A nucleus-dependent valence-space approach to nuclear structure

Abstract

We present a nucleus-dependent valence-space approach for calculating ground and excited states of nuclei, which generalizes the shell-model in-medium similarity renormalization group to an ensemble reference with fractionally filled orbitals. Because the ensemble is used only as a reference, and not to represent physical states, no symmetry restoration is required. This allows us to capture 3N forces among valence nucleons with a valence-space Hamiltonian specifically targeted to each nucleus of interest. Predicted ground-state energies from carbon through nickel agree with results of other large-space ab initio methods, generally to the 1\% level. In addition, we show that this new approach is required in order to obtain convergence for nuclei in the upper $p$ and $sd$ shells. Finally, we address the $1^{+}$/$3^{+}$ ground-state inversion problem in ${}^{22}\text{Na}$ and ${}^{46}\text{V}$. This approach extends the reach of ab initio nuclear structure calculations to essentially all light- and medium-mass nuclei.

6 pages, 5 figures

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• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Similarity Renormalization Group for Nucleon-Nucleon Interactions
• Local three-nucleon interaction from chiral effective field theory
• Evolution of shell structure in neutron-rich calcium isotopes
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• In-Medium Similarity Renormalization Group for Open-Shell Nuclei
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• Ab Initio Multi-Reference In-Medium Similarity Renormalization Group Calculations of Even Calcium and Nickel Isotopes
• Correlated density-dependent chiral forces for infinite matter calculations within the Green's function approach
• Three-nucleon forces and spectroscopy of neutron-rich calcium isotopes
• In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei
• Ab-initio shell model with a core
• Ab initio effective interactions for sd-shell valence nucleons

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• Precision mass measurements of magnesium isotopes and implications on the validity of the Isobaric Mass Multiplet Equation
• Spectroscopy of ${}^{50}$Sc and ab initio calculations of $B(M3)$ strengths
• Toward a systematic strategy for defining power counting in the construction of the energy density functional theory
• High-precision $Q_{EC}$-value measurement of the superallowed ${\beta }^{+}$ emitter ${}^{22}$Mg and an evaluation of the $A=22$ isobaric triplet