Abstract
We improved the accuracy of calculating the exchange \ensuremath{\alpha}-nucleus real potential by suggesting a simple expression for the nondiagonal density matrix of \ensuremath{\alpha}-particle ${{\ensuremath{\rho}}_{\ensuremath{\alpha}}(\stackrel{\ensuremath{\rightarrow}}{r},{r}^{\ensuremath{'}})}.$ We found that this expression reduces the error in calculating the total \ensuremath{\alpha}-nucleus potential by more than 20% compared with using the density matrix expansion method to treat ${\ensuremath{\rho}}_{\ensuremath{\alpha}}(\stackrel{\ensuremath{\rightarrow}}{r},{r}^{\ensuremath{'}}).$
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