Effect of Compression on the Decay Rate ofTc99mMetal

Abstract

Motivated by Bainbridge's measurement, we have attempted a theoretical calculation of the change in lifetime of the internal conversion of ${\mathrm{Tc}}^{99m}$ in compressed Tc metal. We have employed the Thomas-Fermi statistical potential, corrected for the self-potential of the electron in question, to obtain the initial and final state electronic wave functions for two volumes: the normal uncompressed state, and ten percent compression. Because the energy available is so low (\ensuremath{\sim}2 kev), the only contributions to the internal conversion coefficient come from the $M$ and higher shells, and mainly from the $3p$ and $3d$ levels. The principal contribution to the change in the internal conversion coefficient comes, however, from the valence electrons, particularly the $4p$, $4d$ and $5s$ levels. In order to relate compression to pressure, we have estimated the compressibility of technetium metal to be 0.27 ${\mathrm{megabar}}^{\ensuremath{-}1}$. From this compressibility and the assumption that the internal conversion coefficient is linear in pressure, we calculate for the experimental pressure of 0.1 megabar a fractional decrease in lifetime of (2 to 4)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$, the quoted variation residing in the uncertainty of the structure of the $4p$ band. This result agrees with Bainbridge's measurement, (2.3\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$, within the accuracy of our calculation.