Related papers: Symplectic no-core configuration interaction frame…
The Similarity Renormalization Group (SRG) is investigated as a powerful yet practical method to modify nuclear potentials so as to reduce computational requirements for calculations of observables. The key feature of SRG transformations…
In this paper, a symplectic structure on a Leibniz algebra is defined to be a {\em symmetric} nondegenerate bilinear form satisfying certain compatibility condition, and a phase space of a Leibniz algebra is defined to be a symplectic…
The geometrical mapping of algebraic nuclear cluster models is investigated within the coherent state formalism. Two models are considered: the Semimicroscopic Algebraic Cluster Model (SACM) and the Phenomenological Algebraic Cluster Model…
The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this…
We perform \textit{ab initio} no-core shell-model calculations for $A=18$ and $19$ nuclei in a $4\hbar\Omega$, or $N_{\rm max}=4$, model space by using the effective JISP16 and chiral N3LO nucleon-nucleon potentials and transform the…
We present quantitative evidence that high-quality internucleon forces derived from $\chi$EFT exhibit a striking dominance of Wigner's supermultiplet symmetry, without invoking the large-$N_c$ limit of QCD or assumptions about specific…
While the no-core shell model is a state-of-the-art microscopic approach to low-energy nuclear structure, its intense computational requirements lead us to consider time-honored approximations such as the Hartree-Fock (HF) approximation and…
In typical microscopic approaches, particularly when pairing correlations are present, nuclei and nuclear fragments do not have well defined quantum numbers and symmetries should be restored. I present here a formalism for the simultaneous…
The interacting shell model, a configuration-interaction method, is a venerable approach for low-lying nuclear structure calculations; but it is hampered by the exponential growth of its basis dimension as one increases the single-particle…
We apply the ab initio no-core shell model/resonating group method (NCSM/RGM) approach to calculate the cross section of the 7Be(p,gamma)8B radiative capture. This reaction is important for understanding the solar neutrino flux. Starting…
Elements of a restricted variational approach to the nuclear mean-field dynamics, providing the microscopic structure of the low energy collective modes, are summarized. The results are illustrated for the isovector states produced by the…
The quest to understand multi-neutron systems has a long history, and recent experimental efforts aim to probe candidate four-neutron configurations in neutron-rich light nuclei such as ${}^8$He and ${}^7$H via quasi-free knockout…
Developing a predictive capability for inelastic scattering will find applications in multiple areas. Experimental data for neutron-nucleus inelastic scattering is limited and thus one needs a robust theoretical framework to complement it.…
The dynamic equation of mass point in rotating coordinates is governed by Coriolis and centrifugal force, besides a corotating potential relative to frame. Such a system is no longer a canonical Hamiltonian system so that the construction…
In this paper, we explore scaling symmetries within the framework of symplectic geometry. We focus on the action $\Phi$ of the multiplicative group $G = \mathbb{R}^+$ on exact symplectic manifolds $(M, \omega,\theta)$, with $\omega =…
We implement and investigate the numerical properties of a new family of integrators connecting both variants of the symplectic Euler schemes, and including an alternative to the classical symplectic mid-point scheme, with some additional…
The no-core configuration-interaction model based on the isospin- and angular-momentum projected density functional formalism is introduced. Two applications of the model are presented: (i) determination of spectra of 0+ states in 62Zn and…
A symmetry-based approach for describing shape-coexistence, is presented in the framework of the interacting boson model of nuclei. It involves a construction of a number-conserving Hamiltonian which preserves the dynamical symmetry of…
Symplectic integrators are the tool of choice for many researchers studying dynamical systems because of their good long-term energy conservation properties. For systems with a dominant central mass, symplectic integrators are also highly…
We explore, within the framework of an algebraic sp(4) shell model, discrete approximations to various derivatives of the energies of the lowest isovector-paired 0^+ states of atomic nuclei in the 40 <A < 100 mass range. The results show…