Calculation of the stability domain for Coulomb systems

A variational method is proposed for calculating the values of particle mass corresponding to the dissociation threshold of an atomic-molecular system. The calculations of the dissociation stability domain for three-particle Coulomb systems demonstrate the high effectiveness of the method as compared to the traditional variational principle for calculating energy.     

Ground-state energy and stability of three-particle coulomb systems versus the masses of the particles involved

The ground-state energy of three-particle Coulomb systems (trions) is investigated versus the masses of the particles involved. Variational calculations are performed for 34 asymmetric trions X^±Y^±Z^? consisting of electrons, muons, pions, kaons, nuclei of hydrogen isotopes and their antiparticles, as well as for more than 100 auxiliary three-particle systems involving particles of masses chosen arbitrarily. Wide bases of Laguerre exponential-polynomial functions depending on perimetric particle coordinates are used. Approximate analytic formulas for the ground-state energies of all trions X^±Y^±Z^? with arbitrary particle masses are constructed on the basis of the values found here for the energies of asymmetric trions and the values calculated previously for the energies of symmetric trions X^±X^±Z^?. Particle-mass regions are determined where trions are stable with respect to dissociation. In addition to symmetric trions X^±X^±Z^?, which are stable at any particle masses, asymmetric trions X^±X^±Z^? possess the stability property if the masses of the particles X and Y exceed the mass of the particle Z, where, by Z, we mean, for example, an electron, a muon, a pion, or a kaon. The t⁺d⁺p^? and t⁺d⁺d^? combinations of hydrogen nuclei and antinuclei are also stable with respect to dissociation. The general properties of the ground-state trion energy as a function of the particle masses are discussed.     

Integral equations for three-particle systems with coulomb interaction

Modified Faddeev equations are formulated that may be used for studying the wave functions below and also above the threshold.     

Calculation of proton-deuteron phase parameters including the coulomb force

A previously proposed exact method for including the Coulomb force in three-body collisions is applied to proton-deuteron scattering. We present phase shifts for angular momenta up to L = 9, from elastic threshold to 50 MeV proton laboratory energy. Separable rank-one potentials are taken for the nuclear interactions. A charge-independent and a charge-symmetric choice, while leading to different neutron-deuteron and proton-deuteron phase parameters, nevertheless yield practically the same Coulomb corrections. We investigate, moreover, the question of P-wave resonances. A critical comparison of our results with those obtained in a coordinate-space formalism is performed. Furthermore, proposals for an approximate inclusion of the Coulomb potential are tested, and found unsatisfactory.     

Symmetry and boundness of four-particle coulomb systems

The problem of boundness of a ⁺ b ⁺ c ⁻ d ⁻ four-particle Coulomb systems (quadrions) is studied versus the masses of the particles involved. Inequalities that make it possible to deduce that, if some reference quadrions form a bound state, the same is true for a large number of quadrions formed by particles having various masses were derived. A compendium of calculations for energies of reference systems that possess various symmetries [positronium molecules (e ⁺ e ⁺ e ⁻ e ⁻) and quadrions of the a ⁺ b ⁺ b ⁻ b ⁻, a ⁺ b ⁺ a ⁻ b ⁻, and a ⁺ a ⁺ b ⁻ c ⁻ types] is given, and groups of bound asymmetric quadrions corresponding to them are determined. An inequality for kinetic energies of particles that makes it possible to find out, by using asymmetric reference systems, whether specific quadrions are bound is obtained. It is shown that the boundness of many quadrions is ensured by the boundness of respective three-particle systems. The entire body of the present results permits proving that, of the total number of 406 quadrions containing electrons, muons, pions, kaons, protons, deuterons, and tritons and their antiparticles, 227 quadrions are bound.     

Stability of coulomb systems with magnetic fields

The ground state energy of an atom in the presence of an external magnetic filedB (with the electron spin-field interaction included) can be arbitrarity negative whenB is arbitrarily large. We inquire whether stability can be restored by adding the self energy of the field, B ². For a hydrogenic like atom we prove that there is a critical nuclear charge,z _c , such that the atom is stable forz<z _c and unstable forz>z _c .Work partically supported by U.S. National Scinece Foundation grant DMS-8405264 during the author's stay at the Institute for Advanced Study, Princeton, NJ, USAWork partially supported by U.S. National Science Foundation grant PHY-8116101-A03Work partially supported by U.S. and Swiss National Science Foundation Cooperative Science Program INT-8503858. Current address: Institut f. Mathematik, FU Berlin, Arnimallee 3, D-1000 Berlin 33     

