Radiative decays of ρ and ω mesons

The results of the measurements of radiative decays of ρ and ω mesons with the Neutral Detector at thee ⁺ e ^? collider VEPP-2M are presented. The branching ratio of the decay ω→π ⁰γ was measured with higher than in previous experiments accuracy: $${\rm B}(\omega \to \pi ^0 \gamma ) = 0.0888 \pm 0.0062$$ . The ρ⁰→π ⁰ γ branching ratio was measured for the first time: $$B(\rho ^0 \to \pi ^0 \gamma ) = (7.9 \pm 2.0) \cdot 10^{ - 4} $$ . The decays ρ, ω→ηγ were studied. Their branching ratios with the assumption of constructive ρ?ω interference are: $$\begin{gathered} B(\omega \to \eta \gamma ) = (7.3 \pm 2.9) \cdot 10^{ - 4} , \hfill \\ B(\rho \to \eta \gamma ) = (4.0 \pm 1.1) \cdot 10^{ - 4} \hfill \\ \end{gathered} $$ . The branching ratios of ρ, ω→ηγ and ω→e ⁺ e ^? decays were also measured: $$\begin{gathered} B(\omega \to \pi ^ + \pi ^ - \pi ^0 ) = 0.8942 \pm 0.0062, \hfill \\ B(\omega \to e^ + e^ - ) = (7.14 \pm 0.36) \cdot 10^{ - 5} \hfill \\ \end{gathered} $$ . The upper limit for the ω→π ⁰ π ⁰ γ branching ratio was placed: B(ω→π ⁰ π ⁰ γ)<4·10^?4 at 90% confidence level.     

Nuclear mass form factors from coherent photoproduction of πmesons

Data for coherent photoproduction of π⁰ mesons from nuclei ( ¹²C, ⁴⁰Ca, ⁹³Nb, ^natPb), recently measured with the TAPS detector at the Mainz MAMI accelerator, have been analyzed in view of the mass form factors of the nuclei. The form factors have been extracted in plane-wave approximation of the A(γ,π⁰)A reaction and corrected for final-state interaction effects with the help of distorted-wave impulse approximations. Nuclear mass rms radii have been calculated from the slope of the form factors for q² → 0. Furthermore, the Helm model (hard-sphere form factor folded with Gaussian) was used to extract diffraction radii from the zeroes of the form factor and skin thicknesses from the position and height of its first maximum. The diffraction radii from the Helm model agree with the corresponding charge radii obtained from electron scattering experiments within their uncertainties of a few per cent. The rms radii from the slope of the form factors are systematically lower by up to 5% for PWIA and up to 10% for DWIA. Also the skin thicknesses extracted from the Helm model are systematically smaller than their charge counterparts.     

A bound on the number of bound states in the Schrödinger equation

A boundS _l is given for the number of bound statesn _i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given by whereV _a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r ². Extensive comparative study ofS _i and the Bargmann inequality is made.     

η-nucleus bound states in nuclei

The binding energies η and widths Γη of η-mesic nuclei are calculated.We parameterize the η self-energy in the nuclear medium as a function of energy and density.We find that the single-particle energies are sensitive to the scattering length,and increase monotonically with the nucleus.The key point for the study of η-nucleus bound states is the η-nuclear optical potential.We study the s-wave interactions of η mesons in a nuclear medium and obtain the optical potential Uη≈ -72 MeV.Comparing our results with the previous results,we find that the ηN scattering length aηN is indeed important to the calculations.With increasing nuclear density the effective mass of the η meson decreases.     

η-nucleus bound states in nuclei

The binding energies εη and widths Гη of wmesic nuclei are calculated. We parameterize the η self-energy in the nuclear medium as a function of energy and density. We find that the single-particle energies are sensitive to the scattering length, and increase monotonically with the nucleus. The key point for the study of η-nucleus bound states is the η-nuclear optical potential. We study the s-wave interactions of η mesons in a nuclear medium and obtain the optical potential Uη ≈ -72 MeV. Comparing our results with the previous results, we find that the ηN scattering length aηN is indeed important to the calculations. With increasing nuclear density the effective mass of the η meson decreases.     

On concentration of positive bound states of nonlinear Schrödinger equations

We study the concentration behavior of positive bound states of the nonlinear Schrödinger equation $$ih\frac{{\partial \psi }}{{\partial t}} = \frac{{ - h^2 }}{{2m}}\Delta \psi + V\left( x \right)\psi - \gamma \left| \psi \right|^{p - 1} \psi .$$ Under certain condition ofV, we show that positive ground state solutions must concentrate at global minimum points ofV ash→0⁺; moreover, a point at which a sequence of positive bound states concentrates must be a critical point ofV. In cases thatV is radial, we prove that the positive radial solutions with least energy among all nontrivial radial solutions must concentrate at the origin ash→0⁺.     

