and Sm. The
collective potential and inertial functions are determined by means of the
Strutinsky method and the cranking model, respectively. A shell-dependent
parametrization of the Nilsson potential is used. An approximate
particle-number projection is performed in treatment of pairing correlations.
The effect of coupling with the pairing vibrations is taken into account
approximately when determining the inertial functions. The calculation does not
contain any free parameter.Comment: Latex2e source, 20 pages, 14 figures in EPS format, tar gzipped fil
Phase Transitions in Finite Nuclei and the Integer Nucleon Number Problem
The study of spherical-deformed ground--state phase transitions in finite
nuclei as a function of N and Z is hindered by the discrete values of the
nucleon number. A resolution of the integer nucleon number problem, and
evidence relating to phase transitions in finite nuclei, are discussed from the
experimental point of view and interpreted within the framework of the
interacting boson model.Comment: 8 pages Latex + 8 figs (postscript). In Phys Rev Lett, June 199
Solutions of the Bohr hamiltonian, a compendium
The Bohr hamiltonian, also called collective hamiltonian, is one of the
cornerstone of nuclear physics and a wealth of solutions (analytic or
approximated) of the associated eigenvalue equation have been proposed over
more than half a century (confining ourselves to the quadrupole degree of
freedom). Each particular solution is associated with a peculiar form for the
potential. The large number and the different details of the
mathematical derivation of these solutions, as well as their increased and
renewed importance for nuclear structure and spectroscopy, demand a thorough
discussion. It is the aim of the present monograph to present in detail all the
known solutions in unstable and stable cases, in a taxonomic
and didactical way. In pursuing this task we especially stressed the
mathematical side leaving the discussion of the physics to already published
comprehensive material. The paper contains also a new approximate solution for
the linear potential, and a new solution for prolate and oblate soft axial
rotors, as well as some new formulae and comments, and an appendix on the
analysis of a few interesting numerical sequences appearing in this context.
The quasi-dynamical SO(2) symmetry is proposed in connection with the labeling
of bands in triaxial nuclei.Comment: 48 pages, 28 figures, 6 table
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