Twenty-parameter eigenfunctions and energy values of the 23 S States of He and He-like Ions

Twenty-parameter calculations of the energies and wave functions of the first excited states 2³ S of He, Li⁺, Be⁺⁺, B⁺⁺⁺, O⁶⁺, Ne⁸⁺, Mg¹⁰⁺, have been carried out using Hylleraas' method. The energy values have been corrected for mass polarization. The coefficients of the best wave functions are listed. Similar calculations for the 2³ S state of the H^? ion yield an energy value which cannot be distinguished from the energy of a free H atom. For He and Li⁺, in addition, forty-parameter calculations have been carried out. The results compare well with the recent calculations of Pekeris using a somewhat different method. Even after the inclusion of the relativistic correction, the theoretical energy values deviate slightly from the observed. The differences, ?0·10±0·05 cm^?1 for He and ?1·07±0·10 cm^?1 for Li⁺, represent observed values of the Lamb shifts in the 2³ S states. These values agree within their uncertainties with the values predicted from quantum electrodynamics.     

Interaction induced light scattering in orientationally disordered crystals: the translational phonon region

We have derived an expression for the light scattering spectrum of a crystal in which the mechanically regular sites are occupied by point polarizable orientationally disordered molecules when the polarizabilities are assumed to depend on the positions of the surrounding atoms (interaction induced polarizability fluctuations).

Owing to the ‘electrical’ disorder properties of the system all phonons can contribute to the anisotropic scattering measured in all polarization configuration with wavevector, branch index and polarization dependent coefficients. Assuming short range interaction induced polarizabilities we show that the temperature reduced intensity I(ω)/[n(ω) + 1] is given by a superposition of the Brillouin zone centre symmetry ‘projected’ density of states with polarization dependent coefficients. These coefficients are found to be essentially frequency independent for all the projections, exception made for those corresponding to the acoustic phonons. For the acoustic branches the coefficients vanish in a first approximation. They can however be treated on more rigorous grounds and, as already found by other authors, their contribution is proportional to the density of states multiplied by ω².

In addition zone centre (k?0) totally symmetric phonons can also be present in the ‘isotropic’ term (which appears only in the polarized VV configuration).

A procedure is suggested to obtain the total density of states from the spectra measured in different polarization configurations.     

Double resonance interference in third-order light mixing

The first observation of interference effects between two sharp resonant contributions to the third-order nonlinear susceptibility χ₍₃₎ (ω₃=ω₀+ω₁?ω₂) is reported. Using two tunable near ir frequencies, ω₀=ω₁ and ω₂, the was seen in crystalline CuCl when 2ω₁ and ω₁?ω₂ were close to the sharp Z₃ exciton at 3.21 eV and the 210 cm^-1 Raman line, respectively. Three different tunable visible frequencies were used to observe similar interference effects in a benzene-cyclohexane mixture when ω₀?ω₂ and ω₁?ω₂ were close to the 992 cm^-1 Raman line of benzene and the 801 cm^-1 Raman line of cyclohexane, respectively.     

柱形量子点中弱耦合磁极化子的性质

应用线性组合算符方法和幺正变换方法,研究在抛物势作用下的柱形量子点中磁极化子的性质。对ZnS量子点的数值计算表明,量子点中磁极化子的基态能量随特征频率、回旋共振频率的增大而增加,这是由于特征频率增加时振动能量、回旋共振频率增加时外磁场中的附加能量增加所致。当特征频率(或回旋共振频率)增加到某一值时,磁极化子能量由负变为正。基态能量随柱高的减小而增加,且柱高越小,增加越快;当柱高减小到某一值时,磁极化子能量也由负变为正。总之,柱形量子点中的磁极化子,其基态能量与量子点的尺度、外磁场、特征频率等有关。     

Regium bonds formed by MX (M═Cu,Ag, Au; X═F,Cl, Br) with phosphine-oxide/phosphinous acid: comparisons between oxygen-shared and phosphine-shared complexes

ABSTRACT

Regium bonds interaction between phosphine oxide (H₃PO), the trans phosphinuous acid (T-PH₂OH), the cis phosphinuous acid (C-PH₂OH) and MX (M═Cu, Ag, Au; X═F, Cl, Br) complexes were investigated by means of ab initio MP2/aug-cc-pVTZ method. For phosphinuous acid and MX complexes, two types of regium bonded interaction (trans and cis complexes) are observed and the two types of structures are very easily transformed from one type to another due to a low energy barrier. The molecular interaction energies are in the order of Au?>?Cu?>?Ag, F?>?Cl?>?Br and increase with the decrease of intermolecular distance R_int. Two resonance-type structures of P:M-X (ωI) ? P–M:X (ωII), O:M-X (ωI) ? O–M:X (ωII) are recognised by the natural resonance theory (NRT) and the natural bond orbitals (NBOs) analysis. The competition between ωI ? ωII resonance structures mainly arises from hyperconjugation interactions, in all phosphor-shared complexes, P–M:X resonance accounts for a larger proportion which leads to the covalent characters. All of complexes have been described in terms of their electron density properties.     

