A Model of Nuclear Shape Oscillations for g?Transitions and Electron Excitation

Abstract

1. INTRODUCTION The liquid drop model (Fierz 1943;Bohr 1952;Jekeli 1952) of the nucleus involves the assumption that the nucleus has a well-defined surface and a uniform charge and mass density. Experiments on the elastic scattering of high energy electrons (Hofstadter, Fechter, and McIntyre 1953;Hofstadter et al. 1954) have demonstrated that these assumptions are not valid even for heavy nuclei. An attempt is made to obtain a modified hydro dynamical model which allows for non-uniform nuclear charge and mass density distributions. In the liquid drop model distortions of the surface of the nucleus are considered; in this model similar distortions are considered not of the surface but of the shape of the nucleus, the distortions having effect throughout the whole nucleus. Excited states of the nucleus are then due to oscillations of the shape of the nucleus, i.e. oscillations involving: departures from spherical symmetry of the mass and charge distributions of the nucleus.Longitudinal compressional waves may be expected in the nucleus, involving nodes in the radial density distributions. As in the liquid drop model (Bohr 1952), the energy of excitation of these modes of radial oscillation should be' much greater than the energy of excitation of the shape oscillations. Thus, in treating low-lying nuclear energy levels, it is assumed that the radial dependence of the density distributions does not alter appreciably. This shape oscillation model is then used to consider y-transitions and electron excitation of nuclei. For a uniform charge distribution this model reduces to the usual liquid drop model.

A density variational approach to nuclear giant resonances at zero and finite temperature

“…A prototype of this kind of dynamics appears to be the highlying giant quadrupole resonance. A particular realisation of the scaling approach to this mode due to Tassie [27] is, indeed, fully consistent with the results of microscopic approaches for the transition density (see, e.g., Ref. [28)).…”

“…In order to analyze strength distributions and sum rules, one must therefore guess the precise form of &. A rather popular form of simple operators with multipolarity L and natural parity (-l)L is that of Tassie [27] Q(LI)= $ rfP,(cos 9J[l +Zr,(i)]…”

Coupled channel description of 16O+142,144,146Nd scattering around the Coulomb barrier using a complex microscopic potential

“…Tassie Model [50] is assumed to calculate the core polarization contribution. The coefficients obtained are suitably adjusted to reproduce the experimental electric transition rates.…”

Properties of the Inelastic Form Factors of the Nucleus

“…For many years a simple hydrodynamical model (Tassie 1956) has been extensively used for the analysis of electron scattering data (UberallI971; Fukuda andTorizuka 1972, 1976;Nagao and Torizuka 1973). The work of Deal and Fallieros (1973) on the energy-weighted sum rules (EWSR) has given an understanding of the success of the hydrodynamical model by establishing that the result from this model is a consequence of the assumption that a single state, called the doorway state, completely dominates the EWSR.…”

“…Thus there is a need for corrections to the simple hydrodynamical model. More formally, for isoscalar transitions, Tassie (1975) inverted the EWSR to obtain the transition charge densities and transition form factors as infinite sums of the EWSR, so that the first term of the sum is the result of the hydrodynamical model while the subsequent terms, which become more important as the momentum transfer is increased, correspond to the double doorway correction, triple doorway correction and so on.…”