Non-adiabatic potentials for H2 +

In principle exact non-adiabatic pseudo-potentials for H₂ ⁺ and D₂ ⁺ are formulated in terms of the theory of conditional probability amplitudes in wave mechanics. Numerical results for the v = 0 and v = 1 (J = 0) states of H₂ ⁺ are derived from previously computed accurate non-adiabatic wave-functions. These results indicate that the non-adiabatic pseudo-potentials only differ from the adiabatic potential by small energies of the same magnitude as the non-adiabatic corrections to the adiabatic energy levels.     

Balmer Hβ vs. Dβ line intensity in the collisions of H+, H2 +, H3 +, D+, D2 +, and D3 + ions with “realistic” metal surface at energies below 1 keV

The intensities of hydrogen H_β and deuterium D_β spectral lines of the Balmer series were measured as a function of collision energy when H⁺, H₂ ⁺, H₃ ⁺, D⁺, D₂ ⁺, and D₃ ⁺ ions impinged on Al, Ti, Cu, Mo, W, and Pb targets. The collision energies were kept in the 100–1000 eV range. The target surface was contaminated with hydrocarbons from the vacuum pumping system and possibly also by oxygen molecules due to limited vacuum conditions. At projectile velocities above 200 km/s the luminescence of backscattered deuterium atoms is about 30–50% weaker than that of hydrogen atoms.     

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.     

Accurate rest frequencies of submillimeter-wave lines of H2D and D2H

We re-examined the submillimeter-wave transition frequencies of H₂D⁺ (J = 1₁₀ − 1₁₁ at 372.4 GHz) and D₂H⁺ (J = 1₁₀ − 1₀₁ at 691.7 GHz) to resolve suggested slight difference in velocity (v_LSR) of these species detected in the cold pre-stellar core 16293E recently. Both H₂D⁺ and D₂H⁺ were generated in a magnetically confined extended-negative glow discharge of a gaseous mixture of H₂/D₂/Ar. A combination of small improvements in various aspects of the measurements such as double modulation technique combined with a conventional frequency modulation and magnetic field modulation and more efficient signal accumulation method allowed us to improve signal-to-noise ratio, and thus to determine the transition frequencies more accurately. Both transition frequencies for the H₂D⁺ and D₂H⁺ lines have been thus determined to be 372421.385(10) and 691660.483(20) MHz, respectively. These precise rest frequencies suggest that the v_LSR of H₂D⁺ and D₂H⁺ in the pre-stellar core 16293E are indeed different as indicated in a recent astronomical observation. In addition, in this investigation, another transition of H₂D⁺ which falls in this frequency region, J = 3₂₁ − 3₂₂ transition, has been observed at 646430.293(50) MHz. As H₂D⁺ is a lightest asymmetric-top molecule and it is difficult to predict the rotational transition frequencies by using the effective asymmetric rotor Hamiltonian, any new observation of the rotational lines will be useful to improve the molecular parameters. The molecular constants for the ground state have been obtained for H₂D⁺ and D₂H⁺ by fitting these new measured frequencies together with the combination differences.     

P.E.HSQC: a simple experiment for simultaneous and sign-sensitive measurement of (1JCH+DCH) and (2JHH+DHH) couplings

The angular information content of residual dipolar couplings between nuclei of fixed distance makes the accurate and sign-sensitive measurement of (¹J_CH + D_CH) and (²J_HH + D_HH) couplings highly desirable. Experiments published so far are typically highly specialized for the effective measurement of a subset of couplings. The P.E.HSQC presented here, is an E.COSY based experiment which allows the simultaneous measurement of all heteronuclear and homonuclear couplings within CH, CH₂, and CH₃ groups in a single spectrum with the necessary precision and sign information. The simplicity of the approach and the absence of artefacts like phase distortions due to antiphase evolution make it ideally suited for coupling determination of organic molecules at natural abundance.     

