Fission rate in multi-dimensional Langevin calculations

Experimental data on nuclear dissipation have often been interpreted using one-dimensional model calculations of the Langevin or Fokker-Planck type. In the present work, the influence of the dimensionality of the deformation space on the time dependence of the fission process has been investigated in a systematic and quantitative way. In particular, the dependence of the transient time and the stationary value of the fission rate on the number of collective coordinates involved in Langevin calculations is investigated for the one-body and two-body dissipation mechanisms. We show that the results of Langevin-type calculations change appreciably if the deformation space is extended up to three dimensions.

Figure 1

The potential energy surface for the compound nucleus ${}^{248}\mathrm{Cf}$ in the collective coordinates $q_1$ and $q_2$. The dashed curve corresponds to the case of $h=\alpha =0$. The numbers at the contour lines indicate the potential energy in MeV. The cross corresponds to the spherical deformation. The solid curve corresponds to the water divide, which separates the metastable region from the stable region; for more details, see text.

Figure 2

The potential energy surface for the compound nucleus ${}^{248}\mathrm{Cf}$ in the collective coordinates $q_1$ and $q_3$. The parameter $h$ is fixed and equal to zero. The numbers at the contour lines indicate the potential energy in MeV. The solid curve corresponds to the water divide, which separates the metastable region from the stable region.

Figure 3

The fission rate calculated for the nucleus ${}^{248}\mathrm{Cf}$ in the case of one-body dissipation for excitation energy $E^{*}=30$ MeV (a) and $E^{*}=150$ MeV (b). The solid, dashed, and dotted curves correspond to the three-, two-, and one-dimensional Langevin calculations, respectively.

Figure 4

The same as in Fig. 3, but for the case of two-body dissipation.