Background: The no-core shell model (NCSM) is an ab initio method that solves the nuclear many-body problem by expanding the many-particle wave function into a (typically) harmonic oscillator basis and minimizing the energy to obtain the expansion coefficients. Extensions of the NCSM, such as its coupling with microscopic-cluster basis states, further allow for an ab initio treatment of light-ion nuclear reactions of interest for both astrophysics and nuclear technology applications. A downside of the method is the exponential scaling of the basis size with increasing number of nucleons and excitation quanta, which limits its applicability to mass $A\lesssim 16$ nuclei, except for variants where the basis is further down-selected via some truncation scheme.

Purpose: We consider a basis selection method for the NCSM that was first introduced in the context of the large-scale shell model and captures the essential degrees of freedom of the nuclear wave function leading to a favorable complexity scaling for calculations and enabling ab initio reaction calculations in $sd$-shell nuclei.

Methods: The particle configurations within the NCSM basis are ordered based on their contribution to the first moment of the Hamiltonian matrix that results from the projection onto the many-body basis. The truncation scheme then consists in retaining only the lowest-first-moment configurations, which typically contain only few many-body basis states (Slater determinants). As the energy threshold above which configurations are disregarded is increased, the size of the basis becomes an almost-continuous variable, allowing for tunable fidelity in the obtained wave functions. The resulting wave functions can then be used directly in ab initio reaction calculations.

Results: We present calculations for ${}^7\mathrm{Li}$ and $n+{}^{12}\mathrm{C}$ scattering using nucleon-nucleon interactions derived from chiral effective field theory and softened using the similarity renormalization group method. The obtained energy levels invariably demonstrate exponential convergence with the size of the basis, and we find improved convergence in scattering calculations. To demonstrate the possibilities enabled by the approach, we also present a first calculation for the scattering of neutrons from ${}^{24}\mathrm{Mg}$.

Conclusions: The method presented in this work appears promising for future studies of nuclei with mass $A>16$, opening multiple future research directions impacting both nuclear astrophysics and nuclear technology applications.

• Received 4 February 2024
• Accepted 17 April 2024

DOI:https://doi.org/10.1103/PhysRevC.109.054603