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Abstract

We investigate the effects of different basis model spaces on the calculation of reduced width amplitude (RWA) and asymptotic normalization coefficient (ANC) for the $^{7}$Li and $^{7}$Be nuclei. The two-cluster model ($\alpha+t/^3$He) and three-cluster model ($\alpha+d+n/p$) with the generator coordinates method (GCM) are applied to calculate the wave function of $^7$Li and $^7$Be. Specifically, the model space for the three-cluster model is constructed upon a sufficiently broad space of two-cluster configuration bases by further including three-cluster configuration bases. We compare the impact on the results from two basis sets for these added three-cluster bases: one with a compact and one with a broad spatial distribution. The final results reveal that the two-cluster model cannot accurately reproduce the binding energies of $^7$Li and $^7$Be, and tends to overestimate their ANCs. Regarding the calculations with the three-cluster model, while the two basis sets do not give significant differences in energy or energy spectrum, the basis set with a compact model space fails to describe the asymptotic behavior of the RWA adequately. This introduces excessive uncertainty into the ANC calculation. In the end, we conclude that when calculating ANC via a microscopic framework, particular attention must be paid to ensuring sufficient model space, especially for the components describing the breakup channels. This approach provides ANC values for $^7$Li and $^7$Be that agree well with experimental results.