Transition energy and dipole oscillator strength of 1s23d- 1s2nf transitions for Sc18+ ion

The transition energies of the 1s²3d-1s² nf (4⩽n⩽9) transitions and fine structure splittings of 1s² nf (n⩽9) states for Sc¹⁸⁺ ion are calculated with the full-core plus correlation method. The quantum defect of 1s² nf series is determined by the single-channel quantum defect theory. The energies of any highly excited states with n⩾10 for this series can be reliably predicted using the quantum defect as function of energy. Three alternative forms of the dipole oscillator strengths for the 1s²3d-1s² nf (n⩽9) transitions of Sc¹⁸⁺ ion are calculated with the transition energies and wave functions obtained above. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for 1s²3d-1s² nf (n > 9) transitions and the oscillator strengths densities corresponding to the bound-free transitions are obtained. __________ Translated from Chinese Journal of Atomic and Molecular Physics, 2005, 22(4) (in Chinese)     

Energy and Oscillator Strength of V20+ Ion

The ionization potentials and fine structure splittings of 1s² nl (l = s, p, and d; n ⩽ 9) states for lithium-like V²⁰⁺ ion are calculated by using the full-core plus correlation (FCPC) method. The quantum defects of these three Rydberg series are determined according to the single-channel quantum defect theory (QDT). The energies of any highly excited states with n ⩾ 10 for these series can be reliably predicted using the quantum defects that are function of energy. The dipole oscillator strengths for the 1s²2s–1s² np and 1s²2p–1s² nd (n ⩽ 9) transitions of V²⁰⁺ ion are calculated with the energies and FCPC wave functions obtained above. Combining the QDT with the discrete oscillator strengths, the discrete oscillator strengths for the transitions from the given initial state to highly excited states (n ⩾ 10) and the oscillator strength density corresponding to the bound-free transitions are obtained. Translated from Chinese Journal of Atomic and Molecular Physics, 2005(2) (in Chinese)     

Hadron diffractive processes: the structure of soft pomeron and colour screening

On the basis of the experimental data on diffractive processes in πp, pp and pˉp collisions at intermediate, moderately high and high energies, we restore the scattering amplitude related to the t-channel exchange by vacuum quantum numbers by taking account of the diffractive s-channel rescatterings. At intermediate and moderately high energies, the t-channel exchange amplitude turns, with a good accuracy, into an effective pomeron which renders the results of the additive quark model. At superhigh energies the scattering amplitude provides a Froissart-type behaviour, with an asymptotic universality of cross sections such as σ^tot _πp/σ^tot _pp→ 1 at s→∞. The quark structure of hadrons being taken into account at the level of constituent quarks, the cross sections of pion and proton (antiproton) in the impact parameter space of quarks, σ_π(r _1⊥, r _2⊥; s) and σ_p(r _1⊥, r _2⊥, r _3⊥; s), are found as functions of s. These cross sections implicate the phenomenon of colour screening: they tend to zero at |r _i⊥−r _k⊥|→ 0. The effective colour screening radius for pion (proton) is found for different s. The predictions for the diffractive cross sections at superhigh energies are presented. Received: 15 December 1998     

Ferromagnetism of the electron gas

The ground-state energy of the ferromagnetic electron gas is calculated for the relative polarizationζ=0−1 and the interelectron separationr _s =5−12. The method consists in describing the electron gas approximately by a quadratic boson Hamiltonian, and contains the random-phase approximation as a special case. Numerical studies show that in both the random-phase and the present approximations the paramagnetic state has the lowest energy: the energy increases withζ for all values ofr _s considered. In the present approximation instabilities are found to occur forr _s above a critical value, due to exchange processes of finite momentum transfers. Forζ=0 this critical value ofr _s is 9.4; it decreases with increasingζ. However, the fully-polarized state (ζ=1), which lies above the rest, is always stable. The conclusions are as follows: (1) Forr _s <9.4 the electron gas is paramagnetic. (2) Atr _s =9.4 it goes over to the fully-polarized ferromagnetic state. (3) This phase transition requires an energy absorption of 0.03 rydberg per electron. (4) The fully-polarized state is not obtainable as the limitζ→1.     

