Laplace expansion method for the calculation of the reduced width amplitudes

We derive the equations to calculate the reduced width amplitudes (RWA) of the different size clusters and deformed clusters without any approximation. These equations named Laplace expansion method are applicable to the nuclear models which uses the Gaussian wave packets. The advantage of the method is demonstrated by the numerical calculations of the ${}^{16}\mathrm{O}+\alpha$ and ${}^{24}\mathrm{M}\mathrm{g}+\alpha$ RWAs in ${}^{20}\mathrm{N}\mathrm{e}$ and ${}^{28}\mathrm{S}\mathrm{i}$.