The predissociation of the 2σ u −1 (c 4Σ u − , v states of the oxygen molecular ion

The dynamics of predissociation of the 2σ _u ^?1 (c ⁴Σ _u ^? ), v vibrational states of the O ₂ ⁺ ion was studied theoretically using the method of coupled differential equations. The main equations describing the vibrational motions of nuclei in the adiabatic and diabatic approximations are given. The applicability scope of approximate methods for solving these equations was studied. The predissociation widths for the v = 0 and 1 vibrational levels were found to be Γ₀ = 0.054 meV and Γ₁ = 9.71 meV. This substantiated the results of recent observations of neutral fragments formed after the dissociation of the O₂ molecule. About 99% of the O ₂ ⁺ ions in the 2σ _u ^?1 (c ⁴Σ _u ^? ), v states were found to decompose to the O(¹ D) + O⁺(⁴ S) dissociation products.     

Calculation of molecular constants for the X 1Σ g + , A 1Σ u + , B 1Πu, and a 3Σ u + electronic states of 39K2

The molecular constants are calculated for the X ¹Σ _g ⁺ , A ¹Σ _u ⁺ , B ¹Π_u, and a ³Σ _u ⁺ and electronic states of a potassium dimer. The wave functions and vibrational energies necessary for calculating the molecular constants are determined by solving the radial wave equation with the use of potential energy curves constructed by the semiempirical method. The vibrational terms, the rotational constants, and the centrifugal distortion constants calculated from the potential curves are compared with those determined from the experimental data.     

Study of the absorption characteristics of molecular oxygen in the Schumann-Runge system at high temperatures: II. Experiment and comparison with calculation

Absorption cross sections of oxygen molecules in the UV spectral range are experimentally determined in the temperature range 1600–6000 K. The absorption cross sections are measured in oxygen or in its mixtures with argon behind the shock wave front. Measurements are performed for the spectral range 190–270 nm, which pertains to the electronic transition X ³Σ _g ^? → B ³Σ _u ^? of the Schumann-Runge system. The absorption cross sections are also measured at temperatures 291 and 3300 K in the range 160–185 nm. The measured absorption cross sections are compared with the calculated spectra of the O₂ molecule.     

Ab initio calculation of transition dipole moments for transitions between valence states in oxygen molecules

Results of ab initio calculations of potential-energy curves for 20 singlet and 20 triplet valence states of oxygen with configuration interaction taken into account in the 6-31G basis are presented. Transition dipole moments of triplet-triplet (1³Π_g ← B ³Σ _u ^? , 1³Π_g ← A ³Σ _u ⁺ , 1³Π_g ← A′ ³Δ_u, B ³Σ _u ^? ← X ³Σ _g ^? , 2³Π_u ← 1³Π _g, 2³Σ _g ^? ← B ³Σ _u ^? , 1³Π_u ← X ³Σ _g ^? , 2³Π_u ← X ³Σ _g ^? , 2³Π _g ← A′³Δ_u, 3³Π_g ← A′ ³Δ _u, 2³Δ_u ← 2³Π_g, 3³Π_g ← B ³Σ _u ^? , and 2³Π_g ← A ³Σ _u ⁺ ) and singlet-singlet (2¹Σ _g ⁺ ← 2¹Π_u, 2¹Π_u ← 1¹Π ^g, ¹Π_u ← 2¹Δ_g, 1¹Π_g ← c ¹Σ _u ^? , ¹Π_u ← b ¹Σ _g ⁺ , 1¹Δ _u ← a ¹Δ_g, 2¹Π_u ← a ¹Δ_g, 2¹Δ_g ← 1¹Δ_u, ¹Π _u ← a ¹Δ _g, 1¹Π_u ← b ¹Σ _g ⁺ , 2¹Π_g ← 1¹Π_u, 2¹Π _g ← c ¹Σ _u ^? , 1¹Δ _u ← 1¹Π _g, f′Σ _u ⁺ ← b ¹Σ _g ⁺ , 2¹Σ _g ⁺ ← f ′¹Σ _u ⁺ , 3¹Π_g ← 1¹Δ_u) radiative transitions are calculated as functions of internuclear separation. The possibility of observing these transitions under experimental conditions is discussed.     