Wavelength and oscillator strength of dipole transition 1s<Superscript>2</Superscript>2p—1s<Superscript>2</Superscript><Emphasis Type="Italic">n</Emphasis>d for Mn<Superscript>22+</Superscript> ion

The transition energies, wavelengths and dipole oscillator strengths of 1s²2p—1s² nd (3⩽n⩽9) for Mn²²⁺ ion are calculated. The fine structure splittings of 1s² nd (n</9) states for this ion are also evaluated. In calculating energy, the higher-order relativistic contribution is estimated under a hydrogenic approximation. The quantum defect of Rydberg series 1s² nd is determined according to the quantum defect theory. The results obtained in this paper excellently agree with the experimental data available in literatures. Supported by the National Natural Science Foundation of China (Grant No. 10774063)     

Peculiarities of the amplitude of elastic subbarrier impurity scattering

A formula for the amplitude of electron elastic subbarrier (in the domain of imaginary momenta) scattering by an impurity modeled as a spherical potential well is derived. An equation is obtained to find the features (poles) of this amplitude in a complex energy plane in the close vicinity of which the energy spectrum of quantum resonant percolation trajectories in M-I-M contacts (M = N (normal metal) or S (superconductor) and I is an insulator) with weak (low impurity concentration) structural disorder in the I layer is concentrated [1–4].     

Collisions of fast electrons with positronium atoms

Summary Elastic and inelastic collisions of fast non-relativistic electrons with positronium atoms have been studies in the Born-Ochkur approximation. It has been shown that exchange plays an important role for transitions between states with the same parity as in this case the direct scattering amplitude vanishes. Numerical results for the total and ortho-para conversion cross-sections for the 1s→1s, 1s→2s and 1s→2p transitions have been presented for projectile energies varying from 0.1 to 10 keV. According to charge symmetry, presented results apply also to positron projectiles.     

Lattice dynamical study of alkali metals: An unified approach based on CGW model

The phonon dispersion relations for lithium, sodium, potassium, rubidium and cesium along the principal symmetry directions as well as their lattice specific heats have been deduced using Clark, Gazis and Wallis angular force model. This model which conforms to the translational symmetry of the lattice, reproduces the observed crossover in lithium along [ζ00] direction at ζ = 0·49, without producing any crossovers in other alkali metals. Besides, the theoretical dispersion curves of all alkali metals are in excellent agreement with the corresponding experimental or homologous dispersion relations and theirϑ _D values compare well with the experimental values over a wide temperature range. It is shown that the strength of electron-ion interactions plays a significant role in the success of any unified lattice dynamical study of alkali metals while the three-body interactions of thecgw model do not. The importance of umklapp processes, failure of the earlier models to produce a crossover and the experimentalϑ _D-T curve in lithium as well as the apparent variation in the nature and range of atomic interactions of alkali metals are discussed.     

Field-induced confinement in (TMTSF)2ClO4 under accurately aligned magnetic fields

We present transport measurements along the least conducting c direction of the organic superconductor (TMTSF)₂ClO₄  performed under an accurately aligned magnetic field in the low temperature regime. The experimental results reveal a two-dimensional confinement of the carriers in the (a, b) planes which is governed by the magnetic field component along the b^′ direction. This 2-D confinement is accompanied by a metal-insulator transition for the c axis resistivity. These data are supported by a quantum mechanical calculation of the transverse transport taking into account in self consistent treatment the effect of the field on the interplane Green function and on the intraplane scattering time.     

Theoretical study on behaviors of 1s22s-1s2np transition for Co24+ ion in the whole energy region

Non-relativistic energies of 1s²2s and 1s² np (n⩽9) states for Co²⁴⁺ ion are calculated by using the full-core plus correlation method. Our results of 1s²2s and 1s²2p states agree well with the high-precision results of Yan et al. Based on calculating the first-order corrections to the energy from relativistic and mass-polarization effects, we estimate the higher-order relativistic contribution and QED correction to the energy under a hydrogenic approximation. The transition energies, wavelengths and oscillator strengths for the 1s²2s−1s² np (n⩽9) transitions of this ion are calculated. The results agree with the experimental data available in literature satisfactorily. By combining with quantum defect theory, our theoretical predictions on the energy and oscillator strength of this ion are extrapolated to the whole energy region including continuous states.     

