Static Fission-Barrier Calculations of a Two-Parameter Liquid Drop

Abstract

Calculations based on a two-parameter description of a uniformly charged liquid drop are reported. Results include fission-barrier energy and other saddle-point properties. The electrostatic energy of the drop was computed by a novel and highly accurate method. The saddle-point properties and corresponding drop shapes are compared with calculations that use nine parameters. Agreement is best for fissionability parameters greater than 0.70, suggesting that these calculations may provide a few-parameter basis for dynamical calculations of adequate precision at the larger fissionability parameters.

Fission fragment distributions within dynamical approach

“…When calculating the mass tensor, it was found that the Werner-Wheeler approximation provides very high accuracy for the elongation degree of freedom. For example, when describing the nuclear shape using the Lawrence parametrization [124], mass tensor components calculated from the elongation coordinate in the Werner-Wheeler approximation coincide with the exact solution of the corresponding hydrodynamic Neumann problem [125], which was obtained by a method based on potential theory [126]. In ref.…”

Revisiting the island of hexadecapole-deformation nuclei in the A ≈ 150 mass region: focusing on the model application to nuclear shapes and masses

“…There is no doubt that the accessibility of the corresponding parameterization will be inhibited to a large extent once the computational cost, brought by considering excessive degrees of freedom, is strongly increased. So far, several popular parameterizations are available, such as spherical harmonics [15,19], the Cassinian ovals [20], the funny-Hills parameterization [21], the matched quadratic surfaces [22] and the generalized Lawrence shapes [12,23,24]. In this work, see equation (10) in section 2, we define the nuclear surface with the help of the spherical-harmonic functions and introduce some 'deformation parameters' to express nuclear shapes [25].…”

“…Nowadays, the β 4 measurements are still attracting considerable interest in nuclearphysics research. For instance, more recently, the importance of hexadecapole deformation in 238 U was confirmed at the relativistic heavy ion collider [2] and, in the light-mass nucleus 24 Mg, the hexadecapole β 4 deformation was determined using quasi-elastic scattering measurements [26]. In 2022, we performed a systematic investigation on the shapes of even-even nuclei across the nuclear chart, focusing on the evolution of the β 2 , γ and β 4 deformations under rotation [31].…”

Modified Boltzmann Factor on Rupture Probability

“…The PES model is the model proposed by Strutinsky [8]. The shape of the core deformation greatly influences PES, for the shape of the core deformation refers to the standard form of Lawrence [9]. Furthermore, this Lawrence form is used together with the total energy of the nucleus through the liquid drop model (LDM) [10].…”