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We discuss the approximate inclusion of three-nucleon interactions into ab initio nuclear structure calculations using a multi-reference formulation of normal ordering and Wicks theorem. Following the successful application of single-reference normal ordering for the study of ground states of closed-shell nuclei, e.g., in coupled-cluster theory, multi-reference normal ordering opens a path to open-shell nuclei and excited states. Based on different multi-determinantal reference states we benchmark the truncation of the normal-ordered Hamiltonian at the two-body level in no-core shell-model calculations for p-shell nuclei, including 6-Li, 12-C, and 10-B. We find that this multi-reference normal-ordered two-body approximation is able to capture the effects of the 3N interaction with sufficient accuracy, both, for ground-state and excitation energies, at the computational cost of a two-body Hamiltonian. It is robust with respect to the choice of reference states and has a multitude of applications in ab initio nuclear structure calculations of open-shell nuclei and their excitations as well as in nuclear reaction studies.
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We extend the ab initio coupled-cluster effective interaction (CCEI) method to deformed open-shell nuclei with protons and neutrons in the valence space, and compute binding energies and excited states of isotopes of neon and magnesium. We employ a nucleon-nucleon and three-nucleon interaction from chiral effective field theory evolved to a lower cutoff via a similarity renormalization group transformation. We find good agreement with experiment for binding energies and spectra, while charge radii of neon isotopes are underestimated. For the deformed nuclei $^{20}$Ne and $^{24}$Mg we reproduce rotational bands and electric quadrupole transitions within uncertainties estimated from an effective field theory for deformed nuclei, thereby demonstrating that collective phenomena in $sd$-shell nuclei emerge from complex ab initio calculations.
We introduce a hybrid many-body approach that combines the flexibility of the No-Core Shell Model (NCSM) with the efficiency of Multi-Configurational Perturbation Theory (MCPT) to compute ground- and excited-state energies in arbitrary open-shell nuclei in large model spaces. The NCSM in small model spaces is used to define a multi-determinantal reference state that contains the most important multi-particle multi-hole correlations and a subsequent second-order MCPT correction is used to capture additional correlation effects from a large model space. We apply this new ab initio approach for the calculation of ground-state and excitation energies of even and odd-mass carbon, oxygen, and fluorine isotopes and compare to large-scale NCSM calculations that are computationally much more expensive.
We present an approach to derive effective shell-model interactions from microscopic nuclear forces. The similarity-transformed coupled-cluster Hamiltonian decouples the single-reference state of a closed-shell nucleus and provides us with a core for the shell model. We use a second similarity transformation to decouple a shell-model space from the excluded space. We show that the three-body terms induced by both similarity transformations are crucial for an accurate computation of ground and excited states. As a proof of principle we use a nucleon-nucleon interaction from chiral effective field theory, employ a $^4$He core, and compute low-lying states of $^{6-8}$He and $^{6-8}$Li in $p$-shell model spaces. Our results agree with benchmarks from full configuration interaction.
Generalized seniority provides a truncation scheme for the nuclear shell model, based on pairing correlations, which offers the possibility of dramatically reducing the dimensionality of the nuclear shell-model problem. Systematic comparisons against results obtained in the full shell-model space are required to assess the viability of this scheme. Here, we extend recent generalized seniority calculations for semimagic nuclei, the Ca isotopes, to open-shell nuclei, with both valence protons and valence neutrons. The even-mass Ti and Cr isotopes are treated in a full major shell and with realistic interactions, in the generalized seniority scheme with one broken proton pair and one broken neutron pair. Results for level energies, orbital occupations, and electromagnetic observables are compared with those obtained in the full shell-model space. We demonstrate that, even for the Ti isotopes, significant benefit would be obtained in going beyond the approximation of one broken pair of each type, while the Cr isotopes require further broken pairs to provide even qualitative accuracy.
The physics of radioactive ion beams implies the description of weakly-bound nuclear systems. One key aspect concerns the coupling to low-lying collective-type excited states, which for these systems might not be stable levels, but particle emitting resonances. In this work we describe how the scattering cross section and compound spectra change when the colliding fragments have such collective excitations featuring particle emission. We explore this question in the framework of a multi-channel algebraic scattering method of determining nucleon-nucleus cross sections at low energies. For a range of light-mass, particle-unstable nuclear targets, scattering cross sections as well as the spectra of the compound nuclei formed have been determined from calculations that do and do not consider particle emission widths for nuclear states. Assuming a resonance character for target states markedly varies evaluated cross sections from those obtained assuming the target spectrum to have entirely discrete states.
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