National Superconducting
Cyclotron Laboratory

A Novel Many-Body Method for Open-Shell Nuclei

by H. Hergert

The vast majority of isotopes in nature are open-shell nuclei. Approaches like the interacting nuclear Shell Model or Density Functional Theory can be used to calculate the properties of such nuclei, but they usually rely on phenomenological interactions that are fit to data. Progress has been made to construct Shell Model interactions that are more firmly rooted in Quantum Chromodynamics [1, 2], but the method's factorial computational scaling makes calculations for many nuclei of interest infeasible, especially for neutron-rich isotopes.

The Multi-Reference In-Medium Similarity Renormalization Group (MR-IM-SRG) allows us to address this limitation by combining a polynomial computational scaling with the capability to use arbitrary correlated many-body bases that efficiently incorporate nuclear pairing, deformation, etc.

The MR-IM-SRG is an ideal tool to study the evolution of nuclear structure properties along isotopic chains. The exotic neutron-rich nuclei in these chains are particularly suited to study the interplay of NN and 3N interactions, as well as a many-body effects. In Ref. [1], we have used the MR-IM-SRG (along with other methods) to study the oxygen isotopic chain in the most consistent way to date (Figure 1). Chiral 3N interactions are crucial to properly describe the location of the neutron drip line at ${}^{24}$O, the heaviest bound oxygen isotope observed in nature.

Thanks to the MR-IM-SRG's numerical efficiency, we can extend our first-principles calculations to heavier nuclei, like the calcium and nickel isotopes [2].  While then-current chiral interactions overestimate the absolute binding energy of these isotopes, relative quantities like the calcium two-neutron separation energies agree well with experimental data (Figure 2). These results confirm the magicity of ${}^{52}$Ca and ${}^{54}$Ca, and again, chiral 3N forces are crucial for a proper description. The flat separation-energy beyond ${}^{54}$Ca  has prevented us from identifying the calcium neutron drip line conclusively. It illustrates the delicate interplay between nuclear interactions and many-body effects in these nuclei, and suggests that forthcoming experimental data will provide strong constraints for theory.

[1]    S. K. Bogner, H. Hergert, J. D. Holt, A. Schwenk, S. Binder, A. Calci, J. Langhammer, and R. Roth, Phys. Rev. Lett. 113, 142501 (2014)
[2]    G. R. Jansen, J. Engel, G. Hagen, P. Navrátil, A. Signoracci, Phys. Rev. Lett. 113, 142502 (2014)
[3]    H. Hergert, S. Binder, A. Calci, J. Langhammer, and R. Roth,  Phys. Rev. Lett. 110, 242501 (2013)
[4]    H. Hergert, S. K. Bogner, T. D. Morris, S. Binder, A. Calci, J. Langhammer, and R. Roth, Phys. Rev. C 90, 041302 (2014)

Ground-state energies of the oxygen isotopes, calculated in MR-IM-SRG and other
many-body approaches, using chiral NN+3N forces as input. Black bars indicated
experimental values. See Ref. [4] for further details.

Two-neutron separation energies of calcium isotopes for chiral NN+3N forces with
different cutoffs (shaded bands). Black bars indicate experimental values. See Ref. [5] for
further details.