Decay widths at the scission point in nuclear fission

An outstanding problem in the theory of nuclear fission is understanding the Hamiltonian dynamics at the scission point. Here we apply the generator coordinate method to calculate decay widths for prescission configurations into the two-fragment continuum. Transitions that are allowed under diabatic dynamics can have widths up to several MeV. For nondiabatic decays through the pairing interaction, typical widths to a specific final-state channel are two to three orders of magnitude smaller. The nucleus ${}^{236}\mathrm{U}$ is taken as a representative example in the calculations.

Figure 1

Neck size $N_{\mathrm{neck}}$ [Eq. (3)] of Glider configurations constrained by the $z_{\mathrm{rel}}$ operator [Eq. (3)].

Figure 2

Mass quadrupole moments $Q_2$ of Glider configurations constrained by ${\langle z\rangle }_{\mathrm{rel}}$, Eq. (2).

Figure 3

Overlap distance $\zeta$ along the elongation path from $z_{\mathrm{rel}}=16.1$.

Figure 4

Hartree-Fock energy as a function of the separation between centers of mass of the two nascent fragments. The red line shows their Coulomb interaction approximated as $V_c=e^2{Z}_L{Z}_R/z_{\mathrm{rel}}+C$ where $C$ is an offset to cross the energy curve at the scission point, marked by an arrow.

Figure 5

Energies of configurations used to build the continuum wave functions. Black circles are GCM-constrained Glider configurations; arrow marks the scission point between the second and third state. Red diamonds are simulated configurations for large separations, characterized by $S$ and $H$ matrix elements as described in Eq. (12) and (13). The energy scale is with respect to the HF energy of the second configuration.

Figure 6

Coordinate space wave function $\psi \left(z_{\mathrm{rel}}\right)$ for the fifth eigenstate at $E_5=-1776.4$ MeV in the GCM spectrum. The fit to $A$ in the asymptotic wave function $Asin(k{z}_{\mathrm{rel}}+\delta )$ is shown as the dotted line in the range $z_{\mathrm{rel}}=17.5$–18.5.

Figure 7

The strength function for the Glider configuration at $z_{\mathrm{rel}}=16.71$ fm dissolving into the discretized continuum eigenstates. The horizontal axis is the energy of the eigenstates $E_{\alpha }$ in MeV with respect to the flat potential in the external region. See text for construction of the discretized basis. The curve shows the strength function smoothed by convoluting the discretized strength function with Gaussian envelopes.

Figure 8

Off-diagonal matrix elements between the initial state and final states in the $H^{\gamma }$ matrix. The horizontal axis is the energy of the eigenstates $E_{\gamma }$ with respect to the flat potential in the external region. Units are MeV for both axes.