Neutron Cross Section of Xenon-135 as a Function of Energy

Abstract

The neutron cross section of ${\mathrm{Xe}}^{135}$ as a function of energy was measured, using as velocity selector a focusing-type single-crystal spectrometer designed for transmission measurements of very small samples. The total cross section in the energy interval from 0.015 ev to 0.20 ev was measured. The samples, produced from neutron irradiated uranium metal, were in the form of Pd${\mathrm{I}}_2$ and were contained in sealed Pyrex capillary tubing. The largest initial strength of the samples was 10 curies of ${\mathrm{I}}^{135}$ activity, corresponding to 12×${10}^{15}$ atoms of ${\mathrm{I}}^{135}$. The daughter ${\mathrm{Xe}}^{135}$ grew from the ${\mathrm{I}}^{135}$ as a known function of time, reaching a maximum value of about 5×${10}^{15}$ atoms of ${\mathrm{Xe}}^{135}$ 11.3 hours after the ${\mathrm{I}}^{135}$ begins to decay. In the absolute assay of sample strengths, absolute $\beta$ counting of pure ${\mathrm{I}}^{135}$ samples, and $\beta -\gamma$ coincidence counting of pure ${\mathrm{Xe}}^{135}$ samples served as primary standards. Hard gamma rays from ${\mathrm{I}}^{135}$ served as a secondary standard. The total cross section of one entire sample of Xe was of the order of 1.5 square millimeters. The transmission of the sample was measured during the period of growth and decay of the Xe. The radioactive sample was placed inside the shield of the ORNL graphite reactor. A thermal beam of neutrons from the reactor was allowed to pass longitudinally through the sample along the axis of the capillary tube onto the quartz crystal spectrometer. The desired energies were selected by use of the Bragg reflection law, $\lambda =2dsin\theta$. A resonance in the cross section of ${\mathrm{Xe}}^{135}$ was discovered at 0.085 ev. The total cross section measurements were fitted to the single-level Breit-Wigner formula equally well with the following two sets of parameters: $g=\frac{3}{8}$, $E_0=0.0851\mathrm{}\pm 0.0011$ ev, ${{\Gamma }_n}^0=0.0305\mathrm{}\pm 0.0008$ ev, ${\Gamma }_{\gamma }=0.0828\mathrm{}\pm 0.0031$ ev; $g=\frac{5}{8}$, $E_0=0.0849\mathrm{}\pm 0.0010$ ev, ${{\Gamma }_n}^0=0.0182\mathrm{}\pm 0.0005$ ev, ${\Gamma }_{\gamma }=0.0942\mathrm{}\pm 0.0032$ ev. $E_0$ is the resonance energy, ${{\Gamma }_n}^0$ is the neutron width at resonance, ${\Gamma }_{\gamma }$ is the gamma ray width of the level, and $g$ is the statistical weight factor. The factor $g$ has two possible values because the spin of the compound state is not known. The capture cross section at resonance for state with $g=\frac{5}{8}$ is 55% of the theoretical maximum possible, and the corresponding capture cross section for the state with $g=\frac{3}{8}$ is 80% of the theoretical maximum value.