Quantum bifurcations and quantum phase transitions in rotational spectra

An interconnection between quantum bifurcations and quantum phase transitions is investigated. It is shown that the quantum phase transition is the limiting case of the quantum bifurcation in macroscopic systems. Critical phenomena in microscopic many-body systems such as nuclei and molecules are described by quantum bifurcations. They are characterized by a large transition region, which conceals a critical point. Both the quantum bifurcation and quantum phase transition show that a change in the internal structure of a system manifests itself in the modification of its rotational spectrum. Such an intimate connection between internal and rotational motion allows a critical phenomenon to be established. The text was submitted by the author in English.     

On intensity perturbations in vibronically induced radiative transitions

Intensity perturbations in forbidden radiative transitions due to cubic anharmonic mixing involving the inducing mode and a totally symmetric progression-forming mode are discussed. It is shown that such mixing will lead to deviations from mirror symmetry of the absorption and fluorescence structure because the destructive-constructive interference pattern which prevails in absorption is different to that in emission. This analysis is applied to intensities in the 2600 Å system of benzene. Moderate cubic coupling energies (ca. 10 cm^-1) have marked effects on intensity distributions even when the interacting levels are 200 cm^-1 apart. The splitting of the progressions 1₀ ⁿ 6₁ ² and 1 _n ⁰6₂ ¹ into two sub-progressions (l=0, 2) is linearly dependent on the extent of vibronic excitation in the a _1g mode v ₁. These effects are amenable to experimental detection.     

Rydberg transitions for positron-hydrogen collisions

e⁺ + H(ns) ↦e⁺ + H(n^′s) transitions for arbitrary n and n^′ have been studied using the distorted-wave formalism in the momentum space [Ghoshal and Mandal, Phys. Rev. A 72, 032714 (2005)]. The distorted-wave scattering amplitudes have been written in a simple closed analytical form. A detailed study has been made on differential and total cross sections in the energy range 20–300 eV. Resonance-like behaviour of the differential cross section has been observed in the the region of lower scattering angles for high Rydberg transitions. To the best of our knowledge the distorted-wave results for differential and total cross sections for such arbitrary transitions are reported for the first time in the literature.     

Far-wing light absorption induced by resonant or near-resonant collisions

Summary We have studied the absorption of light induced by a resonant or near-resonant collision between two atoms. The calculations have been performed by taking into account also the magnetic sublevels, which makes our theoretical predictions more applicable to realistic cases. Analytical expressions for the far-wing absorption cross-section have been obtained.     

Noise induced transitions due to external additive noise

The stationary Fokker-Planck equation in the two-dimensional case is solved locally using an antisymmetric tensor which transforms the problem into the potential case. Several examples are discussed which show that even additive external noise influences the extremal behaviour of the stochastic potential.     

The Kosterlitz-Thouless transitions by the mayer expansion finiteness of the perturbations

The Kosterlitz-Thouless transitions in 2D XY and Coulomb gas models are discussed by the Mayer expansion. After transforming the 2D XY model into a (generalzed) 2D Coulomb gas model by the duality transformation, it is shown that the free energy (pressure) and the two point correlation function 〈cos(θ₀?θ_ζ)〉 are expressed as Σa_N(β) and $\text{exp}\text{[(}\text{2}\text{β}\text{) C}{}_0\text{(ζ) + Σb}{}_{\mathrm{N}}\text{(β:ζ)]}$, respectively, for large inverse temperature β > β_c, where {a_N(β)} are the usual virial coefficients and {a_N, b_N} are the contributions from N-electron system. Moreover C₀(ζ) ? ? (2π)^?1 log(|ζ| + 1), |a_N(β)| ≤ C₁(N) exp[?βK₃N] and |b_N(β:N) ≤ C₂(N) exp[?βK₄N] |C₀(ζ)| (K_i > 0). By comparing this system with the dipole gas system in which these series converge absolutely, it is conjectured that these series converge absolutely for large β.     

He-HI碰撞的转动激发分波截面

基于作者所发展的分子间相互作用势,采用密耦方法计算了入射He原子能量分别为40,75和100　meV时与HI分子碰撞的弹性和非弹性分波截面.研究表明：激发分波截面比弹性分波截面收敛得快;激发态越高,激发分波截面收敛得越快;能量越高,激发分波截面收敛得越慢. 关键词： 分波截面 密耦方法 He-HI复合物     

Fission induced by heavy-ion collisions

Fission fragment angular distributions from sequential fission induced in heavy-ion reactions will depend on the angular momentum exchange occuring in such reactions in considerable detail. Theoretical expressions for the angular distributions of fission products from totally and partly polarized nuclei are presented. They are compared with recent measurements and discussed in relation to the deep inelastic reaction mechanism.     