An application of a representation theorem for entropy functionals

The vibrational predissociation of HD₂ ⁺ is modelled in terms of quantum-mechanical tunnelling through a minimal centrifugal barrier at given total angular momentum, J, and with statistical intermode coupling behind the barrier. It is shown that the observed strong preference for the H⁺ + D ₂ predissociation channel (over D⁺ + HD) is consistent with an experimental preference for J values in the range 0 < J < 25, a range which is also shown to be consistent with the observed H₃ ⁺ preferred range of kinetic energy release. A correlation between the total angular momentum and the kinetic energy release is also predicted.     

Morse Franck-Condon Factors and R-Centroids for Some Lyman Bands of H2, HD and D2

Using new rotational and vibrational constants, Morse Franck-Condon factors and r-centroids are computed for 108 Lyman bands of astrophysical importance H₂, HD and D₂ molecules. Experimental oscillator strengths conjoint with Morse Franck-Condon Factors for six Lyman bands of molecular hydrogen yield radiative lifetimes for v = 0–5 levels of the B 1σ_u ⁺ state that are inconsistent with the experimental lifetime measurements. The limitation of analytic Morse function in the region of small internuclear separation for the B 1σ_u ⁺ state of H₂ is discussed. The r-centroids (r_v′v″) are found to increase with frequencies of the Lyman bands of H₂, HD and D₂. For a sequence, Δr = r_{v′+1,v″+1} - r_v′v″ is constant. A comparison of r_v′v″ values of the Lyman bands shows that r_v′vv″ of the band (v′v″) increases in going from H₂ to D₂.     

Properties of the adiabatic energy curves for the ground states of H2+, HD+, and D2+

Equilibrium internuclear distances, energies, and force constants are reported for the diatomic molecules H₂⁺, HD⁺, and D₂⁺ at the adiabatic level of approximation. The differences between these values and those calculated previously at the Born-Oppenheimer level of approximation are analyzed.     

Calculation of the cross sections for the photoionization of H2 and D2 into different vibrational states of the ion

The dependence of the electronic transition moment on the internuclear distance is explicitly taken into account in the calculation of the photoionization cross section. Thus, the partial ionization cross sections for producing different vibrational states of the residual ion are obtained without invoking the Franck-Condon factor approximation. The exact electrostatic potential of H₂⁺, as well as the two-center Coulomb field, is used in the evaluation of the continuum wave function. The result can explain fairly well the ratios of the partial cross sections measured at 584 Å. The effect of the polarization of H₂⁺ due to the departing photoelectron is also studied and found to be small as far as the relative cross section is concerned. The total photoionization cross sections of H₂ and D₂ are compared with previous results obtained by other authors.     

Rotational excitation of H2 and N2 molecules by electron impact

The rotational excitation of the H₂ and N₂ molecules from (J→J+2,J=0) and (J→J+2,J=1) states by electron impact is studied, in the framework of the regional-plane-wave approximation. The empirical cut-off parameterρ, involved in these calculations, is varied to give the best fit to the experimental data of Srivastava and co-workers.     

Studies of the positive muon behavior in solid H2 and D2

Using a pulsed muon beam, we have investigated the microscopic μ⁺ behavior in solid H₂ and D₂ down to 0.6 K by the μ⁺SR method. From the studies of μ⁺ spin relaxation phenomena in solid para‐ H₂ and ortho‐ D₂, we have found that μ⁺ forms three distinct microscopic states; H₂μ⁺( D₂μ⁺)(20\sim25\%), muonium (15\sim20\%) and μ⁺(\sim60\%). In H₂μ⁺, the μ⁺ spin is depolarized in solid para‐ H₂ and a local magnetic field B_loc=1\sim2 G is deduced from LF‐μ⁺SR measurements. The magnitude of B_loc is inconsistent with the magnetic dipolar field (\sim25 G) expected from the magnetic moments of two protons in the H₂μ⁺ molecule and suggests that the H₂μ⁺ molecule might be in the rotationally excited state. From LF‐μ⁺SR measurements, muonium and μ⁺ have been found to diffuse in solid o‐ D_2. The diffusion rate of muonium is two order of magnitude larger than that of μ⁺. This revised version was published online in August 2006 with corrections to the Cover Date.     

