Intense interactions of molecules with a short-wavelength electromagnetic radiation field: I. The fundamentals of the nonadiabatic theory

The intense interactions between short-wavelength (SW) electromagnetic radiation with a wavelength λ ≥ 1 Å and intensity up to 10¹⁴ W/cm² and simple and polyatomic molecules are studied with the coherent excitations of high-lying Rydberg and autoionizing states taken into account. The Hamiltonian of a system “molecule + SW radiation” is obtained by using the methods of quantum electrodynamics. Conditions for the applicability of the dipole approximation to describe the interactions of molecules with radiation of the UV, VUV, XUV, and soft X-ray range are found. The fundamentals of the theory of resonance scattering of SW radiation from diatomic, triatomic, and symmetric-and asymmetric-top polyatomic molecules are outlined.     

Formation of chemical compounds in a laser plasma

Using the methods of laser-induced fluorescence and emissive spectroscopy, we carried out investigations of the formation of TiO molecules in a laser plasma produced by focusing the radiation of an AYG:Nd³⁺ laser on the surface of a titanium target in air. The radiation flux density varied within the range 10⁸–10¹⁰ W/cm². We investigated the distribution of molecules over internal states and the space-time distributions of Ti atoms in the ground, metastable, and excited states, as well as of TiO molecules in the ground and excited states. We found that gas-phase reactions with participation of Ti atoms in the ground state provide the most probable channel for the formation of TiO molecules; the role of reagents in ionized, excited, and metastable states is of secondary importance. Institute of Molecular and Atomic Physics, National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 1, pp. 109–115, January–February, 1999.     

Dynamics of electronic and nuclear motion in a molecular hydrogen ion in a strong laser field

The dynamics of the electron and ion subsystems of a molecular hydrogen ion in the field of femtosecond titanium-sapphire laser radiation is investigated by using numerical simulation. The dependence of the probability of ionization and excitation of various electron states of H ₂ ⁺ on the radiation intensity and on the orientation of the molecule axis relative to the direction of polarization of the electric field of the wave is investigated. It is shown that the population of all electronic states of the molecule (except the ground state and the first excited state) is negligibly low in a wide range of radiation intensity. In such a situation, if the probability of system ionization is also low, the dynamics of vibration-rotation motion of nuclei in the molecule can be considered in the approximation of two potential surfaces (energy levels). The possibility of the effective orientation of the molecular axis along the direction of the electric field of the wave in the absence of dissociation of the system is considered.     

Propagator estimates of the transition characteristics for the 23 electronic states of the CH+ ion in a wide range of internuclear distances

Based on the method of approximation of the poles and residues of the polarization propagator in the first-order multireference perturbation theory, a software package was developed, which was applied to calculate the characteristics of transitions from the ground state to 23 excited electronic states of the CH⁺ ion in a range of internuclear distances R from 0.5 to 10 a.u. A comparison of the determined estimates of the transition energies with the results of calculations by means of the full configuration interaction method in the selected DZ orbital basis gives reasons to consider a balanced approximation of the energies of valence-type electronic transitions to be attainable with our method at a fixed value of R and when it is varied over a wide range. This conclusion does not apply to the estimates of the transition probabilities with our method.     

Excitation of 31,3 P and 31,3 D states of helium from the ground 11 S state by electrons and positrons

A systematic theoretical study is carried out for the electron and positron impact excitation of the 3^1,3 P and 3^1,3 D states of helium from the ground 1¹ S state. The results are reported for the differential cross sections, Stokes parameters and alignment and orientation parameters. To calculate the scattering amplitude which relate these parameters, a distorted wave approximation theory with different choices of distortion potential has been used. The results are compared with available theoretical and experimental data in the energy range of 40–100eV.     

Simulation of emission spectra of the gas-discharge plasma of a krypton-xenon mixture

The narrow-band radiation observed in the range of the resonance line of xenon at 147 nm in the VUV emission spectra of the gas-discharge plasma of a krypton-xenon mixture is proposed to interpret as a manifestation of bound-bound transitions between the vibrational levels of the excited electronic states 0⁺(³ P ₁) and 1(³ P ₁) and the ground electronic state 0⁺(¹ S ₀) in the KrXe* molecule. A correction of the potential curves of the electronic states under consideration is proposed from a comparison of the calculated and experimental spectra.     

A new particle-hole approach to collective states

The relevance of the particle-hole space is demonstrated by showing that in some commonly used formalisms the first excited state lies entirely within the particle-hole space generated from the correlated ground state. This property is proved for several cases of angularmomentum projection — projected Hartree-Fock method (PHF) — and for the generator coordinate method in the Gaussian overlap approximation, while in other cases it has been verified only numerically. A new method is presented for the approximate calculation of energies and transition amplitudes of particle-hole excited states. Only hermitian one-body operators are used to generate the excited states. The two-body density matrix of a correlated state approximating the ground state is required as input data. The formula is tested on the 2⁺ and 3^? states of ⁸Be and ¹²C by using the PHF ground state. Where comparison is possible the method gives better agreement with PHF and experiment than the extended random-phase approximation.     

