Microscopic quadrupole and hexadecapole moments of rare earth nuclei

Abstract

The theoretical calculations of multipole moments of even-even rare earth nuclei are presented. The potential energy surface is evaluated by the shell correction method. The condition ensuring the equality of the density distribution of the macroscopic liquid droplet part of the potential energy and the density generated by the single particle potential is added. A single particle Nilsson potential is used. New, less stiff potential surfaces versus e~ are obtained while the multipole moments calculated at the equilibrium deformations agree well with experimental data.

Surface symmetry energy of nuclear energy density functionals

“…It was therefore argued (see Refs. [138,139] and references quoted therein) that a mapping between the two sets of shape deformations can be best achieved by using the surface multipole moments defined asQ λ ≡ r 2 Y λ0 , which have a much softer radial dependence than volume moments. Deformation parametersβ l can therefore be extracted by requiring that the set of equations for dimensionless surface moments [138,139] Q λ (β l )…”

New estimates for the parameters of the modified oscillator potential of the rare earth nuclei

“…The values of the parameters of the single particle potential depend sensitively on the assumed equilibrium deformation. In the papers [2][3][4] it was found that the shape of the microscopic density distribution of the nucleus does not agree with the shape of the equipotential surface of the single particle potential which generates the density distribution. This means that one gets two different sets of equilibrium deformation parameters.…”

“…Because of the large difference in equilibrium deformations of the potential (~) and the density (e~) obtained with the simple consistency condition of Ref. 4 it seems to us that it was necessary to find a new set of (x, #) values for correctness (2). To do this we followed the method we have used previously in [5].…”

“…Circles correspond to points for which the calculation of (t<, #) was done. The curve I corresponds to the average equilibrium deformations obtained in the paper [4], the curve II to that from paper [1,7] 6.5 ~ -~ Fig. 4.…”

“…Deformation parameters eP(= e~, ~) and e~(= 8~, e~,) at the equilibirium in the rare earth region were calculated on the basis of the Nilsson potential with an old version of the 0c, #) parameters A = 185 set, see Ref. 4 entered into the modified oscillator potential:…”