  We derive the separate helicity amplitudes involving the partial wave
analysis in the process of pseudo-scalar meson photon productions with
$J^P=3/2^+$, which is independent on model. According to parity, the general
amplitude in the case of $J^P=1/2^-$ is given out. We prove this general
amplitude is corresponding to the situation of $\lambda=-1$ as adopting the
circular polarization. Finally, the formulas of scattering amplitudes involving
the photon-meson production with $J^P=3/2^+$ are obtained from the chiral quark
model.