Influence of dilution on magnetization properties of geometrically frustrated magnetic systems: Effective-field theory cluster approximations on kagome lattice

The influence of the site dilution on the magnetization properties of the antiferromagnetic spin-1/2 Ising model on the kagome lattice is systematically investigated using various n-site cluster effective-field theory approximations up to the cluster size $n=12$. It is shown that, regardless of the cluster approximation, the site dilution of the system leads, in addition to the existence of the standard saturated ground state, to the formation of four nontrivial plateau ground states together with five single-point ground states that separate them in the zero temperature limit. It is also shown that, while magnetization properties of the saturated ground state and two single-point ground states are stable with respect to the used cluster approximation, the magnetization properties of all four nontrivial plateau ground states and three single-point ground states that separate them strongly depend on the used approximation and have tendency to approach each other with increasing of the cluster approximation.     

The structure of 16O; A review of the theory

The nucleus ¹⁶ ₈O₈ is the prototype for a large number of developments in nuclear structure theory. It is a doubly magic N=Z nucleus, light enough that an isotopic spin formalism should be a valid approximation. The Brueckner-Hartree-Fock procedure in a spherical basis should be capable of describing the gross properties of the ground state. The excited states of negative parity exhibit the characteristic low-lying ‘octupole vibrational state’ and there is a much studied ‘giant dipole region’ which should be amenable to the analysis of the ‘random phase approximation’. The first excited state is the ‘mysterious second zero’ par excellence and a great deal of work on describing it via the method of ‘deformed state admixtures’ has been carried out. The first excited state and a number of other excited states appear to support spectra reminiscent of rotational bands and the collective character of these states has been extensively studied in both the Bloch-Horowitz and α-cluster model schemes.     

Laser stimulation of low-temperature dissociative recombination of electrons and oxygen molecular ions

A theory of dissociative recombination of slow electrons and molecular ions in a strong monochromatic light field is developed. The theory takes into account interference between various reaction channels and is constructed in a rigid basis adiabatic with respect to rotation (the approximation of a fixed molecular axis). The mathematical apparatus of the theory is based on the stationary formalism of the matrix of radiation collisions, whose poles correspond to “quasi-energy” states of a composite system. Along with transitions into dissociative configurations, field-induced nonadiabatic transitions into bound intermediate states of valence (non-Rydberg) configurations are considered. As a particular application of the theory, the e^? + O ₂ ⁺ (²Π _g ) → $ O(^{2s_1 + 1} l_1 ) + O(^{2s_2 + 1} l_2 ) A theory of dissociative recombination of slow electrons and molecular ions in a strong monochromatic light field is developed. The theory takes into account interference between various reaction channels and is constructed in a rigid basis adiabatic with respect to rotation (the approximation of a fixed molecular axis). The mathematical apparatus of the theory is based on the stationary formalism of the matrix of radiation collisions, whose poles correspond to “quasi-energy” states of a composite system. Along with transitions into dissociative configurations, field-induced nonadiabatic transitions into bound intermediate states of valence (non-Rydberg) configurations are considered. As a particular application of the theory, the e⁻ + O₂⁺(²Π _g ) → reaction is analyzed. A study of this reaction requires detailed information about the potential curves of the states participating in it with taking into account the external electromagnetic field (l and s are the electronic angular momenta and reaction product spins). For this purpose, the general problem is divided into three stages. At the first stage, the theoretical approach is formulated, and at the second stage, the corresponding potential curves are calculated and the main reaction mechanisms are determined. The third stage should include calculations of the total and differential cross sections. This work is concerned with the first two stages; that is, the adiabatic potential curves of the singlet and triplet dissociative states of the O₂^** oxygen molecule are calculated, a classification of all possible transition types is given, and reaction mechanisms in the presence of monochromatic laser radiation are determined. The frequency regions of external radiation in which these mechanisms are most effective are found. Original Russian Text ? S.O. Adamson, R.J. Buenker, G.V. Golubkov, M.G. Golubkov, A.I. Dement’ev, 2009, published in Khimicheskaya Fizika, 2009, Vol. 28, No. 4, pp. 26–42.     

Radiative quenching and excitation of metastable states upon differential scattering of atoms: II. The He(1<Superscript>1</Superscript><Emphasis Type="Italic">S</Emphasis>–2<Superscript>1</Superscript><Emphasis Type="Italic">S</Emphasis>)-Ne molecule

The differential cross sections of radiative-collisional quenching (absorption) of a metastable state of a colliding atom are calculated for the first time. As a particular example, the reaction of quenching (excitation) of the metastable state He(2¹S) in collisions with Ne atoms in the ground state is considered. The calculations are performed for the thermal collisional energy E = 10^?3 au for a wide range of radiation frequencies, including both wings and the center of the line of a forbidden atomic transition, and are based on the uniform quasi-classical approximation, which generalizes the Franck-Condon approximation to the case of an exponential dependence of the transition dipole moment on the internuclear distance, as well as to the case of nonintersecting terms. The calculated differential cross sections have an oscillating structure, which, for the blue wing of the forbidden spectral line, is interpreted as Stückelberg oscillations. At a radiation frequency close to the frequency of the forbidden atomic transition, a sharp maximum in the differential cross section—the giant glory effect—is observed in the range of small scattering angles. This effect is shown to occur as a result of superimposition of the rainbowlike feature of the differential cross section on the glory feature.     