Observation of perturbations in the rovibronic transition probabilities for the (4d)r 3Π g − , (4d) s 3 Δ g − → (2p) c 3Π u ± band systems of the H2 molecule

The ratios of the radiative transition probabilities for the lines of the P, Q, and R branches of the (4d)r ³Π _g ^? , (4d)s ³Δ _g ^? → (2p) c ³Π _u ^± band systems of the H₂ molecule have been measured for the first time. Significant (to two orders of magnitudes) differences are found between the experimental values and the adiabatic theory predictions. It is established that the results of the nonadiabatic calculation performed by us in the pure-precession approximation taking into account the electronic-rotational interaction of the 4d ³Π_g and 4d ³Δ_g states are in agreement with the experimental data. The optimal energies of rovibronic levels of the r ³Π _g ^? , s ³Δ _g ^? , c ³Π _u ^? , and c ³Π _u ⁺ states have been found and reidentification of 11 from 54 spectral lines, assigned previously to the (0-0) and (1-1) bands, was performed.     

Comparative study of the semiempirical three-parameter potential energy functions for diatomic molecules

A comparative study is made of four three-parameter semiempirical potential energy functions for 32 electronic states of diatomic molecules and their ions:n ₂:X¹gS _g ⁺ ,B ³π_g,A ³ gS_u,C ³ _u,B′ ³ gS_u.a ¹ π_g, a′gS _u ^? ,Ω ¹δ_u N ₂ ⁺ :X ² gS _g ^gS +A ² π,C ² gS _u ⁺ ,B ² gS _u ⁺ CO:X¹gS⁺,a ³ π, a′³ gS_u,e ³ gS^?,d ³gD₁,A ¹π CO⁺:X²gS⁺,A ² π,B ²gS⁺ O₂:X³gS _g ^? ,B ³ gS_u,c ¹ gS _u ^? ,b ¹gS _g ^s ,a ¹ δ_g,c ³ δ_u O ₂ ⁺ :X ²π_g,A ² π_g, a¹ π_g,b ⁴ gS _g ^? A program for numerically integrating the radial Schrödinger equation by the Cooley method is worked out. Certain additional units are introduced to conserve computer time. The resulting vibrational levels are compared with the experimental levels for all the electronic states studied. It is concluded on the basis of this analysis that it is not possible to describe equally well all the electronic states of various molecules on the basis of any single three-parameter potential function. A method for choosing a potential function for describing some particular electronic state of a diatomic molecule is proposed.     

Investigation of N 2 + (C 2Σ u + → X 2Σ g + fluorescence excited through auger decay of the 1s −1π* resonance

A theoretical investigation of N ₂ ⁺ (C ²Σ _u ⁺ → X ²Σ _g ⁺ molecular fluorescence excited through the Auger decay of the 1s ^?1π* resonance is carried out. The fluorescence cross sections are calculated with due regard for the dependence of the matrix element of the C → X dipole transition on the internuclear distance, the interference between channels of excitation via different vibrational levels v _r of the 1s ^?1π* resonance, the rotational structure of the fluorescence band, and the predissociation of the N ₂ ⁺ C ²Σ _u ⁺ v′ ≥3) states. The calculated cross sections are in good agreement with the experimental results of recent measurements. The results of the calculations have demonstrated that the observed dependence of the cross section of the (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″) fluorescence on the excitation energy and the fluorescence wavelength for a group of bands with equal values of the difference Δv = v′ ? v″ is associated with transitions between the vibrational levels of the electronic states involved in the excitation and subsequent cascade decay of the 1s ^?1π* resonance: N₂ (v ₀ = 0) → N*₂(1s ^?1π*(v _r)) ? N ₂ ⁺ : (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″).     

Study of the lowest electronic states of Xe2, XeKr, and XeAr molecules by the method of multiphoton resonance ionization