Total scattering cross-section and extraction of low energy parameters of Σ±p scattering

The lowest momentum at which the total scattering cross-section data are available for Σ⁺ p and Σ⁻ p scattering is 145 MeV/c and 142.5 MeV/c respectively. Thus extracting low energy parameters amounts to extrapolating the data to still lower energies. Using the analytic structure of foward scattering amplitude to advantage a parameterization of theσ _T is presented which is hoped to be more reliable and stable for deriving results through extrapolation. The scattering lengths and effective ranges for the Σ⁺ p and Σ⁻ p are also estimated.     

Reinvestigation of the second negative (A 2 Π u−X 2 Π g) band system of O 2 +

TheA ² Π _ustate of O₂ ⁺ was earlier established as an inverted state contrary to previous assumptions. The rotational analysis of a few more bands of theA-X system of O₂ ⁺ has now been completed. These studies show that the spin-orbit coupling constantA in theA ² Π _ustate gradually varies with the vibrational quantum numberν and is found to be positive forν⩾6. It has also been observed that the spia-rotation interaction is not negligible in theA ² Π _ustate. The spin splitting constantγ is reported for various vibrational levels of this electronic state.     

Analytical singlet α s4 QCD contributions into the e+e?-annihilation Adler function and the generalized Crewther relations

The generalized Crewther relations in the channels of the non-singlet and vector quark currents are considered. These relations follow from the double application of the operator product expansion approach to the same axial vector-vector-vector triangle amplitude in two regions, adjoining to the angle sides (x, y) (or p ², q ²). We assume that the generalized Crewther relations in these two kinematic regimes result in the existence of the same perturbation expression for two products of the coefficient functions of annihilation and deepinelastic scattering processes in the non-singlet and vector channels. This feature explains the conformal symmetry motivated cancellations between the singlet α _s ³ corrections to the Gross-Llewellyn Smith sum rule S _GLS of νN deep inelastic scattering and the singlet α _s ³ correction to the e ⁺ e ⁻-annihilation Adler function D _A ^V in the product of the corresponding perturbative series. Taking into account the Baikov-Chetyrkin-Kuhn fourth order result for S _GLS and the perturbative effects of the violation of the conformal symmetry in the generalized Crewther relation, we obtain the analytical contribution to the singlet α _s ⁴ correction to the D _A ^V function. Its a-posteriori comparison with the recent result of direct diagram-by-diagram evaluation of the singlet fourth order corrections to D _A ^V function demonstrates the coincidence of the predicted and obtained ζ₃²-contributions to the singlet term. They can be obtained in the conformal invariant limit from the original Crewther relation. Therefore, on the contrary to previous belief, the appearance of ζ₃-terms in the perturbative series in quantum field theory gauge models does not contradict to the property of the conformal symmetry and can be considered as regular feature. The Banks-Zaks motivated relation between our predicted and the obtained directly fourth order corrections is mentioned. It confirms the expectation, previously made by Baikov-Chetykin-Kuhn, that at the 5-loop level the generalized Crewther relation in the channel of vector currents may receive additional singlet contribution, which in this order of perturbation theory is proportional to the first coefficient of the QCD β function.     

Vaidya Space-Time in Black-Hole Evaporation

We take a boundary-value approach to quantum amplitudes arising in gravitational collapse to a black hole. Pose boundary data on initial and final space-like hypersurfaces Σ _F,I , separated at spatial infinity by a Lorentzian proper-time interval T. Quantum amplitudes are calculated following Feynman's approach; rotate: T→|T|exp (−iθ) into the complex, where 0< θ≤π/2, and solve the corresponding well-posed complex classical boundary-value problem. We compute the classical Lorentzian action S _class and corresponding semi-classical quantum amplitude, proportional to exp (iS _class). To recover the Lorentzian amplitude, take the limit θ→ 0₊ of the semi-classical amplitude. For the classical boundary-value problem with given perturbative boundary data, we compute an effective spherically-symmetric energy-momentum tensor 〉 T ^μν〈 _EFF , averaged over several wavelengths of the radiation, describing the averaged extra energy-momentum contribution in the Einstein field equations, due to the perturbations. This takes the form of a null fluid, describing the radiation (of quantum origin) streaming radially outwards. The classical space-time metric, in this region of the space time, is of Vaidya form, justifying the adiabatic radial mode equations, for spins s = 0 and s = 2.     