Phase transitions induced in NaNbO3 crystals by varying the direction of an external electric field

The anisotropic behavior of the electrostatic field characterizing the phase transition from an antiferroelectric state to a ferroelectric state is studied for the first time with NaNbO₃ as an example. Structural changes taking place in the crystal as the direction of the electrostatic field is varied are studied and electrostatic field magnitude-direction phase diagrams are determined. Fiz. Tverd. Tela (St. Petersburg) 39, 1084–1087 (June 1997)     

Charged particle spectra in16O induced nuclear collisions at the CERN SPS

Charged particle multiplicity distributions and pseudo-rapidity density distributions from¹⁶O induced nuclear collisions at 200 and 60A GeV are presented. The data were taken, using a minimumbias trigger, with the WA80 set-up at the CERN SPS. In this presentation we focus on how the yield of charged particles depends on the projectile energy, the mass number of the target nucleus and the energy measured in a uranium-plastic sampling calorimeter covering angles close to zero degrees. The data are compared to simulations from the event generator FRITIOF.     

Calculation of an effective potential in an external gravitational field with torsion and phase transitions induced by external fields

We find a general expression for a one-loop effective potential of an arbitrary massless theory with accuracy up to terms linear in two-dimensional invariants. The potential is constructed from the metric and the torsion. We show that spontaneous symmetry breaking can occur in the form of a first-order phase transition induced jointly by the curvature and the torsion.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 3–9, March, 1987.The authors are grateful to I. V. Tyutin and E. S. Fradkin for discussion.     

A perturbation expansion for external wide band Markovian noise: Application to transitions induced by Ornstein-Uhlenbeck noise

A method is presented which permits to calculate the stationary probability density of non equilibrium systems subjected to wide band external colored noise. It consists of a systematic perturbation expansion in terms of the correlation time of the noise. The method is presented in detail for noise of the Ornstein-Uhlenbeck type. It is used to illustrate the effect of correlations on two examples of noise induced transitions.     

Nonequilibrium transitions driven by external dichotomous noise

The stationary probability densityP _s for a class of nonlinear one-dimensional models driven by a dichotomous Markovian process (DMP)I _t , can be calculated explicitly. For the specific case of the Stratonovich model, x=ax –-x ³ +I _t x, the qualitative shape ofP _s and its support is discussed in the whole parameter region. The location of the maxima ofP _s shows a behavior similar to order parameters in continuous phase transitions. The possibility of a noiseinduced change from continuous to a discontinuous transition in an extended model, in which the DMP couples also to the cubic term, is discussed. The time-dependent moments x_t ⁿ can be represented as an infinite series of terms, which are determined by a recursion formula. For negative even moments the series terminates and the long-time behavior can be obtained analytically. As a function of the physical parameters, qualitative changes of this behavior may occur which can be partially related to the behavior ofP _s . All results reproduce those for Gaussian white noise in the corresponding limit. The influence of the finite correlation time and the discreteness of the space of states of the DMP are discussed. An extensive list of references is contained in U. Behn, K. Schiele, and A. Teubel,Wiss. Z. Karl-Marx-Univ. Leipzig, Mathem.-Naturwiss. R. 34:602 (1985).Contribution to the symposium on the Statistical Mechanics of Phase Transitions —Mathematical and Physical Aspects, Tebo, Czechoslovakia, September 1–6, 1986.     

Cross sections and rate coefficients of transitions in He and He-like ions induced by collisions with heavy particles

An approach to calculating the exitation cross sections and rate coefficients for a wide class of transitions in atoms and ions induced by collisions with heavy charged particles in considered. Calculations were carried out in terms of the Born approximation in the impact parameter representation with the normalization and Coulomb repulsion (in the case of an ionic target). Transitions between levels in He and He-like ions without changes of the principal quantum number are considered for n=2–4. Fitting formulas are suggested for transition rate coefficients. Tables of cross sections and parameters of fitting formulas are given for He and C⁴⁺.     

Invariance of the essential spectra for perturbations with unbounded hard cores

Based on the Feynman-Kac formula and a certain variant of Weyl's theorem, we determine the essential spectra of Schrödinger operators including unbounded hard cores.     

Einstein A-coefficients for rotational transitions in the HN2O+

EinsteinA-values for the electric dipole transitions between the rotational levels up to 540 cm⁻¹ andJ=11 in the ground vibrational state of the protonated N₂O (i.e., HN₂O⁺) are calculated. The coefficients are used to compute the mean radiative lifetimes of the levels. TheseA-values can be used for analysing the spectra from astronomical objects, if observed.     

Computer checking of rotational line intensity factors for diatomic transitions

Previously published analytical formulae for the rotational line intensity factors of diatomic molecules have been compared with results from a comprehensive computer program, which determines numerical intensity factors for both spin-allowed and spin-forbidden electric and magnetic dipole transitions in diatomic molecules. The comparison uncovered several typographical errors and a few algebraic errors in the published formulae. The changes required in the formulae to give agreement with the results from the computer program are tabulated.