Atomic Molecular System Research Articles

Integrals in the theory of four-particle atomic-molecular systems

Explicit expressions for four-particle Coulomb interaction integrals and overlap integrals for exponential basis functions dependent on five interparticle distances have been obtained. These formulas significantly simplify calculations in comparison with the general algorithm and are free from uncertainties arising in its application. The values of the integrals under consideration are calculated for a number of points forbidden in the general algorithm. The results obtained are applicable to analysis of four-particle integrals of the general form and calculation of four-particle atomic-molecular systems with partial allowance for the correlation of particle motion.

Theoretical study of the effect of potential models on scattering cross sections for He-HF system

An anisotropic intermolecular potential of the He-HF complex has been obtained by utilizing the BFW analytic function to fit the intermolecular energy data, which have been calculated at the theoretical level of the single and double excitation coupled-cluster method with noniteractive perturbation treatment of triple excitation CCSD (T). And the reliability of the potential has been verified by comparing it with other potential models. The differential, partial and total scattering cross sections for collisions between He atoms and HF molecules have been calculated respectively by using the quantum close-coupling method at five different potential models, and the calculated results have been compared and analysed in detail. The research shows that the scattering cross sections are sensitive to the position where potential is zero, the well depth, the strength of the repulsive wall of the spherically averaged and to the anisotropy of the region of the well depth. We hope that the results can provide profitable reference for determining exactly the interaction potential of the atomic-molecular collision systems from the scattering cross sections.

Integral Hellmann-Feynman theorem as a criterion of the quality of wave functions of atomic-molecular systems

It is proposed to use the integral Hellmann-Feynman theorem for the quality control and refinement of atomic and molecular wave functions. Its validity is verified for variational wave functions of the positronium ion e+e−e−, the negative ion of the hydrogen atom p∞+e−e− (H−), and mesomolecules μ−π+π+ and μ−p+p+. The relative violation of this theorem (10−2) is six orders of magnitude larger than the error of the energy calculation (10−8), which demonstrates its high sensitivity to the quality of wave functions. A way of refining wave functions on the basis of combination of the integral Hellmann-Feynman theorem for exactly solvable model and real atomic-molecular systems is proposed. A rule for verification of the mutual consistency of the wave functions of any three quantum-mechanical systems is formulated.

Theory of spin polarization phenomena in atomic and molecular photoeffects

A compact invariant expression for the angular distribution of photoelectrons formed as a result of photoionization of axisymmetrically polarized atoms and molecules, including optically active molecules, is derived from the general symmetry considerations and using a recently developed bipolar harmonic reduction technique. In the angular distribution of photoelectrons, as well as in the total photoionization cross section, the dependence on all the geometric parameters is separated completely. The polarization of ionizing radiation can be arbitrary, with the partial polarization being specified by the Stokes parameters. The expression for the angular distribution of photoelectrons escaping from an atomic-molecular system oriented in the first order also determines the structure of the expression for the photoionization cross section of an unpolarized system with allowance for the spin polarization of a photoelectron or a photoion with the spin 1/2. The roles played by circular dichroism, chirality, etc., in the process of photoionization of oriented and aligned systems are analyzed in detail.

Partial hypervirial theorems for atomic-molecular systems

A family of partial hypervirial theorems for physical properties of pairs of particles in three-and four-particle atomic-molecular systems is considered. The partial hypervirial theorems generalize the partial virial theorems proposed earlier. The sum rule is formulated, according to which the expectation values of the derivatives with respect to the interparticle distances are related to the products of the charges of pairs of the particles. This rule is used to check the accuracy of the calculation of variational wave functions for the positronium ion e − e − e +. It is shown that the sum rule is two orders of magnitude more sensitive to the inaccuracy of the calculation of the wave function than the partial virial theorems and is five or six orders of magnitude more sensitive to it than the conventional virial theorem.

COULOMB SYSTEMS IN A STRONG MAGNETIC FIELD

A study of what would the atomic–molecular physics be in an external strong magnetic field is presented. Emphasis is made on one-electron systems which seem the most bound, since two- and more-electron systems are weakly bound due to their maximal total spin nature. We demonstrate that the Coulombic systems (αpe) and (ααe) placed in (astro-physically relevant) magnetic fields B>1011 G become bound. It manifests a theoretical existence of the exotic ions ( HeH )2+ and [Formula: see text] with parallel configuration (the magnetic field is directed along the internuclear axis) as optimal. Both ions are unstable towards dissociation but do have very large lifetimes. At B>1000 a.u. the ion [Formula: see text] becomes stable and even becomes the most stable among one-electron ions made from protons and/or α-particles. A table of one-electron atomic–molecular systems which may exist in a strong magnetic field is given.

