Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method II. Quantization Conditions in the Symmetric Case Expressed in Terms of Complete Elliptic Integrals. Numerical Illustration

The contour integrals, occurring in the arbitrary-order phase-integral quantization conditions given in a previous paper, are in the first- and third-order approximations expressed in terms of complete elliptic integrals in the case that the charges of the Coulomb centres are equal. The evaluation of the integrals is facilitated by the knowledge of quasiclassical dynamics. The resulting quantization conditions involving complete elliptic integrals are solved numerically to obtain the energy eigenvalues and the separation constants of the $1s\sigma$ and $2p\sigma$ states of the hydrogen molecule ion for various values of the internuclear distance. The accuracy of the formulas obtained is illustrated by comparison with available numerically exact results.Comment: 19 pages, RevTeX 4, 4 EPS figures, submitted to J. Math. Phy

Astronomical observatories

The layout and equipment of astronomical observatories, the oldest scientific institutions of human society are discussed. The example of leading observatories of the USSR allows the reader to familiarize himself with both their modern counterparts, as well as the goals and problems on which astronomers are presently working

Self-consistent approach for the quantum confined Stark effect in shallow quantum wells

A computationally efficient, self-consistent complex scaling approach to calculating characteristics of excitons in an external electric field in quantum wells is introduced. The method allows one to extract the resonance position as well as the field-induced broadening for the exciton resonance. For the case of strong confinement the trial function is represented in factorized form. The corresponding coupled self-consistent equations, which include the effective complex potentials, are obtained. The method is applied to the shallow quantum well. It is shown that in this case the real part of the effective exciton potential is insensitive to changes of external electric field up to the ionization threshold, while the imaginary part has non-analytical field dependence and small for moderate electric fields. This allows one to express the exciton quasi-energy at some field through the renormalized expression for the zero-field bound state.Comment: 13 pages, RevTeX4, 6 figure

Non-abelian cubic vertices for higher-spin fields in AdS(d)

We use the Fradkin-Vasiliev procedure to construct the full set of non-abelian cubic vertices for totally symmetric higher spin gauge fields in anti-de Sitter space. The number of such vertices is given by a certain tensor-product multiplicity. We discuss the one-to-one relation between our result and the list of non-abelian gauge deformations in flat space obtained elsewhere via the cohomological approach. We comment about the uniqueness of Vasiliev's simplest higher-spin algebra in relation with the (non)associativity properties of the gauge algebras that we classified. The gravitational interactions for (partially)-massless (mixed)-symmetry fields are also discussed. We also argue that those mixed-symmetry and/or partially-massless fields that are described by one-form connections within the frame-like approach can have nonabelian interactions among themselves and again the number of nonabelian vertices should be given by tensor product multiplicities

Strong fragmentation of low-energy electromagnetic excitation strength in 117^{117}Sn

Results of nuclear resonance fluorescence experiments on $^{117}$Sn are reported. More than 50 $\gamma$ transitions with $E_{\gamma} < 4$ MeV were detected indicating a strong fragmentation of the electromagnetic excitation strength. For the first time microscopic calculations making use of a complete configuration space for low-lying states are performed in heavy odd-mass spherical nuclei. The theoretical predictions are in good agreement with the data. It is concluded that although the E1 transitions are the strongest ones also M1 and E2 decays contribute substantially to the observed spectra. In contrast to the neighboring even $^{116-124}$Sn, in $^{117}$Sn the $1^-$ component of the two-phonon $[2^+_1 \otimes 3^-_1]$ quintuplet built on top of the 1/2$^+$ ground state is proved to be strongly fragmented.Comment: 4 pages, 3 figure

Fragmentation and systematics of the Pygmy Dipole Resonance in the stable N=82 isotones

The low-lying electric dipole (E1) strength in the semi-magic nucleus 136Xe has been measured which finalizes the systematic survey to investigate the so-called pygmy dipole resonance (PDR) in all stable even N=82 isotones with the method of nuclear resonance fluorescence using real photons in the entrance channel. In all cases, a fragmented resonance-like structure of E1 strength is observed in the energy region 5 MeV to 8 MeV. An analysis of the fragmentation of the strength reveals that the degree of fragmentation decreases towards the proton-deficient isotones while the total integrated strength increases indicating a dependence of the total strength on the neutron-to-proton ratio. The experimental results are compared to microscopic calculations within the quasi-particle phonon model (QPM). The calculation includes complex configurations of up to three phonons and is able to reproduce also the fragmentation of the E1 strength which allows to draw conclusions on the damping of the PDR. Calculations and experimental data are in good agreement in the degree of fragmentation and also in the integrated strength if the sensitivity limit of the experiments is taken into account

Angular distributions of scattered excited muonic hydrogen atoms

Differential cross sections of the Coulomb deexcitation in the collisions of excited muonic hydrogen with the hydrogen atom have been studied for the first time. In the framework of the fully quantum-mechanical close-coupling approach both the differential cross sections for the $nl \to n'l'$ transitions and $l$-averaged differential cross sections have been calculated for exotic atom in the initial states with the principle quantum number $n=2 - 6$ at relative motion energies $E_{\rm {cm}}=0.01 - 15$ eV and at scattering angles $\theta_{\rm {cm}}=0 - 180^{\circ}$. The vacuum polarization shifts of the $ns$-states are taken into account. The calculated in the same approach differential cross sections of the elastic and Stark scattering are also presented. The main features of the calculated differential cross sections are discussed and a strong anisotropy of cross sections for the Coulomb deexcitation is predicted.Comment: 5 pages, 9 figure