Nuclear fusion and sticking from resonant states of dtμ

Fusion rates and sticking fractions for s-symmetry resonant states that cluster below the (t)_2s + d threshold in the molecular continuum of dt are analyzed. The fusion rates for some of these states are found to be comparable to their particle decay rates. The associated sticking probabilities appear to be approximately one order of magnitude lower than that of the ground state. This feature is interpreted as a result of quantum interference effects arising from the nonadiabatic character of the metastable states and indicates that the muon catalyzed fusion might proceed more efficiently if it were to occur from molecular resonant states.     

Scattering states and bound states in λ℘(φ)2

By analyzing the Bethe-Salpeter equation for even ()₂ models we show that for weak coupling the mass spectrum is discrete and of finite multiplicity below 2m. Moreover on even states of energy less than 4(m–) we show that theS matrix is unitary. Herem is the physical mass and =()0 as 0. Our results rely essentially only on a simple assumption about the analyticity of the Bethe-Salpeter kernel which has been verified for weak coupling. For the interaction ⁴, (/m _o ² 1) we show that there are no even bound states of energy less than 4(m–).Work supported in part by NSF, Grant MPS 74-13252     

Quantum states of neutral atoms bound in the magnetic field of a Kepler-guide

The spectrum and the wave function of neutral atoms in the magnetic field of a Kepler-guide are presented by reducing a two-dimensional stationary Schrdinger equation to a one-dimensional hydrogen atom in Rydberg states. In addition, we set the scale for     

Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials

In this paper, we study the Lyapunov stabilities of some semiclassical bound states of the (nonhomogeneous) nonlinear Schrödinger equation, We prove that among those bound states, those which are concentrated near local minima (respectively maxima) of the potentialV are stable (respectively unstable). We also prove that those bound states are positive if is sufficiently small.     

Combined analysis of near-threshold production of ω and φ mesons in nucleon-nucleon collisions within an effective meson-nucleon model

Vector meson ( V = ,) production in near-threshold elementary nucleon-nucleon collisions ppppV, pnpnV and pndV is studied within an effective meson-nucleon theory. It is shown that a set of effective parameters can be established to describe fairly well the available experimental data of angular distributions and the energy dependence of the total cross-sections without explicit implementation of the Okubo-Zweig-Iizuka rule violation. Isospin effects are considered in detail and compared with experimental data whenever available.     

Problems of bound states in plasmas—physical and chemical picture revisited

We discuss several problems of plasma physics which were in the center of interest of the Rostock group and the research activities of Gerd Röpke who was appointed a docent in 1977 by Rostock University. In particular we will consider the problem of bound states and several approaches to treat bound states in dense systems.     

Two-vibron bound states in the β--Fermi--Pasta--Ulam model

This paper studies the two-vibron bound states in the β- Fermi Pasta-Ulam model by means of the number conserving approximation combined with the number state method. The results indicate that on-site, adjacent-site and mixed two-vibron bound states may exist in the model. Specially, wave number has a significant effect on such bound states, which may be considered as the quantum effects of the localized states in quantum systems.     

New bounds on the number of bound states for Schrödinger operators

We consider the Schrödinger operatorH = – +V(|x|) onR ³. Letn denote the number of bound states with angular momentum (not counting the 2 + 1 degeneracy). We prove the following bounds onn . LetV 0 and d/dr r ^1-2p (-V)^{1 –p} 0 for somep [1/2, 1) then

Excited states of donors bound toXvalleys in GaAs–AlAs type II structures

We calculate the binding energies of 2s donor states bound tovalleys in type II GaAs–AlAs quantum well structures using an anisotropic variational method which enables us to take into account the effective mass anisotropy and quantum confinement. For a comparative study, we use two sets of effective masses obtained from different measurements [B. Rheinländeret al., Phys. Stat. Sol. (b)49, K167 (1972) and M. Goiranet al., Physica B177, 465 (1992)].     

Nuclear fusion rates from resonant states of 3Hedμ molecular ion

We present new theoretical calculations of nuclear fusion rates λ _f ^J from the resonant states of the muonic molecular ion ³Hedμ ⁺⁺ with total angular momenta J=0,1. As a byproduct, new very accurate variational wave functions for these states have been obtained. Using these wave functions, the probability density |Ψ(R=0)|² in a fusion region has been calculated by extrapolating the variational solution to small internuclear distances by means of the multi-channel adiabatic solution. Calculated fusion rates for the states J=0 and J=1 are: λ _f ⁰ =1.9·10⁵s^-1 and λ _f ¹ =0.65·10³s^-1, respectively. This revised version was published online in August 2006 with corrections to the Cover Date.     

Tetraquark bound states in a Bethe–Salpeter approach

We determine the mass of tetraquark bound states from a coupled system of covariant Bethe–Salpeter equations. Similar in spirit to the quark–diquark model of the nucleon, we approximate the full four-body equation for the tetraquark by a coupled set of two-body equations with meson and diquark constituents. These are calculated from their quark and gluon substructure using a phenomenologically well-established quark–gluon interaction. For the lightest scalar tetraquark we find a mass of the order of 400 MeV and a wave function dominated by the pion–pion constituents. Both results are in agreement with a meson molecule picture for the _f0(600)$f_0(600)$. Our results furthermore suggest the presence of a potentially narrow all-charm tetraquark in the mass region 5–6 GeV.