X(5) Critical symmetry with inverse square potential via a variational procedure

Relative variation between γ coordinate and the potential of the Bohr Hamiltonian producing X(4) from Z(4)

“…Albeit, in the literature [16,24,25,[31][32][33][34], the variation of the potential parameter has provided some shape phase transitions at some constant or approximate values of γ, a simultaneous relative variation between γ and the potential has not been reported until in this present paper. These special shape phase solutions provide some geometric coordinates which link the potential and γ, as their relative variations link Z(4) and X(4) CPSs together.…”

“…Table 2 indicates that T(4) region should lie between this intervals. Consequently, these rational statements should be logically reproduced from the R 0,0 − β 0 distribution [34] if Z(4) and X(4) candidate isotopes are being considered. Briefly, the R 0,0 − β 0 or R 4/2 distribution [34, 54] is a theoretical rotational excitation signature [2] distribution that tends to show the relative positions of nuclei with respect to their collective models.…”

“…The procedure for finding the eigenvalues are stated in [33,34]. If the first condition of the listed procedure is considered, then the acceptable expression for the spectra is written as:…”

“…i and f denote the first and the last states respectively. The consequence of equation (31) with respect to the Eqs (34)(35)(36)(37)(38), yields the B(E2) ratios, B(E2;…”

“…The description of these CPSs, if this present method must be used, requires that a potential with a minimum or a free parameter potential such as Davidson potential used in [16], inverse square potential in [24,33,34], etc., must be used. In this present paper, the minimum of the potential, serves as an entity that can change the axial symmetry between the two CPSs.…”