Shape isomers in Pt, Hg and Pb isotopes with $${\hbox {N}}\le 126$$

Abstract

Deformation-energy surfaces of 54 even-even isotopes of Pt, Hg and Pb nuclei with neutron numbers up to 126 are investigated within a macroscopic-microscopic model based on the Lublin-Strasbourg-Drop macroscopic energy and shell plus pairing-energy corrections obtained from a Yukawa-folded meanfield potential at the desired deformation. A new, rapidly converging Fourier shape parametrization is used to describe nuclear shapes. The stability of shape isomeric states with respect to non-axial and higher-order deformations is investigated.

Spontaneous fission half-lives of actinides and superheavy elements

“…As can be seen from Fig. 3, the component B 22 gradually increases with the elongation coordinate q 2 , but is only weakly dependent on the mass-asymmetry parameter q 3 in the region where it would have the largest influence on the action integral (26), namely the barrier region around q 2 1. The other crucial inertia component, B 33 , changes relatively slowly with q 2 in this region (below q 2 1), but increases dramatically in the vicinity of the scission configuration (q 2 1.5).…”

“…3 for the diagonal components B 11 , B 22 , and B 33 as well as for the off-diagonal component B 23 projected onto the (q 2 , q 1 ) and (q 2 , q 3 ) planes respectively. The values of the remaining two deformation parameters q 3 , q 4 , respectively q 1 , q 4 , are adjusted in such a way that they minimize the action integral (26) along the least-action path.…”

“…Potential energy surfaces for 230 U (a)-(c), 234 U (d)-(f) and 252 No (g)-(i) isotopes projected onto the (q 2 , q 1 ), (q 2 , q 3 ), and (q 2 , q 4 ) deformation subspaces. The projection is performed in such a way that the other two variables q k (q 2 ) and q k (q 2 ) take values that minimize the action (26) between the equilibrium and the exit points. The dashed red and solid black curves correspond respectively to the LAP obtained with the hydrodynamical mass tensor and the least-energy path (LEP).…”

“…The parameter β in front of the B i j mass tensor in (26) gives the possibility of rescaling its six independent components altogether in order to reproduce within a couple of orders of magnitude the measured actinide half-lives. Obviously, such an operation does not touch the relative values between the tensor components that, in addition to the reliability of the PES, are relevant for a realistic determination of the course of the LAP, and thus of the resulting action value.…”

“…In general, spontaneous fission half-life calculations require not only an assessment of the collective potential energy surface (evaluated in a purely microscopical approach or, as will be done is what follows, within the macroscopic-microscopic model), but also of the collective inertia tensor. Commonly, the latter is obtained within the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach [23,24] or the generator coordinate method (GCM) with the generalized Gaussian overlap approximation (GOA) [25,26], or is evaluated within the so-called cranking approximation [27,28]. In the present work the irrotational-flow approach of Ref.…”