Partial virial theorems for atomic-molecular systems

Partial virial theorems for atomic-molecular systems

Erratum to Correlated complex exponential wave functions for atomic-molecular systems

Erratum to Correlated complex exponential wave functions for atomic-molecular systems

The Condition of Invariance of the Energy of an Atomic-Molecular System with Respect to Rotations of the Jacobi Coordinates

An additional condition for the wave functions of the ground and excited states of atomic-molecular systems, which follows from the energy invariance with respect to rotations of the Jacobi coordinates, is studied. This condition makes a substantial contribution to the conventional criterion of the quality of wave functions, based on the variational principle for the average energy value. The explicit form of this condition is found for an arbitrary interaction potential dependent on the particle-particle distances and the requirements for realization of this condition are ascertained. Variational calculations of 3He2+ μ−e− and 4He2+ μ−e− mesoatoms in the basis of correlated exponential functions dependent on the particle-particle distances are performed with a detailed optimization of all nonlinear parameters for each individual energy level. A high sensitivity of the condition under study to the quality of approximate wave functions and the efficiency of the detailed optimization of the nonlinear variational parameters in calculation of each individual energy level are demonstrated.

Optimal Hamiltonian of internal motion of an atomic-molecular system in a magnetic field

The effect of a uniform magnetic field on the state of an atomic-molecular system considered as a united system of N particles (without separation of the motion of acoelightac and particles) is analyzed. It is shown that the Hamiltonian of the internal motion of the system in the magnetic field contains (N-1)(N-2)/2 arbitrary parameters corresponding to the coefficients of the gauge transformation of the vector potential. A method of calculation of the optimal values of these coefficients based on the requirement for the minimum diamagnetic correction to the energy is proposed. New formulas for the diamagnetic susceptibility of atomic-molecular systems are obtained that take into account the simultaneous perturbing effect of the magnetic field on the motion of all particles. The theory is applied for calculation of the diamagnetic susceptibilities of the H, He, Li, and Be atoms; the muonic analogues of helium atoms ∞He2+µ− e −,4He2+µ− e −, and 3He2+µ− e −; and the positron-containing systems t + e + e − e −, d + e + e − e −, p + e + e − e −, µ+ e + e − e −, and e + e + e − e −, with regard for the motion of all particles.

The state of an atomic-molecular system near the stability threshold

The state of an atomic-molecular system near its stability threshold with regard to the detachment of one of the particles is studied. The decay of the system upon a decrease in the charge of a binding particle, as well upon an increasasymmetry of masses of like-charged particles, is considered. A special variational principle that allows one to directly calculate the threshold state of the system without repeatedly calculating its energy for different values of masses and charges of particles is used. With the motion of all particles fully taken into account, the threshold states of two-electron atoms with different nuclear charges and of atomic-molecular systems corresponding to the attachment of a positron of variable mass to a neutral atom are calculated. On the basis of calculation of quantum-mechanical expectation values of the kinetic energy of particles and the potential energy of their interaction, the rearrangement of the wave function upon passage of the system through the decay threshold is examined. The threshold characteristics of a purely adiabatic system containing infinitely heavy particles are considered separately.

Studies of the action of intense laser radiation on elementary atomic-molecular systems

This paper presents a review of the main results of studies of the interaction of powerful laser radiation with atomic systems, carried out by the staff of the scientific school of A. M. Bonch-Bruevich in the period 1964-2003. The review reflects the development stages of the studies and the main achievements, as follows: The action of powerful monochromatic and noisy optical radiation fields on the energy structure and transition probabilities of atoms has been studied experimentally and theoretically; negative absorption has been obtained for the first time in two-level systems without population inversion; multiphoton parametric processes leading to a change of the angular and spectral characteristics of the radiation transmitted through the atmospheric medium have been investigated (the studies of four-wave mixing were pioneering in this case); distinctive nonlinear optical processes in systems of colliding atoms, in particular the phenomenon of "optical impact," were predicted and were observed for the first time; nonlinearity that caused bleaching of the medium without saturating it was detected in these systems; changes in the energy and spectral characteristics of atoms of the alkali metals when they interact with the surface of solids were detected; photodesorption of atoms from the surface was detected, and a phenomenological theory of this process was created; the quenching of excited atoms when they strike the surface of a solid was investigated, and the energy and kinetic characteristics of impacts of the second kind were measured; the phenomenon of photoatomic emission from metals under the action of optical radiation was detected, and the role of structural defects of the surface of metals in this process was pointed out. Results are presented for the developed and verified optical method of fluctuation microscopy, intended for measurements of the geometrical parameters of metallic island films of nanometer size.

