A general numerical solution of collective quadrupole surface motion applied to microscopically calculated potential energy surfaces

Abstract

We present a numerical method based on finite elements capable of solving the general Hamiltonian for quadrupole surface motion including deformation-dependent masses and moments of inertia. We illustrate the power and accuracy of this method by comparing the resulting energies, B(E2)-values, and quadrupole moments to wellknown analytical limits (Harmonic Oscillator, WiletsJean potential). We extend the deformation and spin regions accessible to previous solution methods which allows for a unified description of phenomena like, e.g., very strongly deformed states (fl0 ~ 1.5) and the usual low-energy quadrupole excitations. Finally we apply this model to the microscopically calculated potential energy surfaces of 19~ and 138U derived from the pseudo-symplectic model and calculate energies, B(E2)-, B(E4)-and quadrupole-values, comparing them to experimental data.

Beyond the relativistic mean-field approximation. III. Collective Hamiltonian in five dimensions

“…(12) can be divided into two classes. The first is based on a direct numerical solution of a system of partial differential equations using finite-difference methods [30,31,32]. The second approach uses an expansion of eigenfunctions in terms of a complete set of basis functions, that depend on the deformation variables β and γ, and the Euler angles φ, θ and ψ [33,34,35,36].…”

Theg R -factor of rare-earth nuclei in the Geometric Collective Model

“…Experiment GCM --18 (8) It is, however, well known that systematic deviations exist, i.e. the experimental gg-value is generally smaller than the corresponding Z/A-ratio.…”

“…For the determination of the constant g~) we make use of a numerical experience in connection with the solutions of the Schr6dinger equation of the Hamiltonian (3): the general form for the eigenfunctions of this Hamiltonian expressed in the intrinsic variables reads [8] Table 1.…”

Effects of pairing in the pseudo-SU(3) model

“…From the point of the view of the Geometric Collective Model [11,25], the K-band mixing can be understood within the framework of the very simple asymmetric rotor model picture: The Hamiltonian in Eq. 5 is diagonal so long as γ = 0, since in this case J 1 = J 2 and K is trivially conserved.…”