Distribution of Charge inTh232andU238Determined by Measurements on Muonic X Rays

Abstract

The energies and intensities of the x rays of muonic atoms of ${\mathrm{Th}}^{232}$ and ${\mathrm{U}}^{238}$ were measured. Analysis of the data was performed using the rotational model of strongly deformed nuclei to include dynamic quadrupole interactions. The distribution of nuclear charge was represented by a modified Fermi distribution which involves three parameters, namely, the intrinsic quadrupole moment $Q_0$, the half-density radius $c=c_0{A}^{\frac{1}{3}}$, and the skin thickness $t$. It was found that the allowed ranges of values for $Q_0$, $c_0$, and $t$ were for thorium 9.58-9.83 b, 1.155-1.143 F, and 1.54-1.87 F, and for uranium 11.20-11.41 b, 1.150-1.142 F, and 1.600-1.87 F, respectively. However, if specific values for two of these parameters are chosen, the third is determined with an error smaller than the above ranges: 0.5% for $Q_0$, 0.25% for $c_0$, and 0.6% for $t$.