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Register a new userTowards an ab initio covariant density functional for nuclear structure
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Nuclear structure models built from phenomenological mean fields, the effective nucleon-nucleon interactions (or Lagrangians), and the realistic bare nucleon-nucleon interactions are reviewed. The success of covariant density functional theory (CDFT) to describe nuclear properties and its influence on Brueckner theory within the relativistic framework are focused upon. The challenges and ambiguities of predictions for unstable nuclei without data or for high-density nuclear matter, arising from relativistic density functionals, are discussed. The basic ideas in building an ab initio relativistic density functional for nuclear structure from ab initio calculations with realistic nucleon-nucleon interactions for both nuclear matter and finite nuclei are presented. The current status of fully self-consistent relativistic Brueckner-Hartree-Fock (RBHF) calculations for finite nuclei or neutron drops (ideal systems composed of a finite number of neutrons and confined within an external field) is reviewed. The guidance and perspectives towards an ab initio covariant density functional theory for nuclear structure derived from the RBHF results are provided.
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The extension of ab initio quantum many-body theory to higher accuracy and larger systems is intrinsically limited by the handling of large data objects in form of wave-function expansions and/or many-body operators. In this work we present matrix factorization techniques as a systematically improvable and robust tool to significantly reduce the computational cost in many-body applications at the price of introducing a moderate decomposition error. We demonstrate the power of this approach for the nuclear two-body systems, for many-body perturbation theory calculations of symmetric nuclear matter, and for non-perturbative in-medium similarity renormalization group simulations of finite nuclei. Establishing low-rank expansions of chiral nuclear interactions offers possibilities to reformulate many-body methods in ways that take advantage of tensor factorization strategies.
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.
The neutron and proton drip lines represent the limits of the nuclear landscape. While the proton drip line is measured experimentally up to rather high $Z$-values, the location of the neutron drip line for absolute majority of elements is based on theoretical predictions which involve extreme extrapolations. The first ever systematic investigation of the location of the proton and neutron drip lines in the covariant density functional theory has been performed by employing a set of the state-of-the-art parametrizations. Calculated theoretical uncertainties in the position of two-neutron drip line are compared with those obtained in non-relativistic DFT calculations. Shell effects drastically affect the shape of two-neutron drip line. In particular, model uncertainties in the definition of two-neutron drip line at $Zsim 54, N=126$ and $Zsim 82, N=184$ are very small due to the impact of spherical shell closures at N=126 and 184.
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.
The three-dimensional tilted axis cranking covariant density functional theory (3D-TAC CDFT) is used to study the chiral modes in $^{135}$Nd. By modeling the motion of the nucleus in rotating mean field as the interplay between the single-particle motions of several valence particle(s) and hole(s) and the collective motion of a core-like part, a classical Routhian is extracted. This classical Routhian gives qualitative agreement with the 3D-TAC CDFT result for the critical frequency corresponding to the transition from planar to aplanar rotation. Based on this investigation a possible understanding of tilted rotation appearing in a microscopic theory is provided.
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