Static polarizabilities of helium and alkali atoms,and their isoelectronic ions

A rather simple method of calculation of the scalar and tensor components of static polarizability was developed for a wide range of atoms and ions. The general formulas for polarizabilities of SL terms, J levels, and F components of hyperfine structure are given. The results of calculation for ground and some excited states of He and alkali atoms (Li, Na, K, Rb, Cs) are presented. The comparison of the results with available theoretical and experimental data shows that, in most cases, the differences do not exceed 10%. The polarizabilities for the Li+, Be+, B²+, C³+, Ne⁷+, Mg+, Al²+, Si³+, Ar⁷+, Ca⁺, Sc²+, Ti³+, Sr⁺, and Ba⁺ ions are also given.     

ϱ-ω interference in π−p → π−π+ n at 17.2 GeV

Results are presented of a study of ?-ω interference effects in high statistics, good resolution, π^?p → π⁺π^?n data obtained at 17.2 GeV using the CERN-Munich spectrometer. We investigate the t dependence of ?-ω interference in the various ππ production amplitudes. While effects are observed in all the P-wave production amplitudes, the most pronounced structure occurs in the natural parity exchange amplitude in the t interval 0.1 ? ?t ? 0.4 GeV². Under certain assumptions we determine the relative magnitudes and phases of the ?- and ω-production amplitudes as functions of t.     

Transitions between Zeeman substates of excited He I levels induced by electric radiofrequency fields

Making use of the large tensor polarizabilities of excited He I levels, transitions between Zeeman substates of 1snd ¹ D ₂ levels have been induced by electric radiofrequency fields after ion-impact excitation of He atoms. Resonance signals have been observed near the Larmor frequencyω=ω _L as well as nearω=2ω _L . These signals are interpreted as 2-quantum electric-dipole (2E1) transitions and 1E1 transitions, respectively, between the Zeeman sublevels withM=0 andM=±2. The interaction of this 3-state system {¦M〉;M=?2, 0, +2} with the applied external fields (magnetic fieldH _z and static and alternating electric field?=? ₀+? ₁ cosω t) is discussed. The shape of the resonance signals has been evaluated in the rotating field approximation. In contradiction to the theory, the observed signals show a peculiar narrow structure at the center of the signal which is not yet completely understood. The experimental techniques developed are expected to be useful for investigations of Zeeman-, Stark-, fine and hyperfine splittings of excited He I levels.     

Nonlinear susceptibilities of vapors and solutions of organic dyes

Results of theoretical studies of laser and Kerr nonlinear susceptibilities of vapors and solutions of organic dyes using a series of polycyclic arenes as an example are presented. Nonlinear susceptibilities of the third χ⁽³⁾ (?3ω; ω, ω, ω) and the fifth χ⁽⁵⁾ (?3ω; ω, ω, ω, ω, ?ω) orders of a series of organic dyes responsible for third harmonic generation of Nd:YAG laser radiation are calculated within the context of the free electron model. Results of calculations of their Kerr third-order nonlinear susceptibilities χ⁽³⁾ (?ω; ω, ?ω, ω) and non-linear refractive indices n ₂ are presented. The calculation results are compared with experimental data on third harmonic generation in naphthalene vapors and with χ⁽³⁾ (?ω; ω, ?ω, ω) as well as n ₂ of paraterphenyl and naphthalene solutions.     

Feldgleichungen der TREDERschen Gravitationstheorie,die aus einem Variationsprinzip ableitbar sind. I

In the frame work of TREDER 's gravitational theory we consider two classes of field equations which are derivable from two classes of LAGRANGE ian densities Ω⁽¹⁾(ω₁, ω₂), Ω⁽²⁾(s?₁, s?₂). ω₁, ω₂; s?₁, s?₂ are parameters. Ω⁽²⁾(ω₁, ω₂) gives us field equations which are up to the post-NEWTON ian approximation in the sense of NORDTVEDT , THORNE and WILL equivalent to the field equations given by BRANS and DICKE . For ω₂ = ?1 ?2ω₁ field equations follow from Ω⁽¹⁾(ω₁, ?1 ?2ω₁) which are in the above mentioned sense of post-NEWTON ian approximation equivalent to EINSTEIN 's equations. The field equations following from Ω⁽¹⁾(ω₁, ω₂) have a cosmological model with the well known cosmological singularities for T → ± ∞ in case that ω₁/(1 +3ω₁ +ω₂) ? γ > 0. For ω₁/(1 +3ω₁ +ω₂) ≤ 0 cosmological models with no cosmological singularities exist. From Ω⁽²⁾(s?₁, s?₂) we obtain field equations which at the best give us perihelion rotation 7% above EINSTEIN 's value and light deflection 7% below the corresponding EINSTEIN 's value. But in that case we are able to show the existence of a cosmological model without any cosmological singularity.     