The spectra of Xe₂, XeKr, and XeAr molecules in the range 66 500–68 800 cm^?1 are obtained by the methods of (2 + n) and (3 + n) (n = 1, 2, 3) resonance multiphoton ionization during the registration of molecular and atomic ions. The combining of two-and three-photon resonance excitations of Xe₂ molecules makes it possible to obtain the spectra caused by transitions from the ground state X0 _g ⁺ to the excited states of Xe*6s[3/2] _1,2 ^o Xe¹ S ₀ molecules both of the even (0 _g ⁺ , 1 _g ) and of the odd (B0 _u ⁺ , B′1 _u , 2 _u ) symmetries. The data on the Ω = 2 _u state of the Xe₂ molecule with the dissociation limit Xe*6s[3/2] ₂ ^o + Xe¹ S ₀ and on the Ω = 1 state of the XeAr molecule with the dissociation limit Xe*6s[3/2] ₁ ^o + Ar¹ S ₀ are obtained for the first time. The potential curve of the excited 2 _u state of the Xe*6s[3/2] ₂ ^o Xe¹ S ₀ molecule is repulsive and intersects the potential curve of the B0 _u ⁺ state of the Xe*6s[3/2] ₁ ^o Xe¹ S ₀ molecule. In the case of the three-photon excitation, it is observed that all the bands in the spectra of XeKr and XeAr molecules are broadened and are shifted, which indicates that, in an intense light field, the influence of the dynamic Stark effect is significant.     

Stoßdissoziation von H 2 + - und D 2 + -Ionen

The angular and energy distribution of protons produced by collision-induced dissociations of H ₂ ⁺ ions with energies of 10 and 20 keV were measured in a parabola spectrograph. From these measurements the velocity distribution of the protons in the center of mass system of the H ₂ ⁺ ion can be calculated. This gives information about the type, the abundance, and the anisotropy of the processes involved. The most frequent transitions leading to dissociations are the excitation of the 2pσ_u state, the ionisation of the H ₂ ⁺ ion, the transition into the vibrational continuum, and the electron capture into the 1³ σ _u ⁺ state of the hydrogen. It is shown that the cross section for an electronic transition depends on the velocity of the ion, the distance of the nuclei in the ion, the angle between the internuclear axis and the direction of the primary ion beam, and the excitation energy of the target. The fraction of protons produced by vibrational excitation increases with increasing atomic number of the target. Concerning electronic transitions D ₂ ⁺ ions equal H ₂ ⁺ ions of the same velocity.     

The effect of air impurities on pure neon luminescence

The luminescence decay curves of the 2p ₁ level of the NeI atom (the transition 3p??[1/2]₀?3s??[1/2] ₁ ^° , ?? = 585.2 nm) and the B ²?? _u ⁺ level of the N ₂ ⁺ molecule (the transition B ²?? _u ⁺ (?? = 0)?X ²?? _g ⁺ (??? = 0), ?? = 391.4 nm) in pure and air-containing neon are measured. The gas was excited by electron beam pulses (E _e = 150 keV, ?? = 5 ns, I _max = 500 A). It is shown that the molecular gases contained in air strongly quench the long-lived component of neon luminescence exciting due to dissociative recombination of Ne ₂ ⁺ molecular ions. The relative light yield at a wavelength of 585.2 nm as a function of the partial pressure of air in neon is determined to be ?? = (1+ 2??p)^?1, where p is the air pressure in Torr.     

Electron-vibrational energy exchange in collisions of electronically excited N2(A 3Σ u + ) molecules with Zn(X 1 S) atoms

The interaction matrix between the N₂ molecule in the X ¹Σ _g ⁺ and A ³Σ _u ⁺ states and the Zn atom in the ¹ S and ³ P states calculated earlier by the asymptotic method was used to find the rate constants for the electron-vibrational energy exchange N₂(A ³Σ _u ⁺ , v) + Zn(¹ S) → N₂(X ¹Σ ₈ ⁺ , v′) + Zn(³ P). The calculations were performed by the transition state method, and the probabilities of transitions between intersecting electron-vibrational terms of the system in motion along the reaction coordinate were determined by the Landau-Zener equation. The calculated electron excitation transfer constants between N₂(A ³Σ _u ⁺ , v = 1, 0) and Zn(¹ S) over the temperature range 300–900 K were on the order of 10^?11?10^?12 cm³/s.     

Spectroscopy of molecular ions: Laser induced predissociation of O 2 +

The technique of laser induced predissociation and laser induced fluorescence is applied to study spectra of gas-phase molecular ions. The main feature of the experiment is a beam of mass selected molecular ions illuminated by a pulsed dye laser. Over an extended range of excitation energies spectroscopic information can be obtained about positive and negative ions including transient species. As a first result we present predissociation spectra of O ₂ ⁺ ,b ⁴ bE _g ^? ?a ⁴ π _u Δv=3 andgDv=2 which can well be simulated by calculated spectra assuming a rotational ion temperature of 300δK.     

