Relativistic bound-state equations for fermions with instantaneous interactions

In thispaper three types of relativistic bound-state equations for a fermion pair with instantaneous interaction are studied, viz., the instantaneous Bethe-Salpeter equation, the quasi-potential equation, and the two-particle Dirac equation. General forms for the equations describing bound states with arbitrary spin, parity, and charge parity are derived. For the special case of spinless states bound by interactions with a Coulomb-type potential the properties of the ground-state solutions of the three equations are investigated both analytically and numerically. The coupling-constant spectrum turns out to depend strongly on the spinor structure of the fermion interaction. If the latter is chosen such that the nonrelativistic limits of the equations coincide, an analogous spectrum is found for the instantaneous Bethe-Salpeter and the quasi-potential equations, whereas the two-particle Dirac equation yields qualitatively different results.     

Simple procedure for solving few-body equations

In this work we propose a procedure for iterative improvement of the adiabatic solution of the hyperspherical-harmonics technique. The usefulness of the method is demonstrated by calculating the binding energies of the ground and first excited state of the⁴He nucleus using several nucleon-nucleon interactions. The procedure is found to be simple and very stable. We compare the elastic charge form factor of the⁴He nucleus obtained by the usual adiabatic solutions and the improved version of this work. This comparison gives valuable physical insight into the nature of the adiabatic approximations.     

On smoothness of solutions of some elliptic functional-differential equations with degeneration

We consider second-order differential-difference equations in bounded domains in the case where several degenerate difference operators enter the equation. The degeneration leads to the fact that the multiplicity of the zero eigenvalue for the corresponding differential-difference operator becomes infinite. Regularity of generalized solutions for such equations is known to fail in the interior of the domain. However, we prove that the projections of solutions onto the orthogonal complement to the kernel of the “leading” difference operator remain regular in certain subdomains which form a decomposition of the original domain.     

Euler and correlated harmonic-oscillator wave function for the trinucleon bound-state

The trinucleon bound-state properties have been calculated by means of an Euler variational procedure, subsequently improved by the addition of correlated harmonic-oscillator wave functions. Three realistic model interactions containing only two-body forces have been considered. The results obtained show a satisfactory accuracy when compared with the corresponding estimates from Faddeev theory. The extension to larger nuclei of the method here investigated is a possible goal.Dedicated to Profs. Erich Schmid and Ivo laus on the occasion of their 60th birthdays     

Helicity representation of the N-N bound-state problem

The two-nucleon bound-state problem described in the momentum space is presented in the helicity state formalism.     

Many-exciton effects in the biexciton bound-state potential

Starting from a previously derived many-particle equation describing biexciton states, the influence of dynamical exciton-exciton scattering effects on the biexciton binding energy has been calculated. As a result, we obtain density effects in bound states. In qualitative agreement with experimental data only a small density-induced shift of the biexcitonic luminescence should be observed.     

Variational wave-function study of the triangular lattice supersolid

We present a variational wave function which explains the behavior of the supersolid state formed by hard-core bosons on the triangular lattice. The wave function is a linear superposition of only and all configurations minimizing the repulsion between the bosons (which it thus implements as a hard constraint). Its properties can be evaluated exactly--in particular, the variational minimization of the energy yields (i) the surprising and initially controversial spontaneous density deviation from half-filling (ii) a quantitatively accurate estimate of the corresponding density wave (solid) order parameter.     

Approximation methods in the context of the bound-state Bethe-Salpeter equation

Numerical approximation schemes of the Wick-rotated scalar Bethe-Salpeter equation are discussed for general local potentials with special emphasis on mesh-point methods. Convergence properties are obtained by considering the analytic properties of the kernel. To this end, the four-dimensional partial wave equations are formulated in a new representation-independent way. The close relationship of variational and mesh-point methods is demonstrated and the difficulties which arise if singular potentials are introduced are discussed. For marginal singular potentials those difficulties are overcome in a new way by redefining the corresponding two-particle Green's function. Numerical examples for this case are given.     

Meson-hyperon couplings in the bound-state approach to the Skyrme model

Kaon and pion coupling constants to hyperons are calculated in the bound-state approach to strangeness in the Skyrme-soliton model. The pion and kaon coupling constants are properly defined as matrix elements of source terms of the mesons sandwiched between two single-baryon states. Numerical calculation of the coupling constants shows that the bound-state approach well reproduces the empirical values.     

Simple computer solution of coupled power equations

A numerical method for solution of the coupled power equations in multimode optical fibres is presented. The method is based on the assumption that the contribution of weak mode coupling can be concentrated into discrete points along the fibre. The matrix form of the solution is derived, the accuracy of the method is briefly discussed and an example of practical results is also shown.     

Imaging the wave-function amplitudes in cleaved semiconductor quantum boxes

We have investigated the electronic structure of the conduction band states in InAs quantum boxes embedded in GaAs. Using cross-sectional scanning tunneling microscopy and spectroscopy, we report the direct observation of standing wave patterns in the boxes at room temperature. Electronic structure calculation of similar cleaved boxes allows the identification of the standing waves pattern as the probability density of the ground and first excited states. Their spatial distribution in the (001) plane is significantly affected by the strain relaxation due to the cleavage of the boxes.