TY - JOUR

T1 - Stationary Fokker-Planck equation applied to fission dynamics

AU - Nix, J. Rayford

AU - Sierk, Arnold J.

AU - Hofmann, Helmut

AU - Scheuter, Franz

AU - Vautherin, Dominique

N1 - Funding Information:
We are grateful to A. Gavron for stimulating discussions and for permitting us to use his preliminary unpublished results for neutron-emission times. D. Vautherin would like to thank the Physik-Department der T. U. Mtinchen for the hospitality extended to him. This work was supported by the US Department of Energy and by the German Ministry for Research and Technology under contract 06 MT 749.

PY - 1984/8/6

Y1 - 1984/8/6

N2 - By use of both analytical and numerical techniques, we study the relaxation of time-dependent solutions of the Fokker-Planck equation for an inverted oscillator to Kramers' stationary solution. This is done by integrating over all time the time-dependent solutions for given initial conditions at the saddle point to obtain stationary solutions, whose densities and higher velocity moments are compared as functions of the coordinate with the corresponding quantities calculated from Kramers' stationary solution. For large values of the coordinate an a symptotic expansion of the density is obtained, but for general values of the coordinate and for higher velocity moments the time integration must be done numerically. With increasing dissipation the relaxation to Kramers' stationary solution occurs at successively smaller values of the coordinate. By use of Kramers' stationary solution, we derive analytical expressions as functions of nuclear temperature and dissipation strength for several quantities of interest in fission dynamics, including the mean time from the saddle point to scission, the mean fission-fragment kinetic energy at the scission point and the contribution to the variance in the fission-fragment kinetic energy resulting from fluctuations in the fission degree of freedom. We apply these results to some examples that have been studied experimentally, including the mean saddle-to-scission time for the heavy-ion-induced fission of the compound nucleus 168Yb and the mean fission-fragment kinetic energy at scission and the contribution to its variance for the α-particle-induced fission of the compound nucleus 213At.

AB - By use of both analytical and numerical techniques, we study the relaxation of time-dependent solutions of the Fokker-Planck equation for an inverted oscillator to Kramers' stationary solution. This is done by integrating over all time the time-dependent solutions for given initial conditions at the saddle point to obtain stationary solutions, whose densities and higher velocity moments are compared as functions of the coordinate with the corresponding quantities calculated from Kramers' stationary solution. For large values of the coordinate an a symptotic expansion of the density is obtained, but for general values of the coordinate and for higher velocity moments the time integration must be done numerically. With increasing dissipation the relaxation to Kramers' stationary solution occurs at successively smaller values of the coordinate. By use of Kramers' stationary solution, we derive analytical expressions as functions of nuclear temperature and dissipation strength for several quantities of interest in fission dynamics, including the mean time from the saddle point to scission, the mean fission-fragment kinetic energy at the scission point and the contribution to the variance in the fission-fragment kinetic energy resulting from fluctuations in the fission degree of freedom. We apply these results to some examples that have been studied experimentally, including the mean saddle-to-scission time for the heavy-ion-induced fission of the compound nucleus 168Yb and the mean fission-fragment kinetic energy at scission and the contribution to its variance for the α-particle-induced fission of the compound nucleus 213At.

UR - http://www.scopus.com/inward/record.url?scp=0000451311&partnerID=8YFLogxK

U2 - 10.1016/0375-9474(84)90184-2

DO - 10.1016/0375-9474(84)90184-2

M3 - Article

AN - SCOPUS:0000451311

SN - 0375-9474

VL - 424

SP - 239

EP - 261

JO - Nuclear Physics, Section A

JF - Nuclear Physics, Section A

IS - 2

ER -