Time-dependent generator coordinate method study of fission: Mass parameters

Collective mass tensors derived in the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) method are employed in a study of induced fission dynamics. Together with a collective potential determined in deformation-constrained self-consistent mean-field calculations based on nuclear energy density functionals, the mass tensors specify the collective Hamiltonian that governs the time evolution of the nuclear wave function from an initial state at equilibrium deformation, up to scission and the formation of fission fragments. In an illustrative calculation of low-energy induced fission of ${}^{228}\mathrm{Th}$, ${}^{230}\mathrm{Th}$, ${}^{234}\mathrm{U}$, and ${}^{240}\mathrm{Pu}$, we compare the nonperturbative and perturbative cranking ATDHFB mass tensors in the plane of axially symmetric quadrupole and octupole deformations, as well as the resulting charge yields.

Figure 1

Axially symmetric quadrupole-octupole collective potentials in the ${\beta }_2\text{−}{\beta }_3$ plane for ${}^{228}\mathrm{Th}$, ${}^{230}\mathrm{Th}$, ${}^{234}\mathrm{U}$, and ${}^{240}\mathrm{Pu}$. In each panel, the energies are normalized with respect to the corresponding value at the equilibrium minimum. The contours join points on the surface with the same energy, and the separation between neighboring contours is 2 MeV. The dot-dashed curve is the static, lowest-energy fission path.

Figure 2

Square-root determinants of the perturbative-cranking mass tensor $|{\mathcal{M}}^{Cp}{|}^{1/2}$, and nonperturbative-cranking mass tensor $|{\mathcal{M}}^C{|}^{1/2}$ (in ${\hslash }^2{\mathrm{MeV}}^{-1}$) of ${}^{228}\mathrm{Th}$ in the $({\beta }_2,{\beta }_3)$ plane. The dot-dashed curve is the static, lowest-energy fission path.

Figure 3

The ${\mathcal{M}}_{22}$ (upper panel) and ${\mathcal{M}}_{33}$ (lower panel) components of the mass tensor of ${}^{228}\mathrm{Th}$, as function of the quadrupole deformation ${\beta }_2$ along the static fission path.

Figure 4

Same as in the caption Fig. 3 but for ${}^{230}\mathrm{Th}$.

Figure 5

Same as in the caption Fig. 3 but for ${}^{234}\mathrm{U}$.

Figure 6

Same as in the caption Fig. 3 but for ${}^{240}\mathrm{Pu}$.

Figure 7

Charge yields for induced fission in ${}^{228}\mathrm{Th}$, ${}^{230}\mathrm{Th}$, ${}^{234}\mathrm{U}$, and ${}^{240}\mathrm{Pu}$. The perturbative (${\mathcal{M}}^{Cp}$) and nonperturbative (${\mathcal{M}}^C$) cranking inertia tensors are used in the $\mathrm{TDGCM}+\mathrm{GOA}$ calculation. The experimental thermal neutron induced fission charge yields are from Ref. [33].