Related papers: Eulerian Rotations of Deformed Nuclei for TDDFT Ca…
Effective field theory (EFT) is generalized to investigate the rotational motion of triaxially deformed even-even nuclei. A Hamiltonian, called the triaxial rotor model (TRM), is obtained up to next-to-leading order (NLO) within the EFT…
Techniques from effective field theory are applied to nuclear rotation. This approach exploits the spontaneous breaking of rotational symmetry and the separation of scale between low-energy Nambu-Goldstone rotational modes and high-energy…
Euler angles determining rotations of a system as a whole are conveniently separated in three-particle basis functions. Analytic integration of matrix elements over Euler angles is done in a general form. Results for the Euler angle…
Exact numerical diagonalization of the Bohr Hamiltonian by SU(1,1)xSO(5) methods is used to obtain detailed quantitative predictions for single-phonon and multi-phonon excitations in well-deformed rotor nuclei. Dynamical gamma deformation…
It is fairly well known that rotation in three dimensions can be expressed as a quadratic in a skew symmetric matrix via the Euler-Rodrigues formula. A generalized Euler-Rodrigues polynomial of degree 2n in a skew symmetric generating…
The effective field theory (EFT) for triaxially deformed even-even nuclei is generalized to include the vibrational degrees of freedom. The pertinent Hamiltonian is constructed up to next-to-leading order. The leading order part describes…
Progress towards the energy breakthroughs needed to combat climate change can be significantly accelerated through the efficient simulation of atomic systems. Simulation techniques based on first principles, such as Density Functional…
Background: An electron localization function was originally introduced to visualize bond structures in molecules. It became a useful tool to describe electron configurations in atoms, molecules and solids. In nuclear physics, a nucleon…
The rotating nuclei represent one of most interesting subjects for theoretical and experimental studies. They open a new dimension of nuclear landscape, namely, spin direction. Contrary to the majority of nuclear systems, their properties…
We propose a new theoretical approach to ground and low-energy excited states of nuclei extending the nuclear mean-field theory. It consists of three steps: stochastic preparation of many Slater determinants, the parity and angular momentum…
The effective field theory for collective rotations of triaxially deformed nuclei is generalized to odd-mass nuclei by including the angular momentum of the valence nucleon as an additional degree of freedom. The Hamiltonian is constructed…
We survey approaches to nonrelativistic density functional theory (DFT) for nuclei using progress toward ab initio DFT for Coulomb systems as a guide. Ab initio DFT starts with a microscopic Hamiltonian and is naturally formulated using…
Positive muon spin rotation and relaxation spectroscopy is a well established experimental technique for studying materials. It provides a local probe that generally complements scattering techniques in the study of magnetic systems and…
We present a model-independent approach to electric quadrupole transitions of deformed nuclei. Based on an effective theory for axially symmetric systems, the leading interactions with electromagnetic fields enter as minimal couplings to…
We study the spin-parity distribution P(J$^{\pi}$,E) of $^{156}$Gd excited states above the neutron separation energy that are expected to be populated via the neutron pickup reaction $^{157}$Gd($^{3}$He,$^{4}$He)$^{156}$Gd. In general,…
In this short paper, we review the Euler-Rodrigues formula for three-dimensional rotation via fractional powers of matrices. We derive the rotations by any angle through the spectral behavior of the fractional powers of the rotation matrix…
Denavit and Hartenberg-based methods, such as Cardan, Fick, and Euler angles, describe the position and orientation of an end-effector in three-dimensional (3D) space. However, these methods have a significant drawback as they impose a…
Building on recent results for adiabatic gauge potentials, we propose a variational approach for computing the generator of Schrieffer-Wolff transformations. These transformations consist of block diagonalizing a Hamiltonian through a…
The quantum phase estimation algorithm stands as the primary method for determining the ground state energy of a molecular electronic Hamiltonian on a quantum computer. In this context, the ability to initialize a classically tractable…
Using the shift-operator technique, a compact formula for the Fourier transform of a product of two Slater-type orbitals located on different atomic centers is derived. The result is valid for arbitrary quantum numbers and was found to be…