Analytical solution of the inverse spectroscopic problem: Determination of electron moments of vibrational transitions of diatomic molecules by their probabilities

The inverse problem of spectroscopy of vibrational transitions of diatomic molecules was analytically solved on the basis of wave functions of the Morse oscillator. An example of the determination of the transition dipole-moment function by intensities of several lines of molecule vibrational-rotational spectra measured experimentally was considered. A similar approach based on simple expressions for matrix elements can be applied to consider optimal lasing conditions of the CO electronic transition laser.     

Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

Exact propagator for an electron in a quadratic saddle-point potential and a magnetic field

We study the propagator for an electron moving in a two-dimensional (2D) quadratic saddle-point potential,in the presence of a perpendicular uniform magnetic field. A closed-form expression for the propagator is derived using the Feynmann path integrals.     

Few-electron molecular states and their transitions in a single InAs quantum dot molecule

We study electronic configurations in a single pair of vertically coupled self-assembled InAs quantum dots, holding just a few electrons. By comparing the experimental data of nonlinear single-electron transport spectra in a magnetic field with many-body calculations, we identify the spin and orbital configurations to confirm the formation of molecular states by filling both the quantum mechanically coupled symmetric and antisymmetric states. Filling of the antisymmetric states is less favored with increasing magnetic field, and this leads to various magnetic field induced transitions in the molecular states.     

Analysis of the πN invariant amplitudes in terms of algebraic functions and a new determination of the πN low-energy parameters

We have analysed the energy dependence of the πN invariant amplitudes in terms of algebraic functions which automatically fulfill fixed-t dispersion relations. The amplitudes were taken from several phase shift solutions. The analysis was repeated for nine t-values between 0 ? t ? ?0.3 GeV². By evaluating the resulting analytic amplitudes at threshold and at ν = 0 we recalculate the S, P, D scattering lengths and the current algebra σ term. We also discuss the trajectories of the zeros and poles in the complex energy plane.     

Exact expressions for the precession of a planet and the deflection of light

Exact expressions for the precession of a planet's orbit and for the deflection of light near a massive object are presented.     

A Zakharov-Shabat inverse scattering problem with a polynomial spectral dependence in the potential

The inverse scattering problem for the Zakharov-Shabat system , is considered. It is solved by reduction to the inverse scattering problem for two coupled Zakharov-Shabat systems in a 4n-dimensional space: . This work has been done as part of the program ‘Recherche Coopérative sur Programme No. 264: Etude interdisciplinaire des problèmes inverses’. Physique Mathématique et Théorique, Equipe de recherche associée au CNRS, No. 154.     

Collective electron excitations in a spherical potential well and the polarizability of the fullerene molecule

The collective motion of the electron system of the C60 molecule was investigated within the framework of the linear response theory. The model originally proposed by Mukhopadhyay and Lundqvist [1, 2, 3] and applied for C60 by Östling et al [4] was used with an electron density calculated from a spherical well potential. From the calculated dynamic polarizability a main plasmon peak at 14.4 eV in the photoabsorption cross section of the C60 molecule and a broad double peaked structure around 25 eV in the transmission electron energy loss spectrum of the solid C60 can be derived.     

Dispersion sum rules for the amplitudes of radiative transitions in quarkonium

A dispersion approach is suggested, based on the asymptotic freedom in QCD and on analyticity, which leads to sum rules for the amplitudes of radiative transitions in quarkonium $\text{(}\text{c}\text{c}\text{,}\text{b}\text{b}\text{, …)}$ and allows one to estimate these amplitudes in a model-independent way. As an example such sum rules are derived for the ${}^3\text{P}{}_0\text{?}{}^3\text{S}{}_1$ and ${}^3\text{S}{}_1\text{?}{}^1\text{S}{}_0$ transitions. For charmonium they agree with the available data and with the predictions of nonrelativistic models.     

