Nuclear-Charge Distribution in Low-Energy Fission

Abstract

New information concerning half-lives and fractional independent and fractional cumulative yields of fission products has been obtained from experiments in which adjacent elements in fission-product chains were rapidly separated.Fractional cumulative yields that have been determined for the thermal-neutron fission of ${\mathrm{U}}^{235}$ are: ${\mathrm{Kr}}^{93}$, ${0.075}_{\ensuremath{-}0.002}^{+0.010}$; ${\mathrm{Kr}}^{94}$, ${0.015}_{\ensuremath{-}0.002}^{+0.005}$; ${\mathrm{Kr}}^{95}$, (${1.1}_{0.1}^{+0.3}$)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$; ${\mathrm{Kr}}^{97}$, ${10}^{\ensuremath{-}5}$; ${\mathrm{Xe}}^{137}$, 0.978\ifmmode\pm\else\textpm\fi{}0.003; ${\mathrm{Xe}}^{138}$, 0.956\ifmmode\pm\else\textpm\fi{}0.003. Fractional cumulative yields determined for the spontaneous fission of ${\mathrm{Cf}}^{252}$ are: ${\mathrm{Xe}}^{139}$, 0.67\ifmmode\pm\else\textpm\fi{}0.01; ${\mathrm{Xe}}^{140}$, 0.45\ifmmode\pm\else\textpm\fi{}0.01; ${\mathrm{Xe}}^{141}$, 0.172\ifmmode\pm\else\textpm\fi{}0.005; ${\mathrm{Xe}}^{144}$, 0.007.Fractional independent yields determined for the thermal-neutron fission of ${\mathrm{U}}^{235}$ are: ${\mathrm{Sr}}^{91}$, 0.07\ifmmode\pm\else\textpm\fi{}0.05; ${\mathrm{Nb}}^{95m}$, 4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$; ${\mathrm{Nb}}^{96}$, (1.0\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$; ${\mathrm{Nb}}^{97}$, (1.7\ifmmode\pm\else\textpm\fi{}0.8)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$; ${\mathrm{Cs}}^{136}$, (1.10\ifmmode\pm\else\textpm\fi{}0.15) \ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$; ${\mathrm{Ba}}^{139}$, ${0.012}_{\ensuremath{-}0.003}^{+0.005}$; ${\mathrm{Ba}}^{140}$, 0.066\ifmmode\pm\else\textpm\fi{}0.026; ${\mathrm{Ba}}^{141}$, 0.27 \ifmmode\pm\else\textpm\fi{}0.08; ${\mathrm{La}}^{141}$, 0.004\ifmmode\pm\else\textpm\fi{}0.002; ${\mathrm{La}}^{142}$, 0.019\ifmmode\pm\else\textpm\fi{}0.005; ${\mathrm{Ce}}^{143}$, (4.4\ifmmode\pm\else\textpm\fi{}3.0) \ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$. Fractional independent yields determined for the thermal-neutron fission of ${\mathrm{U}}^{233}$ are: ${\mathrm{Nb}}^{95m}$, 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$; ${\mathrm{Nb}}^{96}$, (1.3\ifmmode\pm\else\textpm\fi{}0.2) \ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$; ${\mathrm{Nb}}^{97}$, 0.011\ifmmode\pm\else\textpm\fi{}0.004. Fractional independent yields determined for the thermal-neutron fission of ${\mathrm{Pu}}^{239}$ are: ${\mathrm{Nb}}^{95m}$, 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$; ${\mathrm{Nb}}^{96}$, (7.7\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$; ${\mathrm{Nb}}^{97}$, 0.015\ifmmode\pm\else\textpm\fi{}0.004. The fractional independent yield of ${\mathrm{Cs}}^{136}$ from spontaneous fission of ${\mathrm{Cf}}^{252}$ is 0.01.The above data together with other published data give direct information about the distribution of nuclear charge among fission products with mass numbers 91, 139, 140, 141, 142, and 143 from thermal-neutron fission of ${\mathrm{U}}^{235}$. The variation of fractional yield with $Z$ for constant $A$ can be represented in cumulative form by the area under a Gaussian curve from $\ensuremath{-}\ensuremath{\infty}$ to $Z+\frac{1}{2}$. The standard deviation of the curve which best represents the data for the six mass numbers is $\ensuremath{\sigma}=0.62\ifmmode\pm\else\textpm\fi{}0.06$.The variation with $A$ of ${Z}_{P}$, the value of $Z$ at the maximum in a charge distribution curve, is discussed, and a new empirical ${Z}_{P}$ function is derived on the assumption that the Gaussian curve is applicable to all mass numbers. The function and curve correlate quite well the available fractional yield data for low-energy fission processes.There are indications from the analysis of charge dispersion, and from some other observed fission phenomena, that primary low-energy fission products with $Z$ less than 50 and greater than the complementary charge (>42 for $_{92}\mathrm{U}$ fission) may be formed in very low yield. It is suggested that observed fission products with atomic numbers in this range may be formed predominantly by beta decay processes starting from products complementary to $_{50}\mathrm{Sn}$ ($_{42}\mathrm{Mo}$ for $_{92}\mathrm{U}$ fission) or from products of lower $Z$.During the course of this work, fission yields of 51-min ${\mathrm{Nb}}^{98}$ from thermal-neutron fission of ${\mathrm{U}}^{235}$, ${\mathrm{U}}^{233}$, and ${\mathrm{Pu}}^{239}$ were determined to be (0.064\ifmmode\pm\else\textpm\fi{}0.012)%, (0.20\ifmmode\pm\else\textpm\fi{}0.03)%, and (0.20\ifmmode\pm\else\textpm\fi{}0.03)%, respectively.New half-life values determined are: ${\mathrm{Rb}}^{91}$, 72\ifmmode\pm\else\textpm\fi{}8 sec; ${\mathrm{Rb}}^{92}$, 11 sec; ${\mathrm{Nb}}^{98}$, 51\ifmmode\pm\else\textpm\fi{}3 min; ${\mathrm{Cs}}^{141}$, 25\ifmmode\pm\else\textpm\fi{}3 sec; ${\mathrm{Cs}}^{142}$, 8 sec; ${\mathrm{Ba}}^{143}$, 12\ifmmode\pm\else\textpm\fi{}2 sec. ${\mathrm{Kr}}^{97}$ and a reported 14-min isomer of ${\mathrm{Rb}}^{91}$ were not found among the fission products; we believe that our data refute the published evidence for their existence.