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Register a new userEmergent Sp(3,R) dynamical symmetry in the nuclear many-body system from an ab initio description
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Ab initio nuclear theory provides not only a microscopic framework for quantitative description of the nuclear many-body system, but also a foundation for deeper understanding of emergent collective correlations. A symplectic Sp(3,R)$supset$U(3) dynamical symmetry is identified in ab initio predictions, from a no-core configuration interaction approach, and found to provide a qualitative understanding of the spectrum of 7Be. Low-lying states form an Elliott SU(3) spectrum, while an Sp(3,R) excitation gives rise to an excited rotational band with strong quadrupole connections to the ground state band.
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Starting from realistic nuclear forces, the chiral N$^3$LO and JISP16, we have applied many-body perturbation theory (MBPT) to the structure of closed-shell nuclei, $^4$He and $^{16}$O. The two-body N$^3$LO interaction is softened by a similarity renormalization group transformation while JISP16 is adopted without renormalization. The MBPT calculations are performed within the Hartree-Fock (HF) bases. The angular momentum coupled scheme is used, which can reduce the computational task. Corrections up to the third order in energy and up to the second order in radius are evaluated. Higher-order corrections in the HF basis are small relative to the leading-order perturbative result. Using the anti-symmetrized Goldstone diagram expansions of the wave function, we directly correct the one-body density for the calculation of the radius, rather than calculate corrections to the occupation propabilities of single-particle orbits as found in other treatments. We compare our results with other methods where available and find good agreement. This supports the conclusion that our methods produce reasonably converged results with these interactions. We also compare our results with experimental data.
In this work we present the first steps towards benchmarking isospin symmetry breaking in ab initio nuclear theory for calculations of superallowed Fermi $beta$-decay. Using the valence-space in-medium similarity renormalization group, we calculate b and c coefficients of the isobaric multiplet mass equation, starting from two different Hamiltonians constructed from chiral effective field theory. We compare results to experimental measurements for all T=1 isobaric analogue triplets of relevance to superallowed $beta$-decay for masses A=10 to A=74 and find an overall agreement within approximately 250 keV of experimental data for both b and c coefficients. A greater level of accuracy, however, is obtained by a phenomenological Skyrme interaction or a classical charged-sphere estimate. Finally, we show that evolution of the valence-space operator does not meaningfully improve the quality of the coefficients with respect to experimental data, which indicates that higher-order many-body effects are likely not responsible for the observed discrepancies.
Background: The nuclear kinetic density is one of many fundamental quantities in density functional theory (DFT) dependent on the nonlocal nuclear density. Often, approximations may be made when computing the density that may result in spurious contributions in other DFT quantities. With the ability to compute the nonlocal nuclear density from ab initio wave functions, it is now possible to estimate effects of such spurious contributions. Purpose: We derive the kinetic density using ab initio nonlocal scalar one-body nuclear densities computed within the no-core shell model (NCSM) approach, utilizing two- and three-nucleon chiral interactions as the sole input. With the ability to compute translationally invariant nonlocal densities, it is possible to directly gauge the impact of the spurious center-of-mass (COM) contributions in DFT quantities such as the kinetic density. Methods: The nonlocal nuclear densities are derived from the NCSM one-body densities calculated in second quantization. We present a review of COM contaminated and translationally invariant nuclear densities. We then derive an analytic expression for the kinetic density using these nonlocal densities, producing an ab initio kinetic density. Results: The ground state nonlocal densities of textsuperscript{4,6,8}He, textsuperscript{12}C, and textsuperscript{16}O are used to compute the kinetic densities of the aforementioned nuclei. The impact of the COM removal technique in the densities is discussed. The results of this work can be extended to other fundamental quantities in DFT. Conclusions: The use of a general nonlocal density allows for the calculation of fundamental quantities taken as input in theories such as DFT. This allows benchmarking of procedures for COM removal in different many-body techniques.
We propose a new Monte Carlo method called the pinhole trace algorithm for {it ab initio} calculations of the thermodynamics of nuclear systems. For typical simulations of interest, the computational speedup relative to conventional grand-canonical ensemble calculations can be as large as a factor of one thousand. Using a leading-order effective interaction that reproduces the properties of many atomic nuclei and neutron matter to a few percent accuracy, we determine the location of the critical point and the liquid-vapor coexistence line for symmetric nuclear matter with equal numbers of protons and neutrons. We also present the first {it ab initio} study of the density and temperature dependence of nuclear clustering.
Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. This endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. This paper reviews some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLO$_{rm sat}$ is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to $^{56}$Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon-nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. The coupling to the continuum impacts the energies of the $J^pi = {1/2}^-,{3/2}^-,{7/2}^-,{3/2}^+$ states in $^{17,23,25}$O, and - contrary to naive shell-model expectations - the level ordering of the $J^pi = {3/2}^+,{5/2}^+,{9/2}^+$ states in $^{53,55,61}$Ca.
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