High-order stimulated electronic Raman scattering from lithium vapor

An intense radiation at 395.0 nm has been observed when lithium vapor is optically pumped in a heat pipe with a pulsed dye laser whose output wavelength is tuned near the Li 2s–4s two-photon resonance transition. The radiation is emitted in the direction along the pump laser beam. It is proposed that the 395.0 nm radiation is mainly generated through three-photon excitation and one-Raman-photon scattering followed by two-cascade (spontaneous) emission. The overall reaction mechanism can be described by a parametric six-wave mixing process. The quantum efficiency of the observed process is estimated to be of the order of 2 × 10^–6.This work was partially supported by the USC Faculty Research and Innovation Fund     

Zeros of the helicity amplitudes of Σ−-p and Λ-p elastic scattering

The forces of interaction as reflected in the cosθ plane analytic structures of the helicity amplitudes of Σ⁻-p and Λ-p scattering are optimally exploited using the conformal mapping technique of Cutkosky and coworkers. A suitable parametrization of these amplitudes in the mapped variable is then chosen so that it can see the zeros better. These zeros are then located by making a good fit to the differential scattering cross-section curves. The effect of these zeros upon the cross-sections is discussed. Values for the phase shifts and coupling parameters between channels of fixedJ values are also computed.     

Anomalies, symmetries and strangeness content of the proton

The matrix elements of the operators of strange quark fieldssГs where Г is 1 orγμγ ⁵ between a proton state is calculated. The sigma term is found to be ≈ 41 MeV and theSU(3) singlet axial matrix element is found to be ≈ 0.22, both in agreement with experiment. The sigma term is found using the trace anomaly, while the determination of the axial vector current matrix element is from QCD sum rules. These correspond to (ie.943-1)≈ 0.12 and for the axial current Δs ≈ −0.12, respectively. The role of the anomalies in maintaining flavor symmetry in the presence of substantial differences in quark masses is pointed out. This suggests that there is no need to invoke an intrinsic strange quark component in the proton wave function.     

A semi-empirical formula for the neutron total cross section and the interpretation of the empirical formula forA ⩾ 40

Weaknesses in Angeli and Csikai’s interpretation of their empirical formula for the neutron total cross section (σ _T) are pointed out. Using the Fourier-Bessel re-presentation of the scattering amplitude a semi-empirical formula forσ _T is obtained which has greater applicability and also explains the success of the empirical formula for mass numberA ⩾ 40 in terms of the established trends in neutron optical potential parameters.     

ΛN Space-exchange effects in thes-shell hypernuclei and Λ 9 Be

Variational Monte Carlo calculations of the ground state separation energiesB _Λ of thes-shell hypernuclei and also of _Λ ⁹ Be have been made for an Urbana-type central space-exchange ΛN potential consistent with Λp scattering, and also including three-body ΛNN forces. Thes-shell hypernuclei are treated asA-body systems (A = baryon number), and _Λ ⁹ Be is analysed as a partially nine-body problem in the Λ — 2α model. The reduction ofB _Λ due to the space-exchange ΛN potential has been calculated for thes-shell hypernuclei for a range of interactions: both ΛN and ΛN + ΛNN forces. ForA = 3,4,5 the exchange energy is approximately, 0.04, 0.15 and 0.50 MeV, respectively. For _Λ ⁹ Be a much more limited study gives ≅ 1.3 MeV. These values are much larger than that for ‘soft’ ΛN +NN potentials when the correlations are weak. Preliminary results were presented at the DAE Symp. on ‘Nuclear Physics’ Vol. 32B (1989).     

Coulomb and strong interactions for Bose-Einstein correlations

We present an analytical formula for the Bose-Einstein correlations (BEC) which includes effects of both Coulomb and strong final state interactions (FSI). It was obtained by using Coulomb wave function together with the scattering partial wave amplitude of the strong interactions describing data on thes-wave phase shift. We have proved numerically that this method is equivalent to solving Schrödinger equation with Coulomb and thes-wave strong interaction potentials. As an application we have analysed, using our formula which includes the degree of coherence and the long range correlation, the data fore ⁺ e ^? annihilations. We have found that the degree of coherence present in our formula approaches approximately unity whereas the long range correlation parameter becomes approximately zero. These results suggest that the physical meanings of the fractional degree of coherence and the long range correlation observed in various other analyses can most probably be attributed to FSI.