PHYSICAL REVIEW C VOLUME 47, NUMBER 3 MARCH 1993 High energy p rays from 5 Cf spontaneous fission D. J. Hofman, B. B. Back, ' C. P. Montoya, S. Schadmand, R. Varma, and P. Paul Department of Physics, State University of Nehru York at Stony Brook, Stony Brook, ¹rv York 117' (Received 12 November 1992) The spontaneous fission decay of Cf has been analyzed in a statistical model with emphasis on describing recently reported high energy p-ray spectra. An enhanced p emission in the range from 3 to 10 MeV which is observed for nearly symmetric mass splits is readily understood as a result of the difFerent fragment excitation energies. The model includes a viscous motion to the scission point with the possibility of prescission p emission. It was found that even with saddle-to-scission times of r„& 66 x 10 s, the maximum consistent with prescission neutron multiplicities, prescission p rays are overwhelmed by fragment p rays. Thus, the recently reported strong angular anisotropy of p rays in the range E~ = 8 — 12 MeV is unexplained within the present understanding of the fission process. PACS number(s): 25.85.Ca, 27.90. +b I. INTRODUCTION Recent measurements have reported high energy p-ray spectra emitted in the spontaneous fission of Cf which show several surprising features. Van der Ploeg et al [1] observe p rays up to about 15 MeV and an enhanced emission of p rays with energies around 10 MeV in the direction of the fission axis. Glassel et al. [2] and then Wiswesser et aL [3] report the Cf p spectrum up to about 10 MeV as a function of fission mass asymmetry, showing a significant enhancement in the region from 3 to 8 MeV for symmetric Gssion events. In spontaneous fission, high energy p rays are emitted by the excited fission fragments, but possibly also by the fissioning nucleus on its path from the saddle to the scis- sion point. Recent measurements of high-energy p rays from the decay of hot (T ~ 2.0 MeV) thorium nuclei [4, 5] have found that high-energy p rays are indeed emit- ted both before and after traversing the saddle point, and that these provide information about the dynamics of the fission process. Specifically, it was concluded from the strong presence of prescission p rays that the fission mass motion was strongly overdamped, with a normal- ized nuclear friction coefficient of p=10, corresponding to a fission time scale ~ 10 is s. Here, p = P/2ao, where P is the reduced friction coefficient and wo is a characteris- tic potential or barrier curvature. In this paper we analyze the spontaneous fission-p data of Refs. [1, 3] using the same formalism as in the anal- ysis of the hot Th fission, with the aim to see if any of the interesting results cited above may be related to p rays emitted from the fissioning system on its way from the saddle to the scission point. Calculations by Nix and On leave from Argonne National Laboratory, Argonne, IL 60439. Sierk [6] of the kinetic energy of fission fragments result- ing from 252Cf at a temperature T = 2.0 MeV have shown that the amount of damping in the saddle-to-scission mass motion results in scission time scales which vary from 2 x 10 21 s fpr np djssipatjpn tp 30 x 10 s fpr full one-body dissipation (corresponding to the wall-window formula). This time is long enough to allow the emission of giant dipole resonance (GDR) p rays. II. ANALYSIS OF FRAGMENT DECAY To calculate the p spectrum and the p yield per fission event, as well as the p-Gssion angular correlation we use a modified version of the statistical code CASCADE [7] which includes the fission process with friction and GDR p emission on the path from saddle to scission [4], as well as from the fission fragments [8]. In order to constrain the parameters of the model as much as possible we re- quire that the calculations reproduce the wealth of data that are available on 252Cf. The most prominent feature of spontaneous fission of ~52Cf is the strongly asymmet- ric mass distribution caused by the shell structure of the nascent fragments near the scission point [9]. The present calculations use the experimental data for the mass dis- tribution, as well as the mean and variance of the kinetic energy distribution measured as a function of fragment mass [10, ll]. The total excitation energy available for statistical decay of the fragments is given by the energy balance (Afrag) = Q(Afrsg) EK(AfrrLg) where the total excitation energy E', the fission Q value Q, and the total kinetic energy E~ depend on the mass Ar, ~g of one of the fragments. For each fragment mass Af, g a charge number is needed to look up the experimental fission Q value Q(Af, ~g). These were assumed to follow the uniform charge distribution [14, 15], i.e. , Zr, ~g = Af, ~g98/252. 47 1103 1993 The American Physical Society