On the bound states in the muonic molecular ions

Absolute cross sections for electron impact ionization and dissociation of OH⁺ and OD⁺ leading to the formation of the OH²⁺, O⁺, O²⁺, O³⁺ and D⁺ ions have been measured by applying the animated electron-ion beam method in the energy range from the respective reaction thresholds up to 2.5 keV. The maximum of the single ionization cross section is found to be (0.95? ± ?0.02) × 10^?19 cm² at 155 eV. The maximum total cross sections for O⁺ and D⁺ fragments production are observed to be (15.7? ± ?0.2) × 10^?17 cm² at 95 eV and (10.8? ± ?0.5) × 10^?17 cm² at 95 eV, respectively. The cross sections for O²⁺ and O³⁺ are much smaller, (5.37? ± ?0.04) × 10^-18 cm² at 135 eV and (7.95? ± ? 0.23) × 10^-20 cm² at 315 eV, respectively. The collected data are analyzed in details in order to determine separately the contributions of dissociative excitation and of dissociative ionization to the O⁺ and D⁺ fragments production.     

Classification scheme for resonant states of muonic molecules

We have performed a hyperradial-adiabatic one-state calculation of resonant states of (dd)⁺ and (dt)⁺ below then=2 level of the muonic atoms. The results are used for a new classification scheme of these states. Comparing our calculation with a recent full variational calculation by Hara and Ishihara and opposing our findings to the analysis of Shimamura we demonstrate that the classical Born-Oppenheimer classification scheme can be misleading. The symmetry-adapted hyperradial-adiabatic potential curves provide better grounds for the classification procedure.     

The bound states problem in quantum electrodynamics and vacuum polarization effects in muonic atoms

Quantum electrodynamic bound states in strong electromagnetic fields are considered. It is shown that the dynamics of the system can not be described completely in the adiabatic S-matrix approach. Vacuum polarization effects in muonic atoms are studied using the paradigm of generalized quantum dynamics. This approach leads to additional correction terms.     

Absence of bound states in extremely asymmetric positive diatomic molecules

It is shown that the Hamiltonian for a diatomic molecule consisting ofN electrons and two dynamic nuclei with chargesZ ₁ andZ ₂ has no bound states if one of the charges is sufficiently large. The nuclear motion is completely unrestricted, and the kinetic energy of both nuclei can be included in the Hamiltonian. One of the nuclear charges can be arbitrarily small, provided that the other is sufficiently large.Research supported in part by NSF grant DMS-8908125     

Particle-hole bound states of dipolar molecules in an optical lattice

We investigate the particle-hole pair excitations of dipolar molecules in an optical lattice, which can be described with an extended Bose-Hubbard model. For strong enough dipole-dipole interaction, the particle-hole pair excitations can form bound states in one and two dimensions. With decreasing dipole-dipole interaction, the energies of the bound states increase and merge into the particle-hole continuous spectrum gradually. The existence regions, the energy spectra and the wave functions of the bound states are carefully studied and the symmetries of the bound states are analyzed with group theory. For a given dipole-dipole interaction, the number of bound states varies in momentum space and a number distribution of the bound states is illustrated. We also discuss how to observe these bound states in future experiments.     

Nonrelativistic Lamb shift for muonic molecules

A recently developed formula [R. Bukowski and B. Jeziorski, Phys. Rev. A46 (1992) 5437]. has been applied to estimate the soft-photon Lamb shift contribution to the energies of the muonic molecules pp, dd, tt, pd, pt and dt. The corresponding corrections to the dissociation energies for the excited P states of dd and dt have been found to be almost identical and equal to 0.048 meV. The magnitude of this stabilizing effect is too small to affect seriously the formation rates predictions.     

Nuclear fusion in charge-asymmetric muonic molecules

Nuclear fusion reactions in hydrogen-lithium muonic molecules, (where h=p,d,t) are considered and fusion rates from rotational states J=0 of the molecules are presented. Results obtained depend on the isotopic composition of the molecules and range between and . The upper limit for fusion rates from rotational states J=0 of hydrogen-helium muonic molecules, and , equal , is also found. Received: 4 December 1997 / Revised: 30 April 1998 / Accepted: 7 May 1998     

Resonant enhancement of the formation of hydrogen-helium muonic molecules

Formation of muonic molecules and , where J is rotational quantum number, in electron conversion process is investigated at collision energies between 0.004 eV and 50 eV. Corresponding reaction rates are calculated in adiabatic approximation for the three-body Coulomb problem. Significant enhancement of the rates for and is found near 7 eV and 30 eV, respectively. It is shown that the enhancement is due to resonances present in elastic and scattering at these energies. Acceleration of dμ atoms up to the resonant energy could be realized in triple H-D-³He mixture due to the muon transfer from protium to deuterium. Experimental investigation of nuclear synthesis from molecular state directly formed in the mixture is suggested.     

Franck-Condon factor phase method for determining the potentials of bound states of piatomic molecules

A new method for determining a fragment of the potential function of a bound state of a piatomic molecule from the phase of the matrix element of an electronic transition is proposed. As opposed to the method of WKB nodes [Opt. Spektrosk. 83, 906 (1997)], the new method (we call it the Franck-Condon factor phase method) is suitable for analyzing only those spectral regions free from interference structures. However, it is less demanding to the quality of experimental data and makes it possible to study situations where only a portion of the electronic band profile is accessible for analysis. Accuracy characteristics of the method are demonstrated using the analysis of the spectra of the transitions in Na₂(2³Σ _g ⁺ (v=15, N=27; v=5, N=39)→³Σ _u ⁺ ) as an example.     

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

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.     

The properties of scalar quark bound states

We discuss the (static) potential for scalar quark bound states, their leptonic and hadronic decays and their radiative transitions.     

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.     

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.     

The inverse problem in the case of bound states

We investigate the inverse problem for bound states in the D = 3 dimensional space. The potential is assumed to be local and spherically symmetric. The present method is based on relationships connecting the moments of the ground state density to the lowest energy of each state of angular momentum ?. The reconstruction of the density ρ(r) from its moments is achieved by means of the series expansion of its Fourier transform F(q). The large q-behavior is described by Padé approximants. The accuracy of the solution depends on the number of known moments. The uniqueness is achieved if this number is infinite. In practice, however, an accuracy better than 1% is obtained with a set of about 15 levels.The method is tested on a simple example, and applied to three different spectra.     

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.     

A cryogenic target to study charge nonsymmetric muonic molecules

An experimental setup, including a cryogenic gas target with temperature control and gas filling systems, has been developed to study muon catalyzed fusion in gas mixtures of hydrogen and helium isotopes. This revised version was published online in August 2006 with corrections to the Cover Date.