Abstract
We studied a resonance-based method using polarized $^3$He to probe its interaction with nonpolarized matter and improve the experimental sensitivity of the spin-velocity-dependent interaction mediated by axion-like particles. For the first time, the analytical solution of the Bloch equation was obtained by the perturbation method. In the Bloch equation, the driving term of the effective magnetic field is regarded as a perturbation, and the amplification of the effective magnetic field in resonance is calculated. When the effect of glass cell parameters on the magnetic field amplification is analyzed, optimized special glass cells of radius 1$-$2 mm can achieve a factor of $10^6$ in magnetic field amplification. Relying on our on-site facility and techniques for glass cells, the sensitivity of the previous experiment can be improved by five orders of magnitude.
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