Nuclear bremsstrahlung and electron-positron pair creation in heavy-ion collisions

Nuclear bremsstrahlung is investigated as a background effect in the X-ray-spectroscopy of superheavy electronic molecules. The intensity ratio between electric dipole and quadrupole radiation as function of frequency is given. The total cross section for electron-positron pair creation due to conversion of bremsstrahlungs-photons was found to beσ=3.8·10^?8b for the ₅₄ ¹³² Xe- ₉₂ ²³⁸ U system andσ=5.8·10^?8b for the ₉₂ ²³⁸ U? ₉₂ ²³⁸ U system at the Coulomb barrier. This demonstrates that bremsstrahlung pair creation can be neglected compared with the induced positron production in overcritical quasimolecules.     

The production and loss ofN 2 + ions in the nitrogen afterglow

The time dependence of the number density of nitrogen ions was studied in the pressure range of about 0.1 to 1.7 Torr by means of mass spectrometric probing of decaying nitrogen plasmas. The analysis of theN ₂ ⁺ decay curves showed thatN ₂ ⁺ ions are produced in the afterglow by collisions between metastable nitrogen molecules. Energy level and radiative lifetime considerations indicate that one of the metastable molecules is in thea′ ¹∑ _u ^} state, while the other metastable molecule may be in the same state or in theA ³∑ _u ⁺ or³ Δ _u state. The surface catalytic efficiency for de-excitation of the metastable molecules involved upon striking the molybdenum covered plasma container walls was estimated to be smaller than 2×10^?3 at a pressure of 0.09 Torr. If both interacting metastable molecules are in the a′¹ bE _u ^} state the measurements result in a value of 1.3×10^?18 cm² for the cross section for destruction of this state by collisions with ground state nitrogen molecules.     

Electronic branching ratios of spontaneous emission for transitions between states of the 3d and 2p singlet complexes of terms of H2

The ratios of probabilities (the electronic branching ratios) for the rovibronic spontaneous transitions are for the first time measured for transitions from the rotational levels with J′≤6 of the I ¹Π _g ^? , v′=0–2 and J ¹Δ _g ^? , v′=0 states to the vibrational-rotational levels of different low-lying electronic states B ¹Σ _u ⁺ , v″, J′ and C ¹Π _u ^? , v?, J′?1 of the H₂ molecule (for the vibrational quantum numbers v″≤4 and v?≤2). Values of these quantities provide a new channel of information on the internal structure of the hydrogen molecule thus far unused and should be particularly sensitive to the adiabatic values of the electronic transition dipole moments. In studying the entire set of rovibronic radiative transitions, they may significantly add to the experimental data on rovibronic terms, radiative lifetimes, and vibrational and rotational branching ratios used before. The experimental data obtained are compared to the corresponding values derived from the results of an earlier semiempirical determination and ab initio calculation of the absolute transition probabilities. Our experimental data are in remarkable agreement with the semiempirical results and significantly differ from the ab initio results. This fact directly suggests the necessity of performing more accurate ab initio calculations of the rovibronic transition probabilities for the given systems of bands.     

Some structural features induced by the space-time metrical fluctuation in the theory of gravitational fields

Under the assumption that the so-called space-time fluctuationy(x) in a classical sense, attached to each point of the gravitational field at some microscopic stage, is summarized as the metrical fluctuation in the formg _λκ (x)=g_λκ (x)·exp2σ(y(x)), some new physical aspects induced by the conformal scalarσ(x) (≡σ(y(x))) are found: By introducing the torsionT _κ ^λμ (x) from a general standpoint, the resulting micro-gravitational field is made to have a conformally non-Riemannian structure, where a special form ofT _κ ^λμ (i.e.,T _κ ^λμ =δ _κ ^λ σ_μ?δ _κ ^μ σ_λ(σ_μ=?σ/?x ^μ)) shows some peculiar features. An averaging process with respect toy is taken into account, by which the spatial structure of the corresponding macro-field is shown, in general, to have a somewhat “non”-Riemannian structure due to the contributions of the torsionT _κ ^λμ .     

