On the Mössbauer Effect and the Rigid Recoil Question

Abstract

Various theories for the M\"ossbauer rigid-recoil effect, which enables a crystal to absorb momentum but not appreciable energy, are compared. These suggest that the recoil may not be instantaneous, and that the recoil time could be used to distinguish between them. An experiment is proposed to measure this time. The idea is to use a small sphere whose outer surface is coated with an electrically charged M\"ossbauer-active element, and then to measure the amount of energy lost due to Bremmsstrahlung during the recoil of this sphere when a M\"ossbauer event occurs. As the energy radiated is proportional to the square of the acceleration from Larmor's formula, the amount of energy so radiated varies inversely proportional to the recoil time, and proportional to the charge squared. Although this energy is quite small, it can in principle be measured with the extreme sensitivity available in M\"ossbauer experiments. It is found that the most information would be gained with more long-lived isomers such as Rhodium-103m as the M\"ossbauer agent, and that correction terms to Larmor's formula need to be considered due to the finite radius of a small particle, and some of these corrections are included in the paper. These corrections are taken from the extensive literature on radiating spherical shells which were developed to analyze the Abraham-Lorentz model for a classical charged particle. This problem is interesting because a perfectly rigid crystal seems to pose questions about relativity, and because the M\"ossbauer effect is a phenomenon where the solid-state environment dramatically influences the probability of a nuclear process. Moreover, if the experiment proposed can measure the recoil time, then such measurements might provide a new class of analytical methods for material science and chemistry.