Verification of I-131 Yield from the Neutron Irradiation of Tellurium

Radioactive isotopes of iodine have many uses in modern medicine due to the thyroid gland's affinity for iodine. The University of Missouri Research Reactor (MURR) plans to begin commercial production of iodine-131 (I-131) via the neutron irradiation of tellurium-130 (Te-130) and the subsequent beta decays of the products of the neutron absorption reaction, Te-131 and Te-131m. However, various discrepancies in literature and nuclear databases regarding a range of system parameters have convoluted the expected I-131 yield. In this work, a model constructed by integrating a system of one-group, nuclide-activation, differential rate equations to acquire analytical solutions to the number of atoms of each nuclide during activation formulated a more accurate calculation of the I-131 yield. To obtain the integrated result, the model linearized the equations in matrix form via the Laplace transform before solving them by employing Gaussian elimination. Cauchy's residue theorem was finally applied to this result to acquire the inverse Laplace transforms. These symbolic analytical solutions were left as functions of the user's desired parameters and formed a non-linear regression problem between the model's equations and experimental data provided by MURR, which the Gauss-Newton method determined the best-fit parameters for in a Monte Carlo analysis. A functional estimate for the thermal Te-130 neutron absorption cross-section was determined to be approximately 0.127 ± 0.007 barns for a 170.7 g natural tellurium target. The fractional yield of Te-131 resulting from the neutron absorption of Te-130 followed a normal distribution with a mean and standard deviation of 0.960 ± 0.003. These best fit parameters and the model were then validated against additional experimental data provided by MURR. Finally, the optimal cooling time of the sample to acquire the maximum I-131 activity did not exceed 3.87 ± 0.02 hours.