Charge-magnetic-dipole bound states using the Klein-Gordon equation

We investigate bound states of a composite system consisting of a charged particle orbiting a neutral, stationary magnetic dipole. We find all bound states are metastable and none exist with angular momentum less than eleven. Our calculations is performed in two space dimensions.     

The integral equation approach to four-nucleon bound states

Within the framework of the Yakubovsky four-body equations the 0⁺ bound states of ⁴He are determined. The two-particle interactions used are of the separable Yamaguchi type and include spin-dependent forces. The problem is reduced to the solution of four coupled integral equations in two variables. The separable approximation of the kernels makes it possible to reduce the problem to a set of single variable integral equations. The separable approximation method employed is based on the Hilbert-Schmidt expansion applied to the kernels of four-body equations. The ground state energy of ⁴He is found to be ?45.73 MeV, the excited 0⁺ level lies at ?11.69 MeV. In conclusion we discuss the accuracy of various approximate methods in the four-nucleon problem.     

Heavy-quark bound states in potentials with the Bethe-Salpeter equation

The spinless Bethe—Salpeter equation is solved for three attractive static quark-antiquark potentials of the form V(r)=–ar^–+br+c, 01, and the effective non-Coulombic power-law potential of the formV(r)=ar ^0.1+c to obtain the spin-averaged energy levels in bottomonium (b ) and charmonium (c ) families. The shifted 1/N expansion technique is used. Calculations of the energy eigenvalues are carried out up to third order and parameters of each potential are adjusted to obtain the best agreement with the experimental spin-averaged data (SAD). Flavor-dependent and flavor-independent cases are considered in this work.     

Three-boson bound states calculated by a non-connected kernel equation

A non-connected kernel equation for three-boson bound states has been solved numerically. No partial-wave expansion has been used. Numerical stability is demonstrated.     

Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation

Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.     

Exact solutions for Ostrovsky equation

This paper obtains solutions to the Ostrovsky equation by employing the mapping method. Several solutions are determined including the cnoidal waves, shock waves, solitary waves, periodic singular waves and others in the case of no rotation. Finally, the ansatz method is applied to solve the equation with the rotation term present.     

Three-particle bound states for partly nonlocal interactions with continuum bound states

We determine the binding energies of the model triton for two partly nonlocal interactions consisting of a local potential with a strong repulsive core and a nonlocal separable interaction acting only inside the core region, which is responsible for the occurrence of a continuum bound state at very high energies in the total interaction. The ground state of the three-particle system does not collapse in this case as for purely nonlocal interactions. The occurrence of a continuum bound state is therefore only a necessary but not a sufficient condition for such an unphysical collapse in few particle systems.     

Unstable bound states of the Dirac equation by an algebraic approach

It is shown that by using a nonunitary discrete irreducible representation of the su(1, 1) Lie algebra one can determine the eigenenergies of unstable bound states of the Dirac-Coulomb potential. The phase shift of the Dirac-Coulomb waves is also discussed.     

Asymmetric bound states via the quadrupled Schrödinger equation

An efficient iterative method of construction of bound states in an asymmetric potential well is suggested and tested on V(x) = ax² + bx³ + cx⁴.     

Four-quark bound states

In the framework of simple non-relativistic potential models, we examine the system consisting of two quarks and two antiquarks with equal or unequal masses. We search for possible bound states below the threshold for the spontaneous dissociation into two mesons. We solve the four body problem by empirical or systematic variational methods and we include explicitly the virtual meson-meson components of the wave function. With standard twobody potentials, there is no proliferation of multiquarks. With unequal quark masses, we obtain however exotic \(\left( {\bar Q\bar Qqq} \right)\) bound states with a baryonic antidiquark-quark-quark structure very analogous to the heavy flavoured (Q′qq) baryons.     

Hadron-nucleus bound states

A new type of nuclear spectroscopy to study hadron-nucleus bound states is described. The first successful experiment was to search for deeply bound π⁻ states in heavy nuclei using the ²⁰⁸Pb(d,³He) reaction at GSI, in which a narrow peak arising from the 2p π⁻ orbital coupled with the neutron-hole states was observed at 135 MeV excitation energy. An improved experiment has just been carried out to separately identify the 1s and 2p π⁻ states. These experiments provide important information on the local potential strength, from which the effective mass of π⁻ is deduced to be 20 MeV. This method will be extended to search for η and ω bound states as well as for K⁻ bound states. The advantage of the bound-state spectroscopy versus invariant mass spectroscopy is emphasized.     

Topological bound states

In the tight binding approximation, it has been shown that a peculiar type of electronic states localized near the topology change point exists in branching molecules and quantum conductors. Bound states of this type exist both below and above the allowed band, i.e., for both electrons and holes; this property fundamentally differentiates these states from the bound states formed in the minimum of the potential energy. The damping decrement of the wavefunction is independent of the band parameters and is an invariant determined by the characteristic of topology. The tunnel interaction between the topological bound states significantly determines the change in the electronic spectrum of the molecular systems in configuration transitions.     

Threshold bound states

Relationships between the coupling constant and the binding energy of threshold bound states are obtained in a simple manner from an iterative algorithm for solving the eigenvalue problem. The absence of threshold bound states in higher dimensions can be easily understood.     

Supersymmetric bound states

We investigate the bound-state spectrum of a supersymmetric version of QED and calculate the energy of the lowest states of the theory to O(α⁴). These states involve a degenerate quartet of $\text{spin}\text{-}\text{1}\text{2}$ and spin-zero states (para-states) and a degenerate quartet of $\text{spin}\text{-}\text{1}\text{2}$ states associated with an additional spin zero and spin one state (ortho-states). Because of the supersymmetry, the ortho-para splitting in positronium is changed from $\text{7}\text{12}\text{mα}{}^4\text{to}\text{1}\text{2}\text{mα}{}^4$.     

Perturbation theory for QED bound states

A new method is presented for deriving a systematic perturbative expansion for QED bound states, which does not rely upon solving any new or old equation. The starting point is a given nonperturbative zeroth order Green's function, obtained by a suitable “relativistic dressing” of the nonrelativistic Green's function for the Schrödinger equation with Coulomb potential, which embodies the Coulombic bound states and is known. The comparison with the complete Green's function as given by standard perturbative QED gives a perturbative kernel which is then used for the expansion of the QED Green's function in terms of the given non-perturbative zeroth order Green's function.