High-Energy Ejection of Molecules and Gas-Dust Outbursts in Coal Mines

In the current work, using the framework of the formalism found in the Bogolyubov–Born–Green–Kirkwood–Yvon (BBGKY) equations for the distribution functions of particle groups, the effective single-particle potential near the surface of the liquid was analyzed. The thermodynamic conditions under which a sudden opening of the liquid surface leads to high-energy ejection of atoms and molecules were found. The energies of the emitted particles were observed to be able to significantly exceed their thermal energy. Criteria of the ejection stability of the liquid surface and the self-acceleration of ejection were formulated. The developed theory was used to explain the phenomenon of the self-acceleration of gas-dust outbursts in coal mines during the explosive opening of methane traps. The results also explained the mechanisms of generating significant amounts of methane and the formation of coal nanoparticles in gas-dust outbursts. The developed approach was also used to explain the phenomenon of the self-ignition of hydrogen when it enters the atmosphere.

Ξ hyper-nuclear states predicted by NLO chiral baryon-baryon interactions

The Ξ single-particle potential obtained in nuclear matter with the next-to-leading order baryon-baryon interactions in chiral effective field theory is applied to finite nuclei by an improved local-density approximation method. As a premise, phase shifts of ΞN elastic scattering and the results of Faddeev calculations for the ΞNN bound state problem are presented to show the properties of the ΞN interactions in the present parametrization. First, the Ξ states in 14N are revisited because of the recent experimental progress, including the discussion on the ΞN spin-orbit interaction that is relevant to the location of the p-state. Then the Ξ levels in 56Fe are calculated. In particular, the level shift which is expected to be measured experimentally in the near future is predicted. The smallness of the imaginary part of the Ξ single-particle potential is explicitly demonstrated.

Kuryshkin-Wodkiewicz quantum measurement model for alkaline metal atoms

The constructive form of the Kuryshkin-Wodkiewicz model of quantum measurements was earlier developed in detail for the quantum Kepler problem. For more complex quantum objects, such a construction is unknown. At the same time, the standard (non-constructive) model of Holevo-Helstrom quantum measurements is suitable for any quantum object. In this work, the constructive model of quantum measurements is generalized to a wider class of quantum objects, i.e., the optical spectrum of atoms and ions with one valence electron. The analysis is based on experimental data on the energy ordering of electrons in an atom according to the Klechkovsky-Madelung rule and on the substantiation of a single-particle potential model for describing the energy spectrum of optical electrons in alkali metal atoms. A representation of the perturbation of a single-particle potential in the form of a convolution of the potential of an electron in a hydrogen atom with the Wigner function of a certain effective state of the core in an alkali metal atom representation allows reducing all calculation algorithms for alkali metals to the corresponding algorithms for the hydrogen atom.

The form factor and the density distribution of the 4He nucleus using the Morse potential

The form factor and the density distribution of the He nucleus are calculated approximately using the Morse single-particle potential. The parameters are determined by fitting the theoretical charge form factor to the corresponding experimental data of the elastic electron scattering by 4He, which are extended to large values of the momentum transfer. The corrections due to the center of mass motion (in the fixed center of mass approach) and of the finite proton size have been taken into account. The calculations can be performed partly analytically and the results show a considerable im- provement with respect to those obtained with the oscillator shell model.

COLLECTIVE POTENTIAL FOR HEAVY ION NUCLEAR REACTIONS

It is shown that the nuclear charge polarisation during heavy ion nuclear reactions enhances the secondary maximum of the collective energy surface and produces a secondary minimum in the deformation energy near R ~ Rmin + 2fm. The potential energy and mass formulas are given as a function of A and Z. It has been shown that charge polarisation without shape deformation and indeed of the prolate type does not produce any secondary minimum. It is also seen that the relativity effect consists in shifting the secondary minimum towards higher rest excentricities. For deformation of the oblate type the collective potential has a similar form like that in the spherical case. Entry and exit channel collective potentials are also given for the case of strong nucléon transfer. The mass for the two-body interacting system has been calculated and for large distances it tends to the corresponding reduced mass. The present theory is based on a particular form of the single particle potential following from the scalar π-meson classical field theory.

Study of energy quantities for a hyperon in hypernuclei using a single particle potential

A single particle hyperon-nucleus potential is adopted for the study of various energy quantities of a hyperon (Y) in hypernuclei.Approximate semi-empirical formulae for the ground state (g.s.) binding energy and for the oscillator spacing hωΛ of a Λ in hypernuclei are proposed. The region of their validity is discussed.The g.s. binding energies of the Ξ- hyperon in the few known Ξ- hypernuclei are also analyzed and a comparison of the volume integrals of the Ξ- nucleon and Λ nucleon potentials |V_{ΞN}I and |V_{ΛΝ)| is made. The value of the ratio γ=V_{ΞΝ}/|V_{ΛN}| is found to be ~0.8. Such a conclusion is also obtained by using in the same way other potential models such as the Woods-Saxon one.

On a single particle potential for atomic clusters

The single-particle potential V(r) = -Vo[1+(r/K)^β)^-1, which has been proposed in the recent years for atomic (metal) clusters, is studied analytically in the case β = 2. By using perturbation-type techniques, approximate analytic expressions are obtained for the energy eigenvalues and other physically interesting quantities showing the variation of these quantities with the number of valence electrons. The accuracy is tested for Al clusters and is usually very good.

Application of information theory in atoms, nuclei and atomic clusters

The position- and momentum-space information entropies of the electron distributions of atomic clusters are calculated using a Woods-Saxon single particle potential. The same entropies are also calculated for nuclear distributions according to the Skyrme parametrization of the nuclear mean field. It turns out that a similar functional form S = α + Μη Ν for the entropy as function of the number of particles Ν holds approximately for atoms, nuclei and atomic clusters. It is conjectured that this is a universal property of a many-fermion system in a mean field.

Analysis of the binding energies of the Λ- particle in hypernuclei with the RHVT approach and the Gauss potential

An analysis is carried out mainly of the ground state binding energies of the Λ-particle in hypernuclei with values of the core mass number AC between 15 and 207 (included) using, as far as possible, recent experimental data.Τhe renormalized (non- relativistic) quantum mechanical hypervirial theorem (RHVT) technique is employed in the form of s- power series expansions and a Gauss single particle potential for the motion of a Λ- particle in hypernuclei is used. Not exact analytic solution is known for the Schrödinger eigenvalue problem in this case. Thus, the approximate analytic expressions (AAE) for the energy eigenvalues which are obtained with the RHVT approach and are quite useful as long as the involved dimensionless parameter s is sufficiently small, are compared only with the numerical solution. The potential parameters are determined by a least-squares fit in the framework of the rigid core model for the hypernuclei. A discussion is also made regarding the determination of the renormalization parameter χ.