# On the nature of the Mossbauer effect

## TL;DR

This paper investigates the quantum emission spectrum of an oscillator in a potential well, highlighting the effects of recoil and phonon interactions on emission lines, with implications for gamma-ray processes in crystals.

## Contribution

It introduces a quantum model accounting for recoil effects and phonon interactions in the Mossbauer effect, extending understanding of emission line behavior in crystal structures.

## Key findings

- Maximum emission intensity occurs when recoil energy matches low-frequency quantum energy.
- Phonon spectrum causes a decrease in emission and absorption line amplitudes.
- Relaxation times of low-frequency oscillations do not affect high-frequency photon emission features.

## Abstract

The spectrum of electromagnetic waves emitted by an oscillator trapped in an external potential well is studied. It is assumed that the natural frequency of the oscillator is much greater than the frequency of oscillations in the potential well. We consider the quantum model of emission with regard to the recoil effect. The highest intensity of the absorption and emission lines is observed on the natural frequency of the oscillator when the recoil energy is equal to the energy of the quantum of low-frequency (LF) oscillations in the potential well. A certain decrease in the amplitude of the emission and absorption lines is noted caused by the oscillations of the potential well due to, for example, the presence of the phonon spectrum. The relaxation times of the oscillator LF motion in the potential well, resulted from the phonon emission, are estimated. It is concluded that these processes have no influence on the observed features of the emission and absorption of high-frequency photons. This model can be applied to description of the emission and absorption of gamma rays in the crystal structures even in the presence of the phonon spectrum on condition that the relaxation time of the LF movements in the potential well is greater than the lifetime of the HF oscillator.