The mixing of metastable states of barium atoms induced by the ac Stark effect

It is shown that the study of the ω-ρ⁰ interference pattern in J/ψ → (ρ⁰+ω)η → π⁺ π^? η decay provides evidence for a large (nearly 9°) relative phase between the one-photon and the three-gluon decay amplitudes.     

The energy dependence of single particle spectra in e+e− annihilation

We present explicit predictions of the statistical bootstrap model for inclusive single particle spectra in e⁺e^? annihilation. The distribution (ω/σ_tot·E) (dσ/p² dp) is found to become, for E ? 3 GeV, a function only of the secondary energy ω, independent of the incident e⁺d^? energy E.     

Influence of the sum frequency on optically pumped parametric amplifiers

Parametric traveling-wave interactions are calculated with the aid of a plane wave approximation, considering the 4 frequencies ω _s , ω _p , ω _I =ω _p ?ω _s and ω _Σ =ω _p +ω _s . Special attention is paid to the case where ω _p ?ω _s . Competition between parametric amplification and upconversion is studied as a function of phase matching and the results are illustrated by means of numerical examples. It is shown that parametric gain disappears if the linear combination of wave vectors, 2k _p-k_I-k_Σ, vanishes. In this situation upconversion with power gain up to about (ω _Σ /ω _s )² is possible. It is concluded that fork _p?k_s the sum frequency ω _Σ can significantly influence parametric forward amplification but does not affect backward wave amplification.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Helium/hydrogen synergistic effect in reduced activation ferritic/martensitic steel investigated by slow positron beam

Here, we investigated the irradiation defect in reduced activation ferritic/martensitic steels by slow positron beam. Three ion-irradiation experiments were carried out: (i) He²⁺ irradiation, (ii) H⁺ irradiation and (iii) He²⁺ irradiation followed by H⁺ irradiation, at temperature 450?°C. The presences of vacancy defects, represented by ?S_He+H parameter, induced by sequential irradiations was larger than the sum of defects, ?S_He parameter + ?S_H parameter, caused by single He ions and single H ions. The synergistic effect of He and H was confirmed clearly from the perspective of positron annihilation spectroscopy.     

On the enhancement of the nonlinear frequency transformation in periodic media

It is theoretically shown that an enhancement of the nonlinear frequency transformation in a periodic medium occurs under definite conditions if it is accompanied by light diffraction in this medium. The enhancement of the phase-matched frequency transformation occurs if the harmonic frequency ω approaches the stop band frequency ω_e. In the nondepleted pump approximation the corresponding increase of the harmonic intensity is proportional to ω_e(ω?ω_e)^?1 and is restricted by a quantity proportional to the fourth power of the sample thickness. The formulas for the enhancement of second harmonic generation are presented.     

The process e + e − → ωπ0 near the Φ resonance

The reaction e ⁺ e ^?→ωπ⁰ near a Φ resonance was studied with a spherical neutral detector at VEPP-2M e ⁺ e ^? collider. Both main modes of decay of a ω meson were investigated: ω→π⁺π^?π⁰ and ω→π ⁰γ. The probability of decay Φ→ωπ⁰ was obtained from the magnitude of the interference wave in the cross section for the reaction e ⁺ e ^?→ωπ⁰→ π⁺π^?π⁰π⁰: B(Φ→ωπ⁰) = (5.5 _?1.4 ^+1.6 ±0.3) ×10^?5. The ratio of the partial widths of the ω meson was obtained from the ratio of the cross sections for the two modes: Γ(ω→π⁰γ )/Γ(ω→π⁺π^?π⁰) = 0.0994 ± 0.0036 ± 0.0038.     

The “transition probability” in the state space of a 1-algebra

Let ω,? be two states of a 1-algebra and let us consider representations of this algebra R for which ω and ? are realized as vector states by vectors x and y. The transition probability P(ω,?) is the spectrum of all the numbers |(x,y)|² taken over all such realizations. We derive properties of this straightforward generalization of the quantum mechanical transition probability and give, in some important cases, an explicit expression for this quantity.