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 + 1 /3 + 1 inversion problem in 22 Na and 46 V. This approach extends the reach of ab initio nuclear structure calculations to essentially all light-and medium-mass nuclei.The development of a first-principles, or ab initio, theoretical description of atomic nuclei is a central challenge in nuclear physics. This task is complicated by the combined difficulties of not having an exact form for nuclear interactions and the great complexity in solving the nuclear many-body problem. Regardless, controlled predictions with uncertainty estimates are vital to guide efforts of rare-isotope beam facilities [1,2], to constrain nucleosynthesis models predicting the origin of heavy elements in the universe [3,4], and to quantify nuclear structure effects in searches for beyond-standard-model physics such as neutrinoless double-beta decay [5], dark matter [6,7], and superallowed beta decay [8]. Developments in chiral effective field theory [9, 10], similarity renormalization group (SRG) [11], and ab initio many-body techniques [12][13][14][15][16][17] provide a unified picture for these efforts, while three-nucleon (3N) forces have emerged as an essential component of nuclear forces [2,[18][19][20][21][22][23][24][25][26][27][28][29].One promising approach to the many-body problem is offered by the shell-model paradigm, where a valencespace Hamiltonian of tractable dimension is decoupled from the much larger Hilbert space and diagonalized. This allows the treatment of excited states, deformation, and transitions in open-shell systems within a single framework. Building upon earlier perturbative approaches [30][31][32], ab initio methods now provide shellmodel Hamiltonians in a nonperturbative manner [33][34][35][36][37][38][39], similar to recent work for chemical systems, see e.g., [40]. However, the inclusion of residual 3N forces [41] among valence particles [42,43] remains problematic in nonperturbative methods and leads to a loss in accuracy compared to large-space ab initio calculations [38].A first attempt to address this shortcoming within the in-medium similarity renormalization group (IM-SRG) framework [38] used normal ordering with respect to closed sub-shells in the valence space, but gave no clear prescription for sys...

In-medium similarity renormalization group for closed and open-shell nuclei

“…A new refinement of the targeted normal ordering procedure was presented in Ref. [198], improving once again the agreement between IMSRG+SM and large-scale MR-IMSRG calculations.…”

Effective proton-neutron interaction near the drip line from unbound states in F25,26

“…In this work, we extend this approach to the ensemble normal-ordering procedure outlined in Ref. [24], which accurately accounts for 3N forces between valence particles and reproduces results of large-space ab initio methods in all cases where those methods are reliable. In all reported results, we use the same initial NN and 3N Hamiltonians as in Ref.…”

“…As in Ref. [9], we choose USDA instead of USDB, since the latter is known to predict a too small excitation energy of the J π = 4 + state in 26 F. Valence-space IM-SRG has been shown to predict ground and excited states throughout the oxygen, fluorine, and neon isotopic chains [22][23][24]33]. Starting from nuclear forces derived from chiral effective field theory (EFT) [34,35], 3N forces between core and valence nucleons are typically captured by normal ordering with respect to the 16 O reference.…”

“…[3], the weakly bound 26 F is one of the few ideal nuclei where we can study the impact of continuum effects on Int(J ). Lying close to the doubly magic 24 O [10][11][12], whose first excited states lie above 4 MeV [10,12], low-energy states in 26 F are, in the IPSM picture, expected to arise from the coupling of a deeply bound π 0d 5/2 proton (S p ( 25 F) = 14.43 (14) MeV [13]) with an unbound ν0d 3/2 neutron (S n ( 25 O) = −749(10) keV [14][15][16]). This (π 0d 5/2 ) 1 (ν0d 3/2 ) 1 coupling results in a J π = 1 1 + − 4 1 + multiplet.…”

“…III: The phenomenological shell model, which implicitly contains some aspects of continuum physics and three-nucleon (3N ) forces, and the ab initio valence-space inmedium similarity renormalization group (IM-SRG) [21][22][23][24] based on two-nucleon (NN) and 3N forces, but neglecting the influence of the continuum.…”