The sub-barrier photo-fission and the232Th fission barrier profile

Abstract

The 232Th sub-barrier photo-fission data have been analysed in terms of the predicted triple-humped barrier. It is shown that these results and particularly the isomeric shelf seen in these data cannot be explained as being due to the 2nd minimum. However, one can explain these results in terms of the 3rd minimum on the assumptions that Eln (the energy of the 3rd minimum relative to the ground state energy) ~3 MeV instead of Em~4.5 MeV as generally thought and the isomeric state in this well is fed and decays like the heavier actinides with double-humped barriers.The static potential calculations [-1, 2] show that for the light actinides such as Th, the outer barrier of the usual double-humped barrier splits into two barriers of comparable heights separated by a shallow minimum. Gavron et al. [3] have recently reviewed the particle induced sub-barrier fission of 227Ac, 228Ra, 228'231'232'233'234Th and concluded that the observation of narrow sub-barrier resonances in these nuclei indicates the presence of the third shallow minimum (Em~4.5 MeV), (see also Ref. 18). We have analysed the photo-fission data for 2aZTh [4] to see whether or not they are consistent with the triple humped barrier picture. Let us start with a double-humped barrier. The compound nucleus excited by a y-ray of energy E~ to a class-II state in the 2nd minimum will decay partly by direct fission through the outer barrier (prompt fission) and partly by y-decay to the isomeric state in the 2nd well, which will then fission with a certain probability (isomeric fission) determined by the characteristics of two barriers. Bowman [5] showed that the prompt fission cross section (~p,,y) goes down much faster with the decrease of the y-ray energy than the isomeric fission cross section (%,f), and at a certain E~ = Esh (shelf energy) we have %,, z = ai,,, z and below this E~, the az~,: starts to dominate the total photo-fission cross section a~,y. As az~,z varies rather slowly with E~,a~,y(E~) shows a plateau (isomeric shelf) below E~=E~h up to E~.=E n (the minimum of the 2nd well). The experimental photo-fission data on 232Th, 23sU and 237Np show the existence of this isomeric shelf [4,6]. Bowman [5] has given the relations to calculate o-pr ' y and ~i,, r as a function of E 7 in terms of barrier parameters as 8p~, y = 5.92 x 10 3 E~, exp( -1.6 Ey)PA PB(1) and ffi~,.r= 5-04 x (2) where PA and PB are the penetrabilities of the inner and the outer barriers for a given El,; R, the ratio of the fission width of the isomer compared to its decay width. The value of R can be considerably less than one due to 7-decay of the isomeric state towards the first minimum, if the inner barrier is more penetrable than the outer one. Furthermore, it can be shown [5] that for Ppr, f~-ffis, f at E~=E~h, one gets where FYbn and D a 1 are respectively the total 7-decay width and the level spacing for the class-II states in the 2nd well. Now with the experimental barrier parameters [7,8] for 238U (E A ~--5.68 MeV, h o) A = 1.0 MeV, E B = 5.68 MeV PB=R[2g F~blt]