A rigorous approach to Debye screening in dilute classical coulomb systems

The existence and exponential clustering of correlation functions for a dilute classical coulomb system are proven using methods from constructive quantum field theory, the sine gordon transformation and the Glimm, Jaffe, Spencer expansion about mean field theory. This is a vindication of a belief, of long standing amongst physicists, known as Debye screening. This states that, because of special properties of the coulomb potential, the configurations of significant probability are those in which the long range parts ofr ^–1 are mostly cancelled, leaving an effective exponentially decaying potential acting between charge clouds.Supported by N.S.F. Grant PHY 76-17191     

Debye-Hückel limit of quantum coulomb systems

In this paper, we consider charge symmetric quantum Coulomb systems with Boltzmann statistics. We prove that the theory of screening of Debye and Hückel is a combined classical and mean field limit of these quantum Coulomb systems.Supported by the Swiss National Foundation for Scientific Research     

The upper and lower bounds of energy for nuclear and coulomb few-body systems

The upper and lower bounds of energy are found for three-, four-, and five-particle nuclear and Coulomb systems in the framework variational method with the trial functions of exponential and Gaussian types. The two-sided estimates of energy not only allow one to fix the limits for the exact value of energy but also provide an additional opportunity for extrapolation of the variational estimates to the exact value of energy. This allows one to reduce the volume of calculations by shortening the number of trial functions without the loss of accuracy.     

A renormalization-group approach to the coulomb gap

The Coulomb Gap is a phenomenon in which the long-ranged Coulomb repulsions between localized electrons cause a soft gap to appear in the density of states at the Fermi surface, dominating transport processes. A standard diagrammatic technique and a renormalization group philosophy are applied to this problem. The density of states (which corresponds to the two-point vertex function in our field theory) is renormalized by interactions, with a correction that is logarithmic in 1D. Thus the RG is valid and an epsilon-expansion gives the density of states in other dimensionalities. It is found that the standard Efros-Shklovskii theory of the Coulomb Gap is identical to the TAP theory of spin glasses. We speculate that by means of a diagrammatic expansion for the beta-function, one can study the weak-disorder case, for which the standard theory breaks down.     

Kinetic theory of charge-density wave systems in the presence of long-range coulomb forces

The coupling between the charge-density weve condensate, and the quasiparticles and normal electrons, due to long-range Coulomb forces is investigated within the framework of the kinetic theory, for finite temperatures and in the presence of impurity scattering. The temperature dependence of the parameters, which enter the phenomenological equations for the transport in CDW systems, is determined. In the absense of normal electrons, a strong enhancement of the damping and the velocity of the phase mode is found for low temperatures, which is due to the freezing out of quasiparticles.     

Effect of the d-f coulomb correlation on the valence transition of intermediate valence systems

The d-f Coulomb repulsion, G, is treated by means of a real space decimation procedure on a Bethe lattice. The valence is calculated as a function of the relative position of the f-level with respect to the conduction band. No discontinuous transitions are found.     

Screening effect of the coulomb interaction on the energy levels of atomic and molecular systems

The energies of atomic and molecular systems with a screened Coulomb interaction are expressed in terms of properties of the system with a conventional Coulomb interaction to the third order in the screening constant. The energy levels of an H atom, an H^? ion, and nonadiabatic systems, namely, the positronium ion e ⁺ e ^? e ^? and the positronium molecule e ⁺ e ⁺ e ^? e ^?, are calculated for screened Coulomb interactions of charged particles. It is demonstrated that, as the screening constant of the Coulomb interaction increases, the stability of the hydrogen atom, the H^? ion, and the positronium molecule e ⁺ e ⁺ e ^? e ^? decreases, whereas the stability of the positronium ion e ⁺ e ^? e ^? increases after a slight decrease.     

The dependence of exchange and coulomb energies on wave functions of the interacting systems

First-order energies have been calculated for the He₂ system using a number of He wave functions. The convergence to the Hartree-Fock limit has been studied and a two-term expansion in Slater orbitals gives about 98 per cent of this limit. The effect of correlation has been examined by adding s′² and p ² configurations to the wave function and a change of approximately 10 per cent in the effective first-order energy has been noted.     

Calculation of the first nonlinear contribution to the general-relativistic spin-spin interaction for binary systems

We use recently developed effective field theory techniques to calculate the third order post-Newtonian correction to the spin-spin potential between two spinning objects. This correction represents the first contribution to the spin-spin interaction due to the nonlinear nature of general relativity and will play an important role in forthcoming gravity wave experiments.     

Free-free radiative transitions for the screened coulomb potential

Free-free transitions form a substantial part of the thermal emission of plasmas at high temperatures and long wavelengths. The modifications caused by charged perturbing particles, especially electrons, are estimated for the case of a hydrogen plasma by the use of the Debye-Hückel potential and compared with other approximations.