Generator Coordinate Method Calculations for Ground and First Excited Collective States in $^{4}$He, $^{16}$O and $^{40}$Ca Nuclei

Abstract

The main characteristics of the ground and, in particular, the first excited monopole state in the $^{4}$He, $^{16}$O and $^{40}$Ca nuclei are studied within the generator coordinate method using Skyrme-type effective forces and three construction potentials, namely the harmonic-oscillator, the square-well and Woods-Saxon potentials. Calculations of density distributions, radii, nucleon momentum distributions, natural orbitals, occupation numbers and depletions of the Fermi sea, as well as of pair density and momentum distributions are carried out. A comparison of these quantities for both ground and first excited monopole states with the available empirical data and with the results of other theoretical methods are given and discussed in detail.Comment: 15 pages, LaTeX, 6 Postscript figures, submitted to EPJ