Fission and the Synthesis of Heavy Nuclei by Rapid Neutron Capture

The role of fission is examined in the synthesis of heavy nuclei by multiple capture of neutrons in thermo-nuclear explosions. We begin by reviewing evidence from the recent Tweed and Cyclamen experiments indicating that neutron-induced fission is a serious source of depletion in neutron capture chains which start from targets of ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}$ and ${}_{}{}^{243}{}_{}{}^{}\mathrm{Am}$. An analysis of Tweed abundances (Sec. 2) is made to obtain capture-to-fission ratios for the odd-$A$ plutonium isotopes through $A=253\mathrm{}$. We next use the liquid-drop model of Myers and Swiatecki plus empirical shell corrections and pairing energies, in order to correlate and predict spontaneous fission lifetimes (Sec. 3) and fission barriers (Sec. 4). For nuclei having $Z\le 101$ and $N\le 157$, we extrapolate the shell correction, assuming it to be a function of $N$ plus a function of $Z$, and thus obtain neutron binding energies, fission barriers, and spontaneous fission lifetimes for neutron-rich heavy nuclei (Sec. 6). Capture-to-fission ratios are estimated for many of these nuclei in Sec. 7, and qualitative agreement is found with laboratory and Tweed results. In Sec. 8, the Sec. 8, extrapolation is continued out to $N=159\mathrm{}$ and $Z=104\mathrm{}$. We conclude that by using the liquid-drop model plus semiempirical shell corrections, one can obtain capture-to-fission ratios and spontaneous fission half-lives which are usefully accurate. However, for predicting properties of nuclei having $Z>\mathrm{}104\mathrm{}$, $N\gtrsim 159$, one needs, in this formalism, an accurate way of predicting shell corrections or nuclear masses.