The Hartree–Fock Approximation Calculation of Electric Polarizability of Atoms with an Open Shell

Within the framework of the restricted Hartree–Fock method, equations of stationary “coupled” perturbation theory have been obtained for atomic-molecular systems with an open shell in orbital representation. Corrections to the Hartree–Fock orbitals are sought in the form of expansions in unperturbed orbitals which are assumed calculated in the LCAO approximation. The resulting inhomogeneous algebraic system for the expansion coefficients admits an exact solution. The static polarizability of atoms with an open shell from Li to Sc has been calculated with the use of an optimized basis set of Slater-type atomic orbitals.

Correlated complex exponential wave functions for atomic-molecular systems

The application of flexible correlated complex exponential basis functions depending on all inter-particle distances in precision variational computations of atomic-molecular systems is considered. In contrast to three-particle systems, the application of such functions for four-particle systems is hindered by the cumber-some nature of the multistep algorithm of evaluation of the integrals determining the matrix elements of the energy operator. Transformations reducing the number of integrals to be evaluated are carried out. As a result, the computation volume is reduced by a factor of six: instead of 43 integrals, it is sufficient to take 6 integrals of the Coulomb interaction of pairs of particles and the overlap integral. The method of direct construction of formulas for many-particle integrals is discussed.

Calculation of the stability domain for Coulomb systems

A variational method is proposed for calculating the values of particle mass corresponding to the dissociation threshold of an atomic-molecular system. The calculations of the dissociation stability domain for three-particle Coulomb systems demonstrate the high effectiveness of the method as compared to the traditional variational principle for calculating energy.

Complex Gaussian functions for four-particle systems

A new type of basis function is suggested for precision variational calculations of many-particle atomic-molecular systems—the Gaussian functions with complex exponential parameters in the form of combinations of exponential-trigonometric functions of the squared interparticle separations. With these basis functions, all required many-particle integrals are evaluated explicitly. The method is applied to totally nonadiabatic calculations of ten four-particle molecules and mesomolecules ranging from the tritium molecule t+t+e−e− to the positronium molecule e+e+e−e−. The dissociation energies of these systems calculated by using 20 complex basis functions coincide with the exact values to within 1%; therefore, their inaccuracy is several times smaller than the inaccuracy of calculations with the basis sets of ordinary real Gaussian functions. This increase in accuracy is attained due to a more correct description of the vibrational part of wave functions of molecular systems by using oscillating complex Gaussian functions as compared to their nodeless real counterparts.

Multimode dynamics of a coupled ultracold atomic-molecular system.

We analyze the coherent multimode dynamics of a system of coupled atomic and molecular Bose gases. Starting from an atomic Bose-Einstein condensate with a small thermal component, we observe a complete depletion of the atomic and molecular condensate modes on a short time scale due to a significant population of excited states. Giant coherent oscillations between the two condensates for typical parameters are almost completely suppressed. Our results cast serious doubts on the common use of the 2-mode model for the description of coupled ultracold atomic-molecular systems and should be considered when planning future experiments with ultracold molecules.

Calculations of Coulomb systems with optimization of nonlinear parameters

Precise variational calculations of the energy and diverse physical characteristics are performed for the ground state of a fully nonadiabatic four-particle system—the positronium molecule e+e−e+e−. The nonlinear exponential parameters of correlated Gaussian basis functions dependent on all interparticle separations are systematically optimized. The dependence of the calculated energy values and the expectation values of interparticle separations (as well as their degrees and Dirac delta functions of interparticle separations) on the basis size N is examined. For N=200, the ground-state energy of the positronium molecule is found to be E=−0.5160028 au. For an extended basis set with N=4700 containing 200 basis functions with the optimized parameters and 4500 additional functions with random values of nonlinear parameters, E=−.5160036 au. At present, this result is the most accurate variational energy value of the positronium molecule, and it demonstrates the high efficiency of optimization of the nonlinear parameters in calculations of atomic-molecular systems. The lifetime of the positronium molecule e+e−e+e− with respect to electron-positron annihilation is calculated to be τ=2.26×10−10 s.

Kinetics of processes in the middle atmosphere during the laser excitation of O2 molecules

Kinetic processes taking place in the atomic-molecular system O-O2-O3 in the middle atmosphere with the participation of oxygen molecules in the excited electronic states O2(a1Δg) and O2(b1Σg+) are analyzed in detail. The possibility of increased ozone production under the influence of solar radiation during the laser excitation of O2 molecules in the a1Δg state is demonstrated on the basis of numerical modeling. Upper and lower bounds are determined for the densities of O2(a1Δg) molecules at which the ozone concentration increases in the irradiated zone.

Competition effect in atomic-molecular system

The competition effects among the processes of atomic ionization, optical pumped stimulated radiation (OPSR), four-wave frequency mixing (FWFM) and molecular stimulated diffuse band radiation at the atomic two-photon resonance of 3S approaches 4D in Na2 - Na mixture were observed. The dip at the two-photon resonance in the excitation spectrum for the diffuse-band radiation was interpreted as suppression of population in 4D state.