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Electromagnetic Sum Rules and Response Functions from the Symmetry-Adapted No-Core Shell Model

Recent developments in ab initio nuclear structure have provided us with a variety of many-body methods capable of describing nuclei into the medium-mass region of the chart of nuclides. One of these, the symmetry-adapted no-core shell model (SA-NCSM), capitalizes on inherent symmetries of the nucleus and is uniquely suited to examine the underlying physics of dynamical quantities, such as the response function. We examine the applicability of the SA-NCSM to calculations of these quantities and assess the quality of its inputs by calculating electromagnetic sum rules and response functions with the Lanczos sum rule method and Lanczos response function method, respectively. Our systematic analysis of He shows good agreement in the sum rules between the SA-NCSM and hyperspherical harmonics, an exact method. We also detail a novel use of a projection technique to remove spurious center-of-mass contributions to our sum rules. Our calculations for the response functions of He, O, and Ne reveal the advantages of the SA-NCSM when examining giant resonances and we detail a straightforward procedure to calculate the compressibility of nuclear matter from only the microscopic calculations of these response functions. The results of this work illustrate the ability of the SA-NCSM to reliably and accurately calculate electromagnetic sum rules, as well as its usefulness in providing physically-informed interpretations of electromagnetic response functions. This suggests future work with the SA-NCSM could provide valuable insights, particularly for open-shell nuclei beyond the reach of other methods.