The Coherent-Path Approach to Forward Scattering of Recoil-Free Resonant Gamma Radiation

Abstract

A coherent-path approach is developed to describe nuclear-resonant gamma-ray transmission through nuclear-resonant matter. The solution is based on mathematical techniques, developed by Heitler and Harris, using time-dependent perturbation theory in the frequency domain. The nuclear-resonant absorber is modeled as a one-dimensional chain of N “effective” nuclei. A closed-form solution is obtained for the forward scattering of recoil-free radiation. The solution is given as a finite sum over N + 1 indistinguishable coherent paths the radiation takes going from the radioactive source through the absorber to the detector. The solution agrees numerically with the well-established theories although it has a completely different form. The major features of the time-differential Mössbauer spectroscopic result, namely the “speed-up” and “dynamical beat” effects, are easily explained in terms of the interference between the different contributing amplitudes. The model is so physically transparent that extension to other situations, e.g. synchrotron radiation, the “gamma-echo” effect, and incoherent processes, is not difficult.