Two-photon inner-shell transitions in molybdenum

The two-photon x-ray emission spectra of inner-shell transitions in metallic Mo have been studied using large-area energy-dispersive Si(Li) detectors and fast, computer-controlled, time-coincidence electronics. The discrete energy-summation spectrum displays a peak at 17.1 keV corresponding to the expected 2s→1s transition, as well as a second, more intense peak at 19.7 keV. Based upon very recent analytical H-atom calculations by Florescu, this latter peak is tentatively identified as due primarily to 3d→1s transitions. The continuous two-photon spectrum has also been measured on an absolute intensity scale and compared with a frozen-orbital calculation based upon direct summation of the second-order perturbation expansion for the relevant matrix elements. For the 2s→1s transition, excellent quantitative agreement is found using the self-consistent-field Hartree-Fock wave functions of Clementi and Roetti. The same calculation predicts that the 3s→1s transition is of negligible relative amplitude. Because the calculational method is inapplicable to d states, a simple closure approximation is developed which is found to be reasonably good for both the $2s$ and $3s$ two-photon transitions, but apparently fails for the $3d$ transition since it predicts a result which is relatively much too small. Our data are the first for inner-shell transitions and it is anticipated that further developments in both instrumentation and in theory will yield a new, rich, multiphoton inner-shell spectroscopy.