Mass distribution of fission fragments within the Born-Oppenheimer approximation

Abstract

Abstract. The fission fragments mass-yield of236 U is obtained by an approximate solution of the eigenvalue problem of the collective Hamiltonian that describes the dynamics of the fission process whose degrees of freedom are: the fission (elongation), the neck and mass-asymmetry modes. The macroscopic-microscopic method is used to evaluate the potential energy surface. The macroscopic energy part is calculated using the liquid drop model and the microscopic corrections are obtained using a Woods-Saxon single-particle levels. The four-dimensional modified Cassini ovals shape parametrization is used to describe the shape of the fissioning nucleus. The mass tensor is taken within a cranking-type approximation. The final fragment mass distribution is obtained by weighting the adiabatic density distribution in the collective space with the neck-dependent fission probability. The neck degree of freedom is found to play a significant role in determining the final fragment mass distribution.

Fission fragment mass and total kinetic energy distributions of spontaneously fissioning plutonium isotopes

“…A neck-size dependent fission probability [12] was used to evaluate the fissionfragment mass and kinetic energy yields from the distribution probability at different elongations of the fissioning nucleus as will be explained in Sect. 3.…”

“…Within the aforementioned deformation space the fission yield is obtained from the probability distribution of the collective wave function on the (q 3 , q 4 ) plane in the vicinity of the scission configuration (q 2 ≈ 2.3). A neck-size dependent fission probability [12] was used to evaluate the fissionfragment mass and kinetic energy yields from the distribution probability at different elongations of the fissioning nucleus as will be explained in Section 3.…”

Mass Yields of Fission Fragment of Pt to Ra Isotopes

“…The present research is a continuation and extension of our previous works [3][4][5][6]. The fundamental idea of the fission dynamics discussed in this work is that the relatively slow motion towards fission, mainly in q 2 direction, is accompanied by the fast vibrations in the "perpendicular" q 3 and q 4 collective variables.…”

“…For u nE (q 2 ) one can use the WKB approximation for a single q 2 mode as it has been done in Ref. [5], in which a 2D collective space has been considered, only. For φ n (q 3 , q 4 ; q 2 ), one can solve the eigenproblem of the underlying Hamiltonian in the perpendicular directions numerically.…”

“…The nonadiabatic and dissipative effects in low energy fission were taken into account in a similar way as in Refs. [3][4][5][6]. The potential energy surface (PES) is obtained by the macroscopic-microscopic (mac-mic) method, where the Lublin-Strasbourg Drop (LSD) model [7] has been used for the macroscopic part of the energy, while the microscopic shell and pairing corrections have been evaluated through the Yukawa-folded (YF) single-particle levels [8,9].…”