Production of Heavy Nuclei in the Par and Barbel Devices

Abstract

In the Par and Barbel thermonuclear devices, heavy nuclei up to $A=257$ were produced by the exposure of ${\mathrm{U}}^{238}$ to intense neutron fluxes. If one tries to interpret the resulting abundance as a function of mass number by assuming that all higher nuclei resulted from multiple neutron capture in ${\mathrm{U}}^{238}$, there are difficulties in reconciling the high-$A$ data with standard semiempirical mass formulas and neutron-capture cross-section theories. Neither the general trend of abundance as a function of $A$, nor the odd-even fluctuation (for $A>249$) which is superimposed on this trend, is consistent with standard theory. In this paper we explore the suggestion that the high-mass isotopes resulted from neutron capture in odd-$Z$ nuclei (Pa and Np). We adopt a simplified model of the thermonuclear devices in which deuterium plus tritium burns to completion and resulting neutrons are captured by various heavy nuclei. We first estimate, in Sec. II, the number of uranium nuclei which will be transformed to odd $Z$ by the reactions ${\mathrm{U}}^{238}(n,p){\mathrm{Pa}}^{238}$; ${\mathrm{U}}^{238}(d,n){\mathrm{Np}}^{239}$, and ${\mathrm{U}}^{238}(d,2n){\mathrm{Np}}^{238}$. A production of about ${10}^{\ensuremath{-}3}$ Pa/U and \ensuremath{\le}${10}^{\ensuremath{-}3}$ Np/U is found and it is estimated that roughly these ratios will be available as targets for multiple neutron capture. In Sec. III statistical theory is used together with Seeger's semiempirical mass formula to calculate 20-keV neutron-capture cross sections for the nuclei $91\ensuremath{\le}Z\ensuremath{\le}93$, $238\ensuremath{\le}A\ensuremath{\le}257$. The average odd-$Z$ cross sections are systematically larger than the even $Z$, and those of Np are larger than Pa. The mass-yield curve can then be calculated for various neutron-flux values and in Sec. IV the results are compared with experiment. For both Par and Barbel, good agreement with the experimental abundance data is found using a 20-keV exposure of 7\ifmmode\times\else\texttimes\fi{}${10}^{24}$ neutrons/${\mathrm{cm}}^{2}$. For Par, a Np/U ratio of ${10}^{\ensuremath{-}3}$ is required while for Barbel the corresponding ratio is about 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$. In both cases the light end of the mass curve ($A<248$) is due to the uranium capture chain, while the heavy end ($A\ensuremath{\ge}250$) arises from capture by Np. A comparison is also made with less complete data from the Mike device, and it is found that for $A\ensuremath{\ge}245$ the data can be fit for $\ensuremath{\phi}=6\ifmmode\times\else\texttimes\fi{}{10}^{24}$ neutrons/${\mathrm{cm}}^{2}$ with Np/U\ensuremath{\simeq}1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$. We conclude that the formation of odd-$Z$ nuclei which undergo multiple neutron capture permits one to understand the mass-yield curves using standard semiempirical mass formulas and conventional capture-cross-section theory.