Cross sections of electron excitation of atomic nuclei in plasma

Abstract

Within the frameworks of the nonrelativistic plane wave Born approximation (PWBA), the analytical formulas for cross sections of $E1$--$E3$ and $M1$--$M2$ excitation of nuclei to the low-energy isomeric state as a result of inelastic scattering of nonrelativistic electrons are derived in the present work. The PWBA cross section of $E1$ excitation of isomer ${}^{181}{\text{Ta}}^{m}$ (9/2${}^{\ensuremath{-}}$, 6.237 keV) by electrons appeared to be two orders less than that one used in a number of works for calculation of isomeric nuclei yield under exposure of ${}^{181}$Ta-target hot dense laser plasma. To test the PWBA method we have calculated excitation cross sections of the nuclei ${}^{181}$Ta, ${}^{110}$Ag, ${}^{169}$Tm, and ${}^{201}$Hg in a relativistic version of the Hartree-Fock-Slater method. It was established that the PWBA method overestimates $E1$ cross sections and underestimates $E2$ and $M1$ cross sections.