Detecting positron-atom bound states through resonant annihilation

A method is proposed for detecting positron-atom bound states by observing enhanced positron annihilation due to electronic Feshbach resonances at electron-volt energies. The method is applicable to a range of open-shell transition-metal atoms which are likely to bind the positron: Fe, Co, Ni, Tc, Ru, Rh, Sn, Sb, Ta, W, Os, Ir, and Pt. Estimates of their binding energies are provided.     

The role of bound states in positronium annihilation

The temperature dependence of the rates of positronium reaction with diamagnetic organic molecules in liquids, and the observed complicated conversive-chemical interaction of positronium with many paramagnetic molecules in the liquid and gas phases lead to the formulation of some general concepts about positronium interaction with quenchers. The positronium and acceptor (Ps-M) complexing is a very essential step of the interaction mechanism. In the case of unstable complexes the contribution of annihilation from the bound state can change depending on the physical conditions of the reaction (pressure in the gas phase, transition from the gas to the liquid phase, heating or replacement of the liquid solvent). The dependence on temperature and on the solvent nature is accounted for by formation of a “bubble” around the positronium in many liquids. At the moment of complexing the “bubble” shrinks with a swiftness depending upon properties of the liquid (surface tension and viscosity). With unstable complexes this leads to complex decomposition and, correspondingly, either to elimination of interaction with the diamagnetic acceptor or, in the case of paramagnetic acceptors, to conversion on the latter, rather than to annihilation from the bound state. With stable complexes further positronium annihilation will occur only from the bound state.     

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.     

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

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.     

Intermediate annihilation states in antiproton-nucleus scattering

We study the annihilations on nuclei paying special attention to the role of unitarity in these processes. Analysing the intermediate states, it is shown that the annihilation cross section is much larger than the difference $\text{p}\text{?}\text{A ?}\text{p}\text{A}$ and for heavy nuclei is even larger than the non-annihilation cross section. The singular way in which unitarity works in annihilations can be used to test several models of particle-nucleus interactions.     

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.     

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.     

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.