Exact solution of the time-dependent harmonic plus an inverse harmonic potential with a time-dependent electromagnetic field

In this paper, the problem of the charged harmonic plus an inverse harmonic oscillator with time-dependent mass and frequency in a time-dependent electromagnetic field is investigated. It is reduced to the problem of the inverse harmonic oscillator with time-independent parameters and the exact wave function is obtained.     

Calculation of the potential energy of the interaction of an electron with a molecule

We set forth a mathematically correct algorithm, simple in computer realization, for calculation of the potential energy of the interaction of an electron with a molecule and for the calculation of electric 2^L-pole molecular moments in the framework of the Hartee-Fock-Roothaan method. The proposed method permits consideration of the dynamics of the problem of the dependence of the energy on oscillatory motion in the molecule.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 30–33, August, 1987.     

Quark-antiquark states and their radiative transitions in terms of the spectral integral equation: Charmonia

Earlier by the authors (Yad. Fiz. 70, 68 (2007)), the bƃ states were treated in the framework of the spectral integral equation, together with simultaneous calculations of radiative decays of the considered bottomonia. In the present paper, such a study is carried out for the charmonium states. We reconstruct the interaction in the c-c sector on the basis of the data for the charmonium levels with J _PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺, 1⁺⁻ and radiative transitions ψ(2S) → γχ _c0(1P), γχ _c1(1P), γχ _c2(1P), γχ _c(1S) and χ _c0(1P), χ _c1(1P), χ _c2(1P) → γJ/ψ. The c-c levels and their wave functions are calculated for the radial excitations with n ≤ 6. Also, we determine the c-c component of the photon wave function using the e ⁺ e ⁻-annihilation data: e ⁺ e ⁻ → J/ψ(3097), ψ(3686), ψ(3770), ψ(4040), ψ(4160), ψ(4415) and perform the calculations of the partial widths of the two-photon decays for the n = 1 states η _c0(1S), χ _c0(1P), χ _c2(1P) → γγ and n = 2 states η _c0(2S) → γγ, χ _c0(2P) → γγ. We discuss the status of the recently observed c-c states X(3872) and Y(3941): according to our results, the X(3872) can be either χ _c1(2P) or η _c2(1D), while Y(3941) is χ _c2(2P). The text was submitted by the authors in English.     

Quark-Antiquark states and their radiative transitions in terms of the spectral integral equation: Bottomonia

In the framework of the spectral integral equation, we consider the states and their radiative transitions. We reconstruct the interaction on the basis of data for the levels of the bottomonium states with J ^PC = 0⁻⁺, 1⁻⁻, 0⁺⁺, 1⁺⁺, 2⁺⁺ as well as the data for the radiative transitions γ (3S) → _γχbJ(2P) and γ(2S) → _γχbJ(1P) with J = 0, 1, 2. We calculate bottomonium levels with the radial quantum numbers n ≤ 6, their wave functions, and corresponding radiative transitions. The ratios Br[_χbJ(2P) → _γγ(2S)]/Br[_χbJ(2P) → _γγ(1S)] for J = 0, 1, 2 are found to be in agreement with data. We determine the component of the photon wave function using the data for the e ⁺ e ⁻ annihilation, e ⁺ e ⁻ → γ(9460), γ(10 023), γ(10 036), γ(10 580), γ(10 865), γ(11 019), and predict partial widths of the two-photon decays ηb0 → γγ, χb0 → γγ, χb2 → γγ for the radial excitation states below the threshold (n ≤ 3). The text was submitted by the authors in English.     

Renormalization group functions for two-dimensional phase transitions: To the problem of singular contributions

According to the available publications, the field theoretical renormalization group approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This property is associated with the existence of nonanalytic contributions in the renormalization group functions. The situation is analyzed in this work using a new algorithm for summing divergent series that makes it possible to determine the dependence of the results for the critical exponents on the expansion coefficients for the renormalization group functions. It has been shown that the exact values of all the exponents can be obtained with a reasonable form of the coefficient functions. These functions have small nonmonotonic sections or inflections, which are poorly reproduced in natural interpolations. It is not necessary to assume the existence of singular contributions in the renormalization group functions.