Calculated spin-spin coupling surfaces in the water molecule; prediction and analysis of J (O,H), J (O,D) and J (H,D) in water isotopomers

Ab initio symmetry and internal valence coordinate oxygen–proton and proton–proton spin–spin coupling surfaces for the water molecule have been computed for the first time. Calculations have been performed at the SOPPA (CCSD) level using a large basis set and a grid of forty-nine geometries on the two surfaces. Equilibrium values differ significantly from some other calculated values especially for the Fermi contact terms. The bond length dependence of J(O, H) is ‘normal’ i.e. J(O, H₁) is much more sensitive to stretching the O–H₁ bond than the O–H₂ bond. This contrasts greatly with the corresponding situation in methane.

The surfaces have been averaged over the nuclear motion using a recent highly accurate force field to give values of J (O, H) and J (O, D) for H₂ ¹⁷O, HD¹⁷O and D₂ ¹⁷O and J(H, D) for HD¹⁶O, HD¹⁷O and HD¹⁸O over a range of temperatures. For J (O, H) and J (O, D) bond stretching at first order is the dominant part of the nuclear motion correction with second order bending making an important contribution. For J (H, D) the second order bending is by far the largest contribution to the nuclear motion corrections although the other terms partially cancel this contribution. Non-additivity can be largely attributed to the bending term for J (O, H). As expected, the bending terms also contribute relatively more to the temperature dependence of the couplings for J (O, H), J (O, D) and J (H, D). Our calculated J (O, H) in H₂ ¹⁷O of -77.22Hz at 293K is in very good agreement with Wasylishen and Friedrich's observed value of -78.70 (±0.02) Hz in cyclohexane at this temperature. Our calculated J(H, D) in HD ¹⁶O at 323K of -1.233Hz is close to a recent experimental value of -1.114 (±0.003) Hz in nitromethane-d ₃ observed by Sergeyev et al. at that temperature.     

Comparison of photoelectron intensities and Franck-Condon factors in the photoionization of H2, HD and D2

The relative intensities of vibrational bands corresponding to the photoionization reactionX¹Σ_g⁺(υ″ = 0) + hv → X²Σ_g⁺(υ′ = 0, 1, 2 …) + e^? have been measured for H₂, HD and D₂, using He I radiation and a cylindrical mirror analyzer. These relative intensities differ significantly from squared overlap integrals (Franck-Condon factors) based on accurate potential curves for X¹Σ_g⁺ and X²Σ_g⁺, but are in good agreement with calculations performed by Itikawa which include the variation of transition moment with internuclear distance and the kinetic energy of the departing electron.     

Collision-induced dissociation of H 2 + ions into the fragmentations H+H(2p) and H++H(2p)

Using a photon-particle delayed coincidence method the energy distributions of H +H(2p) and H⁺+H(2p) fragment pairs have been measured arising from collisional dissociation of 10 keV H ₂ ⁺ ions incident on various target gases. H fragments in their 2p state are identified by the Lymanα radiation emitted. The distribution of H+H(2p) fragment pairs arising from dissociative charge exchange reveals a sharp increase below 0.2 eV in the center-of-mass frame of the H ₂ ⁺ ion. This is ascribed to predissociation of vibrational levels of higher H₂ Rydberg states close above then=2 dissociation limit by those H₂ Rydberg states which separate into H+H(2p) fragments. Only direct transitions into the continuum of theGK ¹ ∑ _g ⁺ state may compete. Some structure at 0.3–0.5 eV is attributed to the three statesI ¹ П _g,i ³ П _g, andh ³ bE _g ⁺ having potential barriers of this height. The distributions for H⁺+H(2p) have maxima at 3.4, 3.8, and 4.2 eV for a H₂, Ar, and He target, respectively, indicating that the 2pπ _u state as well as the 3dσ _g state ofH ₂ ⁺ is excited. The H+H(2p) process has a greater probability than the H⁺+H(2p) process for Ar and H₂ targets, though all electronic H₂ states under consideration are bound.     

