Highest weight irreducible representations favored by nuclear forces within SU(3)-symmetric fermionic systems

The consequences of the attractive, short-range nucleon-nucleon (NN) interaction on the wave functions of nuclear models bearing the SU(3) symmetry are reviewed. The NN interaction favors the most symmetric spatial SU(3) irreducible representation (irrep), which corresponds to the maximal spatial overlap among the fermions. The consideration of the highest weight (hw) irreps in nuclei and in alkali metal clusters, leads to the prediction of a prolate to oblate shape transition beyond the mid–shell region. Subsequently, the consequences of the use of the hw irreps on the binding energies and two-neutron separation energies in the rare earth region are discussed within the proxy-SU(3) scheme, by considering a very simple Hamiltonian, containing only thethree dimensional (3D) isotropic harmonic oscillator (HO) term and the quadrupole-quadrupole interaction. This Hamiltonian conserves the SU(3) symmetry and treats the nucleus as a rigid rotator.

Line of approximate SU(3) symmetry inside the symmetry triangle of the Interacting Boson Model

The U(5), SU(3), and O(6) symmetries of the Interacting Boson Model (IBM) have been traditionally placed at the vertices of the symmetry triangle, while an O(5) symmetry is known to hold along the U(5)–O(6) side of the triangle. We construct [1] for the first time a symmetry line in the interior of the triangle, along which the SU(3) symmetry is preserved. This is achieved by using the contraction of the SU(3) algebra to the algebra of the rigid rotator in the large boson number limit of the IBM. The line extends from the SU(3) vertex to near the critical line of the first order shape/phase transition separating the spherical and prolate deformed phases. It lies within the Alhassid–Whelan arc of regularity, the unique valley of regularity connecting the SU(3) and U(5) vertices amidst chaotic regions, thus providing an explanation for its existence.

Group contractions and conformal maps in nuclear structure models

Group contraction is a procedure in which a symmetry group is reduced into a group of lower symmetry in a certain limiting case. Examples are provided in the large boson mumber limit of the Interacting Boson Approximation (IBA) model by a) the contraction of the SU(3) algebra into the [R5]SO(3) algebra of the rigid rotator, consisting of the angular momentum operators forming SO(3), plus 5 mutually commuting quantities, the quadrupole operators, b) the contraction of the O(6) algebra into the [R5]SO(5) algebra of the ∞-unstable rotator. We show how contrac- tions can be used for constructing symmetry lines in the interior of the symmetry triangle of the IBA model. In mathematics, a conformal map is a function which preserves angles. We show how this procedure can be used in the framework of the Bohr Hamiltonian, leading to a Hamiltonian in a curved space, in which the mass depends on the nuclear deformation Ø, while it remains independent of the collective variable ∞ and the three Euler angles. This Hamiltonian is proved to be equivalent to that obtained using techniques of Supersymmetric Quantum Mechanics.

Hamiltonian Chaos

Nondissipative or Hamiltonian systems are also capable of chaos as phase space volume is twisted and folded in area-preserving maps like the Standard Map. When nonintegrable terms are added to a potential function, Hamiltonian chaos emerges. The Standard Map (also known as the Chirikov map) for a periodically kicked rigid rotator provides a simple model with which to explore the emergence of Hamiltonian chaos as well as the KAM theory of islands of stability. A periodically kicked harmonic oscillator displays extended chaos in the web map. Hamiltonian classical chaos makes a direct connection to quantum chaos, which is illustrated using the chaotic stadium, for which quantum scars are associated with periodic classical orbits in the stadium.

ANALOG COMPUTER FOR STUDYING DIATOMIC MOLECULAR SPECTRA IN TERAHERTZ FREQUENCY

This paper introduces a harmonic oscillator model for rovibronic terahertz spectrum of a model of a rigid diatomic rotor with some control parameters. The model shows a study of rotationally-resolved terahertz band spectra of the vibrational transition in diatomic molecules. THz radiation absorption is used as a closed-form system known as the analog computer dynamics mode. The optical terahertz region spectrum of the diatomic molecule consists of a series of lines. Their separations are not exactly constant. A diatomic molecule is not truly a rigid rotator, because it simultaneously vibrates with a small amplitude. Due to quantized vibrational and rotational energy levels and the selection rules, allowed transitions result in a highly ordered spectrum consisting of a P branch separated by a central gap. Adjacent spectral lines are separated by a spacing of 2B, and since line intensities depend on Boltzmann factor for thermal population and quantum number J, each branch monotonically increases and decreases. As temperature increases, more lines are observed, and line intensities decrease due to the population being spread over more rotational levels. Interactivity research also involves on effects of the fundamental vibrational frequency, rotational constant B and temperature included line width on the observed spectrum.

STATTHERMO® – NEW SOFTWARE FOR CALCULATION OF THERMODYNAMIC FUNCTIONS

A new software StatThermo for calculation of thermodynamic functions using the molecular constants in Rigid Rotator – Harmonic Oscillator approximation has been developed. Program includes various prebuilt algorithms to calculate atom coordinates for the majority of simple compounds (with a number of atoms N ≤ 8). The developed software can make the calculation for two reference temperatures (0 or 298.15 K) and different pressures. One of the prominent features of StatThermo is taking into account the low-lying electronic levels. The software was tested on different organic and inorganic molecules and average errors was found as follows: 0.05 kJ∙mol–1 (H°(T)-H°(0)), 0.01 J∙mol–1∙K–1 (Ф°(T)), and 0.002 J∙mol–1∙K–1 (S°(T)). The program can also approximate by the polynomial the thermodynamic functions defined by user. A wide range of functional possibilities, flexible parameters of calculation, and feature of export results in the Visual Basic macro do the StatThermo powerful software for thermodynamic computations. StatThermo can connect to the MS Office and OpenOffice servers for the export of calculated data. The software can treat the Gaussian, Gamess, FireFly, Jaguar, MolPro, CFour, NWChem, ORCA, Priroda, PSI4, Q-Chem, and VASP output files. A multilingual and cross-platform support makes the StatThermo accessible for a lot of users. Forcitation:Dunaev A.M., KudinL.S. StatThermo® – new software for calculation of thermodynamic functions. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2017. V. 60. N 4. P. 40-46.