The exponential growth of the model space often hinders accurate configuration interaction shell model (CISM) calculations for nuclear structure. To address this, we develop an adaptive CISM (ACISM) approach, adapted from the adaptive configuration interaction (ACI) approach used in quantum chemistry. We first apply ACISM to ground-state calculations of $sd$- and $pf$-shell nuclei. The results show that the ground-state energy converges controllably to the full CISM results as the truncation parameter $\sigma$ is decreased. Furthermore, $\mathit{pf}$-shell calculations demonstrate that ACISM can reduce the model space by at least two orders of magnitude while maintaining energy errors within a few hundred keV, highlighting the method's potential for large-scale model-space computations. The systematic dependence on $\sigma$ enables reliable extrapolation toward the full CISM limit. Then, using a state-specific, orthogonality-constrained extension of ACISM, we obtain a stable low-lying spectrum for ${}^{52}\mathrm{Fe}$ across a wide range of $\sigma$. Our results demonstrate robust spectral convergence even when the model-space dimension is truncated by approximately two orders of magnitude. Finally, the calculations of the expectation value of the square of total angular momentum of eigenstates indicate that ACISM exhibits a relatively small degree of breaking of angular momentum symmetry.

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• Binding energy & masses
• Energy levels
• Nuclear structure & decays
• Nuclear many-body theory
• Shell model