A theoretical study of the lowest 2 B 1, 2 A 1 and 2 B 2 electronic states in H2S+ and a comparison with corresponding states in related systems

Large scale configuration interaction calculations are employed to study the potential energy surfaces of the three lowest lying states in H₂S⁺. The calculated structural data for the X ² B ₁ and A ² A ₁ states are in very good agreement with previous evidence, but the ² B ₂ state is found to exhibit an [S---H₂]⁺ structure with large SH bond separations and a very small internuclear angle of 32°. Energies and wavefunctions are calculated for all three vibrational modes in the X ² B ₁ and A ² A ₁ excited states of H₂S⁺ and D₂S⁺ and the corresponding Franck-Condon factors for the A ² A ₁-X ² B ₁ band are determined; a maximum in absorption intensity is predicted to occur for v′₂ = 5–6 in H₂S⁺ and for v′₂ = 7–8 in D₂S⁺ for the A ² A ₁-X ² B ₁ transition, for which the calculated T ₀ energy of 18 620 cm^-1 is in excellent agreement with the experimentally determined value of 18 520 cm^-1. Extensive comparison is made with the other AH₂ systems PH₂, NH₂ and H₂O⁺ and trends with respect to geometry, vertical excitation and ionization energies as well as vibrational structure are pointed out; for this purpose the ² B ₂ potential energy curve of PH₂ has also been calculated.     

Schwingungsanregung von H2-Molekülen durch Zentralstoß mit Li+-Ionen

An apparatus is described for measuring the inelastic differential cross section for vibrational excitation in collisions of diatomic molecules with monoenergetic ions at laboratory energies between 10 and 50 eV. The method consists of measuring the time of flight of single ions with a time amplitude converter and displaying the results on a 100 channel pulse height analyzer. From the shift in the time of flight relative to that expected for elastic scattering the final state of the molecule excited in a single collision is identified. By studying only central collisions with almost zero impact parameter rotational excitation is strongly suppressed. Measured times of flight after collisions of monoenergetic Li⁺ ions with H₂ show that with increasing energy the most probable vibrational quantum jump increases from 0→1 to 0→2,0→3 etc. Contrary to the usual assumption of a small steric factor for vibrational excitation the results show that the inelastic cross section is larger than the elastic cross section. Using reported potential parameters the energy dependence of the most probable excited state is compared with the calculations of Secrest and Johnson for a one-dimensional collinear collision. The satisfactory agreement suggests that the steric factor is close to 1. From measurements at different scattering angles at 10 eV the integral inelastic cross section is found to be about 0.2 Ų corresponding to a differential cross section of 0.4 Ų/sr. Measured values of integral and differential total cross sections for Li⁺-He andLi⁺-H₂ are reported and compared with theory. Direct dissociation of D₂ by Li⁺ in the energy range from 25 to 55 eV was not observed, yielding an upper limit for the cross section of 4 · 10^?4 Ų/sr.     

Classical radiation spectra of long-lived H+ 3-complexes

Spectral analysis was performed of classical trajectories simulating collisions of H⁺ with H₂ which form long-lived complexes. The dipole moment μ(t) and several geometrical variables are analysed, and their spectra shown and interpreted in terms of known dynamical features of the motion. Correspondence with Einstein's A- and B-coefficients is used to derive estimates for the rates of the spontaneous and induced (laser-assisted) radiative association reaction H⁺ + H₂ → H⁺ ₃ + hv.     

High accuracy Dirac-finite-element (FEM) calculations for H 2 + and Th 2 179 +

A two-dimensional, fully numerical approach to the four-component first-order Dirac-differential-equation utilizing the Finite-Element-Method (FEM) is employed for H ₂ ⁺ and Th ₂ ^{179 +} . Using elliptic-hyperbolic coordinates and further one-dimensional singular transformations, scaling transformations and extrapolation techniques (geometrical over iteration steps and logarithmic over grid points) we achieve for the molecules H ₂ ⁺ and Th ₂ ^{179 +} relative accuracies better than 10^-12 for 1(1/2) g energies. Received 16 February 2001 and Received in final form 12 July 2001