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.     

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.     

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 $\text{7}\text{12}\text{mα}{}^4\text{to}\text{1}\text{2}\text{mα}{}^4$.     

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.     

Two-body QED bound states

The status of theory and experiment is reviewed for two-body systems in quantum electrodynamics, and places where further work would be useful are pointed out.     

Nucleon antinucleon bound states

A system of bound nucleon-antinucleon, with the quantum numbers of various scalar and pseudoscalar existing particles and resonances is studies with a Bethe Salpeter equation in the ladder approximation. The interaction is produced byπ-mesons. The effect of a phenomenological vector interaction is also checked. The bound states are classified according to their isotopic spin,G parities, parities, nucleonic number, spin and masses. To obtain the experimental value for the coupling constant \(g_{N\bar N\pi } \) the used model requires for a cut off values between 0.3 to 5 nucleonic masses. The effect of the vector interaction is always attractive.     

Multiparticle bound states in QED

The relation between multiparticle Schrödinger equations and the underlying field theory for weakly coupled systems is clarified. A systematic perturbation theory for the energy levels is presented the first term of which is the eigenvalue of a Schrödinger equation with relativistic kinematics.     

Pion bound states in nuclei

Bound π-nuclear states can appear under certain realistic conditions in finite nuclei. The best prospects are certain medium-weight nuclei with dense central regions and large neutron excess. Numerical illustrations are given for ¹⁶O, ²⁸Si, ³²Na and ²⁰⁸Pb with realistic parameters for the interaction. Further, we show that the usual low-energy π nuclear potential develops pathological features like an infinity of bound states beyond a certain critical strength. The natural remedies are indicated.     

Instability of nonlinear bound states

We establish a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation,u _tt–u+f(u)=0, and the nonlinear Schrödinger equation, –iu _t–u+f(u)=0.Supported in part by NSF Grants MCS 81-21487 and MCS 82-01599     

Solitons as infinite-constituent bound states

We construct soliton states as quantum corrections to the coherent states constructed from classical solutions of nonlinear field equations. The corresponding field operator applied to the vacuum state allows us to discuss physical features of the (one soliton plus various mesons) states.     

Correlation effects and bound states

Bound states in a simple quark model that are due to correlation effects are analyzed. The confining properties of this model in meson (quark-antiquark and diquark) channels manifest themselves at any quark momenta, and an extra potential field may only enhance the confining effect.     

Baryon-antibaryon bound states and annihilation

In order to gain some insight into the problem of the widths of quasi-nuclear levels in the $\text{B}\text{B}$ systems, we investigate a simple multichannel model for the influence of decay channels on a bound state. The shift and width of a bound-state level is found to depend strongly not only on the range of the annihilation and the $\text{B}\text{B}$ wave function at small distances but also on the position of the level relative to the thresholds. We point out a new mechanism through which a level in the vicinity of open thresholds can remain narrow even for strong coupling to the decay channels.