Nature of halo in light nuclei

A feature peculiar to light neutron-rich nuclei is that their lowest decay thresholds are only slightly above their ground states. Among them, ⁶He and ¹¹Li are two most striking examples. The energy needed to break ⁶He (¹¹Li) into an alpha particle (⁹Li) and two neutrons is about 1 MeV (300 keV). So small a value prompts one to construct their theory by analogy with the zero-range-nuclear-force approximation previously applied to the deuteron. A more detailed analysis shows, however, that the simple version of this approximation applied to systems that decay through a three-particle channel does not take into account some important features of these systems and requires significant improvements. First, with increasing distance between three particles, the potential energy decreases, in contrast to what is observed for binary systems, in inverse proportion to the hyperradius cubed. Second, the Pauli exclusion principle adds complexity even in the asymptotic domain, and we meet its demands in constructing the ⁶He and ¹¹Li wave functions in the continuum. An approach is proposed to analyze weakly bound three-cluster systems that takes into account the aforementioned features and which describes correctly the experimentally observed structure of bound and unbound states above the threshold for three-particle decay.     

An angular momentum projected particle-hole theory for deformed nuclei and its application to theT=1 negative parity states of20Ne

An angular momentum projected particle-hole theory is proposed as an approach to describe excited states of deformed nuclei. Both for the ground and the excited states, angular momentum projections are done before variation. This allows one to look for the effect, with an appropriate constraint, of the difference in the deformations of these states. The theory is applied to the case of Ne²⁰ where the splitting of the giant resonance is observed. Other negative parity states are also studied and their transitions to the 2⁺ member of the ground state band show interesting features which may have experimental implications. On the other hand, the change in the deformation of the excited states has only a small effect on the transition probabilities.     

A uniform quasi-classical description of radiative transitions for asymmetric rare-gas atom-atom collisions

The uniform quasi-classical approximation [14] is used to describe the optical spectra formed during asymmetric collisions between atoms of rare gases in which one of the atoms is in a metastable state. We consider the reactions He(2¹S) + Ne → He(1¹S) + Ne + ?ω and Ar(³P₂) + He → Ar(¹S) + He + ?ω, in which the optical transition mechanisms are typical of most rare gases. Quasi-molecular terms of excited states and radiative widths calculated in a unified semiempirical approach are used. Spectral characteristics are calculated for thermal collision energies in the entire frequency range, including the center and both wings of the forbidden line. For the blue wing, our results are consistent with the widely used Condon approximation at collision energies E ≥200 cm^?1. At lower collision energies and in the region of the red wing and center of the forbidden line, the spectral distributions that cannot be described in the Condon approximation are reproduced in the uniform quasi-classical approximation. Comparison with quantum-mechanical calculations by the strong-coupling method confirms the high accuracy of the uniform quasi-classical approximation in the entire range of radiation frequencies.     

Autoionization resonances in the photoabsorption spectra of Fe<Superscript><Emphasis Type="Italic">n</Emphasis>+</Superscript> iron ions

The photoabsorption cross sections of a neutral iron atom, as well as positive Fe⁺ and Fe²⁺ ions, are calculated in the relativistic random-phase approximation with exchange in the energy range 20–160 eV. The wavefunctions of the ground and excited states are calculated in the single-configuration Hartree–Fock–Dirac approximation. The resultant photoabsorption spectra are compared with experimental data and with the results of calculations based on the nonrelativistic spin-polarized version of the random-phase approximation with exchange. Series of autoionization resonance peaks, as well as giant autoionization resonance lines corresponding to discrete transitions 3p → 3d, are clearly observed in the photoabsorption cross sections. The conformity of the positions of calculated peaks of giant autoionization resonances with experimental data is substantially improved by taking into account additionally the correlation electron–electron interaction based on the model of the dynamic polarization potential.     

Large-angle quasi-free scattering in 6Li(p,pd)4He at 670 MeV

The ⁶Li(p, pd)⁴He reaction was investigated at 670 MeV by a coincidence experiment with a large-angle scattering geometry. The energy sharing and angular correlation of the reaction products were measured and the momentum distribution of the recoil nucleus was determined for transitions leading to residual nuclei in the ground and excited states. Results were analysed in terms of a simplified distorted-wave impulse approximation using cluster-model and three-body wave functions. The observed momentum distribution of the p-n pair in the p-shell of ⁶Li is in agreement with three-body calculations, while the spectroscopic factor is larger than predicted by theory. Transitions to breakup states of the α-particle also have the characteristics of quasi-free scattering on deuteron clusters.