Quadrupole collective inertia in nuclear fission: Cranking approximation

Abstract

Collective mass tensor derived from the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) approach is compared with that obtained in the Gaussian Overlap Approximation (GOA) to the generator coordinate method. Illustrative calculations are carried out for one-dimensional quadrupole fission pathways in 256 Fm. It is shown that the collective mass exhibits strong variations with the quadrupole collective coordinate. These variations are related to the changes in the intrinsic shell structure. The differences between collective inertia obtained in cranking and perturbative cranking approximations to ATDHFB, and within GOA, are discussed.

Fission barriers and probabilities of spontaneous fission for elements with Z≥ 100

“…A detailed discussion is given in [25,28]. Here we only discuss some new aspects concerning the spontaneous fission process.…”

“…This can be seen from formula (3) for the action integral where the mass B(q) and the potential energy V(q) enter the action as a product. A relatively recent discussion of the mass tensor calculations can be found in [28].…”

“…This would 5 predict a valley of fission instability in this particular region of superheavies. On the other hand there is experimental evidence [53] The calculation of main ingredients of the theory, namely the PES and the collective mass parameter were described elsewhere [28,25]. We map the deformation landscape by adding a quadrupole constraint stretching the system successively to scission.…”

“…Since then substantial progress has been made in the development of models and methods especially by Lublin-Madrid collaboration [23,24], LublinOak Ridge-Warsaw group [25,26,27,28,29,30], and Erlangen-Darmstadt team [31] -energy density functional (EDF) HFB approaches -and in the MM model by the Warsaw [32,33,34], Los Alamos school [35] and the relativistic mean-field (RMF) [36].…”

Pairing-induced speedup of nuclear spontaneous fission

“…The one-dimensional path L(s) is defined in the multidimensional collective space by specifying the collective variables {X i } ≡ {Q 20 , Q 22 , λ 2n +λ 2p , λ 2n −λ 2p } as functions of path's length s. Furthermore, to render collective coordinates dimensionless, we define x i = X i /δx i , where δx i are appropriate scale parameters that are also used when determining numerical derivatives of density matrices [30]. Although the collective action is invariant to uniform scaling, working with dimensionless ds is simply convenient when defining the fission path and analyzing results.…”