A Theoretical Study of Pure and Mixed Spin-Polarized Tritium and Helium Triatomic Systems Using Hyperspherical Coordinates

Pure and mixed spin-polarized tritium ( ${{\rm T}\uparrow}$ ) and helium (He) triatomic systems are studied using hyperspherical coordinates. A slow variable discretization approach is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved using basis splines at a series of fixed FEM-DVR hyperradii. By using the best empirical interaction potentials, we study comparatively the bound states of ( ${{\rm T}\uparrow}$ )₃, ⁴He( ${{\rm T}\uparrow}$ )₂, ${^4{\rm He}_2{\rm T}\uparrow}$ , ⁴He₃ and ${^4{\rm He}_2^3{\rm He}}$ in the J ^Π = 0⁺ symmetry. The bound state energy levels are calculated for all these molecular species except ⁴He( ${{\rm T}\uparrow}$ )₂, for which we have found no bound state. The calculated wave functions of these species are found all to exhibit a very large spatial extension, indicating the diffuse nature of these bound states. The molecular structure of these species will also be calculated and analyzed in detail.     

Discussion on Weakly Bound States of Three-Body Systems

The equivalent two-body method for a three-body system has been generalized to an arbitrary three-body system with short-range two-body interactions. An analytical expression for the long-range effective potential is obtained for the Gaussian potential, the Yukawa potential and the exponential potential. The asymptotic behavior of the effective potential at very large distance is found to be universal and an explanation on the significance of universality is given. The weakly bound excited state for the system is first obtained although there is no bound state for two-body subsystems.     

Fugacity and Density Expansion for Systems with Bound States

The fugacity expansion in different approximations for low densities and for systems with bound and scattering states is discussed. The meaning of a mixed expansion and the possibility to introduce a chemical picture for a system in which bound states dominate is proved. The possibility of a thermodynamical instability is shown.     

Representation of Nonequilibrium Steady States in Large Mechanical Systems

Recently a novel concise representation of the probability distribution of heat conducting nonequilibrium steady states was derived. The representation is valid to the second order in the “degree of nonequilibrium”, and has a very suggestive form where the effective Hamiltonian is determined by the excess entropy production. Here we extend the representation to a wide class of nonequilibrium steady states realized in classical mechanical systems where baths (reservoirs) are also defined in terms of deterministic mechanics. The present extension covers such nonequilibrium steady states with a heat conduction, with particle flow (maintained either by external field or by particle reservoirs), and under an oscillating external field. We also simplify the derivation and discuss the corresponding representation to the full order.     

Theoretical Study of Triatomic Systems Involving Helium Atoms

The triatomic ⁴He system and its isotopic species ${^4{\rm He}_2^3{\rm He}}$ are theoretically investigated. By adopting the best empirical helium interaction potentials, we calculate the bound state energy levels as well as the rates for the three-body recombination processes: ⁴He + ⁴He + ⁴He → ⁴ He₂ + ⁴He and ⁴He + ⁴He + ³He → ⁴He₂ + ³He. We consider not only zero total angular momentum J = 0 states, but also J > 0 states. We also extend our study to mixed helium-alkali triatomic systems, that is ⁴He₂ X with X = ⁷Li, ²³Na, ³⁹K, ⁸⁵ Rb, and ¹³³Cs. The energy levels of all the J ≥ 0 bound states for these species are calculated as well as the rates for three-body recombination processes such as ⁴He + ⁴He + ⁷Li → ⁴ He₂ + ⁷Li and ⁴He + ⁴He + ⁷Li → ⁴ He⁷Li + ⁴He. In our calculations, the adiabatic hyperspherical representation is employed but we also obtain preliminary results using the Gaussian expansion method.     

A Microscopic Calculation of Nucleon-Antinucleon Bound States

A microscopic study of nucleon-antinucleon (N N) bound states is achieved starting from the relativistic Pauli-Schrödinger equation for q³q³ bound states. From this equation, a complex off-shell qq one-gluon-exchange potential is derived. Use of this potential and the resonating group method to calculate the NN bound states leads to results which are useful to analyze some of the NN experimental data reported in recent years.     

Universality of Three-Body Systems in 2D: Parametrization of the Bound States Energies

Universal properties of mass-imbalanced three-body systems in 2D are studied using zero-range interactions in momentum space. The dependence of the three-particle binding energy on the parameters (masses and two-body energies) is highly non-trivial even in the simplest case of two identical particles and a distinct one. This dependence is parametrized for ground and excited states in terms of supercircles functions in the most general case of three distinguishable particles.     

