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We derive the equations to calculate the reduced width amplitudes (RWA) ofthe different size clusters and deformed clusters without any approximation.These equations named Laplace expansion method are applicable to the nuclearmodels which uses the Gaussian wave packets. The advantage of the method isdemonstrated by the numerical calculations of the ${}^{16}{\rm O}+\alpha$ and${}^{24}{\rm Mg}+\alpha$ RWAs in $^{20}{\rm Ne}$ and $^{28}{\rm Si}$.

Laplace expansion method for the calculation of the reduced width amplitudes