# Pump-Induced Biphasic Relaxation Model of Xe Spin in Nuclear Magnetic Resonance Gyroscopes

## TL;DR

This paper introduces a new model to describe how the spin relaxation rate of xenon isotopes in NMR gyroscopes depends on pump power.

## Contribution

The novel PBR model explains the biphasic relaxation of Xe nuclear spin with high accuracy across varying pump power.

## Key findings

- The PBR model shows a quadratic dependence between Γ and PRb with high fitting accuracy (R2 = 0.9969).
- Linear and hyperbolic regimes of Γ versus pump power are experimentally confirmed with high R2 values.
- The model's predictions align with measurements, with an average relative deviation of 0.2169%.

## Abstract

The spin relaxation rate of Xe isotopes is a key characteristic of nuclear magnetic resonance gyroscopes (NMRGs). A pump-induced biphasic relaxation (PBR) model is proposed to describe the pump dependence of the transverse relaxation rate of 129Xe nuclear spin. The distribution of electron polarization is theoretically analyzed based on the Bloch–Torrey equations and the volume-averaged polarization is evaluated through NMR frequency shift measurements. Experimental results confirm the theoretical quadratic dependence between Γ and PRb with a high fitting accuracy (R2 = 0.9969). The predicted linear (R2 > 0.9966) and hyperbolic (R2 > 0.9942) regimes of Γ versus pump power are also observed. Validation across different pump power conditions shows agreement between the model and measurements, with an average relative deviation of 0.2169%. The multi-stage process of nuclear spin relaxation is quantified, thereby providing a robust validation for the PBR model.