Stoßdissoziation von H 2 + -Ionen

Inelastic collisions between the hydrogen molecule ion and the hydrogen molecule leading to dissociation are investigated experimentally in the energy range between 3 and 20 keV. The velocity distributions of the protons produced in these processes are compared with calculated distributions using a Born approximation formula. The calculation takes into account the excitation of the 2pσ _u state of the H ₂ ⁺ and a possible simultaneous excitation of the target. It can be shown, that the quantitative knowledge of these processes makes possible a satisfying explanation of the measured distributions. In general a good agreement is obtained between theory and experiment concerning both energy and angular dependence of the velocity distributions.     

Mechanism by which a single water molecule affects primary charge separation kinetics in a bacterial photosynthetic reaction center of Rhodobacter sphaeroides

Using quantum-chemical methods, we have studied the role played by water molecules W-A and W-B that are bound by hydrogen bonds to accessory bacteriochlorophyll molecules B _A and B _B in the process of primary charge separation in the reaction center of Rhodobacter Sphaeroides. We have found that the occurrence of a rotational mode of the W-A molecule at 32 cm^?1 and/or its harmonics in stimulated emission of an electron donor P* and the dynamics of population of the states P⁺B _A ^? and P⁺H _A ^? may be related to the structural heterogeneity of the reaction center and the existence of a conformation in which the W-A molecule is predominantly involved in one hydrogen bond (with BA). Based on the calculated redox potentials B _A and P, it has been shown that the appearance of the W-A molecule in the reaction center reduces the energy of the P⁺B _A ^? state by ??600 cm^?1. This is somewhat smaller than the influence of the amino-acid residue Tyr^M210 (??870 cm^?1) and correlates well with a substantial decrease in the electron transfer rate in mutant forms of reaction centers GM203L (which do not contain W-A molecules) and YM210F (in which Tyr^M210 is replaced with Phe). The data obtained allow us to suggest that rotation of the water molecule with a fixed position of its H atom that is involved in a hydrogen bond with the keto carbonyl group of B _A is initiated due to the charge separation between the halves of special pair P and the formation of the state P _A ⁺ P _B ^? . The large effect of this rotation on the kinetics of population of the states P⁺B _A ^? and P⁺H _A ^? after the excitation of P is quite consistent with its influence on the energy of the state P⁺B _A ^? .     

Comparison of semiempirical and ab initio absolute probabilities of rovibronic transitions for the I 1Π g − , J 1Δ g − →C 1Π u ± system of bands of the H2 molecule

The absolute values of probabilities of the I ¹Π _g ^? , v′, J′; J ¹ Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ spontaneous transitions in the H₂ molecule (for the vibrational and rotational quantum numbers v′=v″=0–3, J′=1–6, and J″=J′, J′ ±1) are calculated by using ab initio and semiempirical data on the dipole moments of the 3dπ ¹Π_g, 3dδ¹Δ_g→2pπ¹Π_u electronic transitions. In both cases, the calculations are performed both in the adiabatic approximation and with an allowance for the nonadiabatic effect of electronic-rotational interaction. The coefficients of expansion of the wave functions of perturbed rovibronic states in the Born-Oppenheimer basis functions used in the calculations were obtained in the approximation of pure precession from experimental values of the terms. It was found that the values of transition probabilities based on the ab initio calculations systematically exceed the corresponding semiempirical data by a factor of 1.2–1.9 for the I ¹Π_g→C ¹Π _u ^± transition and by a factor of 1.4–1.6 for the J ¹Δ _g ^? →C ¹Π _u ^± transition. It was established that the difference between the ab initio and semiempirical values of electronic transition moments virtually has no effect on the dependence of the transition probabilities on the vibrational quantum numbers. The discrepancies between the results of adiabatic and nonadiabatic calculations are significant and reach two orders of magnitude, which is indicative of the important role of perturbations in the probabilities of the transitions considered.     

CP violation in decay rates of charged bottom mesons

In the standard theory we discuss a mechanism of interference between two different tree-level charged current amplitudes to induce CP violation. The asymmetry between conjugate Cabibbo disfavoured modes of charged bottom meson decays is considered. Estimates for two-body decays ofB _u andB _c are presented. We find thatB _u ^? →D ^?+D ₀ ^* , for instance, can give a big CP asymmetry with values ≈1–50%, depending on the angle and phase parameters.