Generation of Lithium Clusters in Helium Plasma Flow

Technical Physics - The formation of lithium clusters in a helium flow is considered within the method considering the widths of energy levels. It is shown that lithium atoms in a plasma flow of...     

Effective Modes Method to Estimate the Temperature of Weakly Bound Molecular Systems

Doklady Physics - The paper proposes an approach to estimate the number of modes of collective movement of particles in weakly bound molecular systems, based on the principal component analysis....     

Mass-Imbalanced Three-Body Systems in 2D: Bound States and the Analytical Approach to the Adiabatic Potential

Three-body systems in two dimensions with zero-range interactions are considered for general masses and interaction strengths. The problem is formulated in momentum space and the numerical solution of the Schrödinger equation is used to study universal properties of such systems with respect to the bound-state energies. The number of universal bound states is represented in a form of boundaries in a mass-mass diagram. The number of bound states is strongly mass dependent and increases as one particle becomes much lighter than the other ones. This behavior is understood through an accurate analytical approximation to the adiabatic potential for one light particle and two heavy ones.     

Narrow Bound States of the DNN System

We report on a recent calculation of the properties of the DNN system, a charmed meson with two nucleons. The system is analogous to the ${{\bar {K}}NN}$ system substituting a strange quark by a charm quark. Two different methods are used to evaluate the binding and width, the Fixed Center approximation to the Faddeev equations and a variational calculation. In both methods we find that the system is bound by about 200 MeV and the width is smaller than 40 MeV, a situation opposite to the one of the ${{\bar {K}}NN}$ system and which makes this state well suited for experimental observation.     

A Study of Confined Helium Atom

The helium atom confined by a spherical parabolic potential well is studied employing the adiabatic hyperspherical approach method. Total energies of the ground and three low-excited states are obtained as a function of the confined potential radii. We find that the energies of a spherical parabolic potential well are in good agreement with those of an impenetrable spherical box for the larger confined potential radius. We find also that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values. The results for the three-dimensional spherical potential well and the two-dimensional disc-like potential well are compared with each other. We find that the energy difference between states in a two-dimensional parabolic potential is also obviously larger than the corresponding levels for a spherical parabolic potential.     

Transfer Matrix Spectrum and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We obtain new properties of general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high-temperature region (1). Each model is characterized by a single-site a priori spin distribution, taken to be even. We state our results in terms of the parameter =s ⁴–3s ²², where s ^k denotes the kth moment of the a priori distribution. Associated with the model is a lattice quantum field theory which is known to contain particles. We show that for >0, small, there exists a bound state with mass below the two-particle threshold. The existence of the bound state has implications for the decay of correlations, i.e., the 4-point functions decay at a slower rate than twice that of the 2-point function. These results are obtained using a lattice version of the Bethe–Salpeter equation. The existence results generalize to N-component models with rotationally invariant a priori spin distributions.     

A Study of Confined Helium Atom

The helium atom confined by a spherical parabolic potential well is studied employing the adiabatic hyperspherical approach method. Total energies of the ground and three low-excited states are obtained as a function of the confined potential radii. We find that the energies of a spherical parabolic potential well are in good agreement with those of an impenetrable spherical box for the larger confined potential radius. We find also that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values. The results for the three-dimensional spherical potential well and the two-dimensional disc-like potential well are compared with each other. We find that the energy difference between states in a two-dimensional parabolic potential is also obviously larger than the corresponding levels for a spherical parabolic potential.     

Scattering States of Three-Body Systems with the Hyperspherical Adiabatic Method

In this paper, we investigate the feasibility of employing the Hyperspherical Adiabatic (HA) basis set to describe continuum states of the Helium trimer molecule.     

Bound States in the continuum in photonics

With examples of two parallel dielectric gratings and two arrays of thin parallel dielectric cylinders, it is shown that the interaction between trapped electromagnetic modes can lead to scattering resonances with practically zero width. Such resonances are the bound states in the radiation continuum first discovered in quantum systems by von Neumann and Wigner. Potential applications of such photonic systems include: large amplification of electromagnetic fields within photonic structures and, hence, enhancement of nonlinear phenomena, biosensing, as well as perfect filters and waveguides for a particular frequency, and impurity detection.     

Bound States in the Quantum Scalar Electrodynamics

The next relativistic correction to α to for bound state mass of two charged scalar particles is calculated in the quantum scalar electrodynamics by the functional integral method. Contribution of the “nonphysical” time variable turned out to be important and leads to nonanalytic dependence of the bound state mass on α.