Related papers: Sommerfeld Fine-Structure Formula for Two-Body Ato…
Energies of (2s2 2p5 3l3l') and (2s 2p6 3l3l') states for sodiumlike ions with Z =14--100 are evaluated to second order in relativistic many-body perturbation theory starting from a neonlike Dirac-Fock potential. Second-order Coulomb and…
A relativistic equation is deduced for the bound state of two particles, by assuming a proper boundary condition for the propagation of the negative-energy states. It reduces to the (one-body)Dirac equation in the infinite limit of one of…
The invariant mass of free particles is used to derive a bound-state equation for the hydrogen atom at rest. This equation has the well-known solutions for the single-particle states. Existence of two-particle bound states, for which the…
The bound-state problem for an uncharged massive scalar particle in the field of a naked Reissner-Nordstr\"om singularity is approached by means of the quasiclassical Bohr-Sommerfeld quantization. An approximate analytical expression for…
Relativistic lepton-proton bound-state eigenvalue equations for Hamiltonians derived from quantum field theory using second-order renormalization group procedure for effective particles, are reducible to two-body Schroedinger eigenvalue…
The sixteen-component, no-pair Dirac--Coulomb--Breit equation, derived from the Bethe--Salpeter equation, is solved in a variational procedure using Gaussian-type basis functions for the example of positronium, muonium, hydrogen atom, and…
We study a bound system of N identical bosons interacting by model pair potentials of the form V(r) = A sgn(p)r^p + B/r^2, A > 0, B >= 0. By using a variational trial function and the `equivalent 2-body method', we find explicit upper and…
Accurate three-body quantal calculations of the system composed of a proton, an antiproton, and an electron are performed in perimetric coordinates with the Lagrange-mesh method, an approximate variational calculation with the simplicity of…
The relativistic equivalent of the Schr\"odinger equation for a two particle bound state having the total angular momentum $S$ is written in the form of a Lorentz covariant set of equations (p_1^mu+p_2^mu+Omega^mu)Psi(p_1,p_2;P)…
The analytical calculation of the complete $\alpha\,(Z\,\alpha)^6$ one-loop radiative correction to energies of two-body systems with the angular momenta $l>0$, consisting of a pointlike particle and an extended-size nucleus with arbitrary…
The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the…
We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. By considering a set of generalized Schr\"odinger equations with different orderings between…
We consider the bound states of a system consisting of a light particle and two heavy bosonic ones, which are restricted in their quantum mechanical motion to two space dimensions. A $p$-wave resonance in the heavy-light short-range…
The four-body bound state with two-body forces is formulated by the Three-Dimensional approach, which greatly simplifies the numerical calculations of few-body systems without performing the Partial Wave components. We have obtained the…
A simple locally accurate uniform approximation for the nodeless wavefunction is constructed for a {\it neutral} system of two Coulomb charges of different masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant uniform magnetic field for the…
A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics [1]. Relativistic corrections to…
We study bosonic systems in the regime in which the two-body system has a shallow bound state or, equivalently, a large value of the two-body scattering length. Using the effective field theory framework as a guide, we construct a series of…
The Relativistic formulation of the three-boson model interacting via a zero-range two-body force in the null-plane is given in 2+1 and 1+1 space-time dimension. The bound state energy is calculed as function of the two-body boson binding…
In this paper, hyperspherical three-body model formalism has been applied for the calculation energies of the low-lying bound $^{1,3}$S (L=0)-states of neutral helium and helium like Coulombic three-body systems having nuclear charge (Z) in…
The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules can equivalently…