Nuclear Theory

The goal of the present paper is twofold. First, a novel expansion many-body method applicable to superfluid open-shell nuclei, the so-called Bogoliubov in-medium similarity renormalization group (BIMSRG) theory, is formulated. This generalization of standard single-reference IMSRG theory for closed-shell systems parallels the recent extensions of coupled cluster, self-consistent Green's function or many-body perturbation theory. Within the realm of IMSRG theories, BIMSRG provides an interesting alternative to the already existing multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei. The algebraic equations for low-order approximations, i.e., BIMSRG(1) and BIMSRG(2), can be derived manually without much difficulty. However, such a methodology becomes already impractical and error prone for the derivation of the BIMSRG(3) equations, which are eventually needed to reach high accuracy. Based on a diagrammatic formulation of BIMSRG theory, the second objective of the present paper is thus to describe the third version (v3.0.0) of the ADG code that automatically (1) generates all valid BIMSRG(n) diagrams and (2) evaluates their algebraic expressions in a matter of seconds. This is achieved in such a way that equations can easily be retrieved for both the flow equation and the Magnus expansion formulations of BIMSRG. Expanding on this work, the first future objective is to numerically implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio calculations of mid-mass open-shell nuclei.

We calculate basis-space converged neutrinoless ββ decay nuclear matrix elements for the lightest candidates: 48Ca, 76Ge and 82Se. Starting from initial two- and three-nucleon forces, we apply the ab initio in-medium similarity renormalization group to construct valence-space Hamiltonians and consistently transformed ββ -decay operators. We find that the tensor component is non-negligible in 76Ge and 82Se, and resulting nuclear matrix elements are overall 25-45% smaller than those obtained from the phenomenological shell model. While a final matrix element with uncertainties still requires substantial developments, this work nevertheless opens a path toward a true first-principles calculation of neutrinoless ββ decay in all nuclei relevant for ongoing large-scale searches.

We report a comprehensive study of 10−14 B isotopes within the \textit{ab-initio} no-core shell model (NCSM) using realistic nucleon-nucleon (\textit{NN}) interactions. In particular, we have applied the inside non-local outside Yukawa (INOY) interaction to study energy spectra, electromagnetic properties and point-proton radii of the boron isotopes. The NCSM results with the charge-dependent Bonn 2000 (CDB2K), the chiral next-to-next-to-next-to-leading order (N 3 LO) and optimized next-to-next-to-leading order (N 2 LO opt ) interactions are also reported. We have reached basis sizes up to N max = 10 for 10 B, N max = 8 for 11,12,13 B and N max = 6 for 14 B with m-scheme dimensions up to 1.7 billion. We also compare the NCSM calculations with the phenomenological YSOX interaction using the shell model to test the predictive power of the \textit{ab-initio} nuclear theory. Overall, our NCSM results are consistent with the available experimental data. The experimental ground state spin 3 + of 10 B has been reproduced using the INOY \textit{NN} interaction. Typically, the 3\textit{N} interaction is required to correctly reproduce the aforementioned state.

Nuclides sharing the same mass number (isobars) are observed ubiquitously along the stability line. While having nearly identical radii, stable isobars can differ in shape, and present in particular different quadrupole deformations. We show that even small differences in these deformations can be probed by relativistic nuclear collisions experiments, where they manifest as deviations from unity in the ratios of elliptic flow coefficients taken between isobaric systems. Collider experiments with isobars represent, thus, a unique means to obtain quantitative information about the geometric shape of atomic nuclei.

Accurate nuclear matrix elements (NMEs) for neutrinoless double beta decays of candidate nuclei are important for the design and interpretation of future experiments. Significant progress has been made in the modeling of these NMEs from first principles. The NME for 48Ca shows a good agreement among three different ab initio calculations starting from the same nuclear interaction constructed within the chiral EFT and the same decay operator. These studies open the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as 76Ge, 130Te, and 136Xe. The ultimate goal is the computation of NMEs in many-body calculations with controllable approximations, using nuclear interactions and weak transition operators derived consistently from chiral EFT. We are expecting more progress towards this goal in the near future.

α -decay always has enormous impetuses to the development of physics and chemistry, in particular due to its indispensable role in the research of new elements. Although it has been observed in laboratories for more than a century, it remains a difficult problem to calculate accurately the formation probability S α microscopically. To this end, we establish a new model, i.e., multistep model, and the corresponding formation probability S α values of some typical α -emitters are calculated without adjustable parameters. The experimental half-lives, in particular their irregular behavior around a shell closure, are remarkably well reproduced by half-life laws combined with these S α . In our strategy, the cluster formation is a gradual process in heavy nuclei, different from the situation that cluster pre-exists in light nuclei. The present study may pave the way to a fully understanding of α -decay from the perspective of nuclear structure.

A consistent set of statistical-model input parameters, validated by analysis of various independent data, makes possible the assessment of an α -particle optical model potential [Phys. Rev. C {\bf 90}, 044612 (2014)] also for nucleon-induced α -emission within A ∼ 60 mass-number range. The advantage of recent data for low-lying states feeding is taken as well. Consideration of additional reaction channels leading to increase of the α -emission beyond the statistical predictions has concerned the pickup direct interaction and Giant Quadrupole Resonance similar features.

Amplitude- and truncated partial-wave analyses are combined into a single procedure and a novel, almost theory-independent single-channel method for extracting multipoles directly from measured data is developed. In practice, we have created a two-step procedure which is fitted to the same data base: in the first step we perform an energy independent amplitude analysis where continuity is achieved by constraining the amplitude phase, and the result of this first step is then taken as a constraint for the second step where a constrained, energy independent, truncated partial-wave analysis is done. The method is tested on the world collection of data for η photoproduction, and the obtained fit-results are very good. The sensitivity to different possible choices of amplitude phase is investigated and it is demonstrated that the present data base is insensitive to notable phase changes, due to an incomplete database. New measurements are recommended to remedy the problem.

Extensive dynamical N/D calculations are made in the study of S 11 channel low energy ? N scatterings, based on various phenomenological model inputs of left cuts at tree level. The subtleties of the singular behavior of the partial wave amplitude at the origin of the complex s plane are carefully analysed. It is found that, relying very little on the details of the dynamical inputs, the subthreshold resonance N ??(890) survives.

An efficient method, preconditioned conjugate gradient method with a filtering function (PCG-F), is proposed for solving iteratively the Dirac equation in 3D lattice space for nuclear systems. The filtering function is adopted to avoid the variational collapsed problem and a momentum-dependent preconditioner is introduced to promote the efficiency of the iteration. The PCG-F method is demonstrated in solving the Dirac equation with given spherical and deformed Woods-Saxon potentials. The solutions given by the inverse Hamiltonian method in 3D lattice space and the shooting method in radial coordinate space are reproduced with a high accuracy. In comparison with the existing inverse Hamiltonian method, the present PCG-F method is much faster in the convergence of the iteration, in particular for deformed potentials. It may also provide a promising way to solve the relativistic Hartree-Bogoliubov equation iteratively in the future.