Octupole Polarizabilities Research Articles

Multipole polarizabilities for hydrogen-like atoms in Hulthén potential with and without spherical confinement

The multipole polarizabilities for hydrogen-like atoms with Hulthen potential are calculated with the sum-over-states formalism where the system bound and pseudocontinuum states are produced by employing the generalized pseudospectral method. Energies for nonzero angular momentum states, transition oscillator strengths, and dipole polarizabilities for the ground state of H atom with HP are calculated with high accuracy and compared with previous calculations. Quadrupole, octupole, and hexadecapole polarizabilities for both the ground and excited states are reported for the first time. The combined effect of Hulthen potential and impenetrable sphere on the polarizabilities is investigated, and the relation of such system with the confined H atom and particle in a box is discussed. Further comparison among Hulthen, screened Coulomb, and exponential cosine screened Coulomb potentials reveals that although the ground state energies follow the comparison theorem very well, their first-order energy corrections show complicated variations.

Dynamic Multipole Polarizabilities of Helium and Screened-Helium Atoms

The precise estimation of atomic polarizabilities impinges upon a number of areas and processes in physical science. We calculate precisely the dynamic multipole polarizabilities of the helium and screened-helium atoms using highly correlated exponential wavefunctions based on the pseudo-state summation method. For screened environments, we consider the Debye–Hückel potential (DHP) as the interaction potentials between the charged particles. The dynamic multipole (quadrupole, octupole, and hexadecapole) polarizabilities for the ground state of the helium atom and the multipole (quadrupole and octupole) polarizabilities of the screened-helium atom for different screening parameters are reported along with magic-zero wavelengths. The reported results for hexadecapole polarizability of the helium atom and dynamic multipole polarizability of the screened-helium atom are new and would be useful for future investigation on this topic.

A new insight into the dipole–quadrupole and dipole–octupole polarizabilities of CCl4 from ab initio calculations and anisotropic light scattering experiment

The dipole–quadrupole and dipole–octupole polarizabilities of CCl4 have been determined from collision-induced light scattering (CILS) spectrum. (Hyper)polarizabilities were calculated at the CCSD(T) level of theory with aug-cc-pVXZ (X=D, T, Q) basis sets. The CILS spectra were analyzed using our new intermolecular potential and those available in literature. The quality of the present potential was checked by comparison between calculated and experimental thermophysical and transport properties over a wide temperature range. Our final estimates from experiment for these properties are |A|=62.7a.u. and |E|=423.8a.u. and the theoretical values of (hyper)polarizabilities calculated at the CCSD(T)/aug-cc-pVQZ level of theory are α=69.27a.u., A=67.15a.u., E=−203.97a.u., C=821.75a.u., β=11.88a.u., and γ=10768.6a.u.

DEUTERON ELECTRIC QUADRUPOLE AND OCTUPOLE POLARIZABILITIES

The direct transition-matrix approach to determination of the electric polarizabilities of quantum bound systems developed in my preceding work is applied to study the electric multipole polarizabilities of a two-particle bound complex with a central interaction between the particles. Expressions for the electric quadrupole and octupole polarizabilities of the deuteron are derived and their values in the case of the S-wave separable interaction potential are calculated.

Electric Multipole Polarizabilities of Quantum Bound Systems in the Transition Matrix Formalism

A new general formalism for determining the electric multipole polarizabilities of quantum (atomic and nuclear) bound systems based on the use of the transition matrix in momentum space has been developed. As distinct from the conventional approach with the application of the spectral expansion of the total Green’s function, our approach does not require preliminary determination of the entire unperturbated spectrum; instead, it makes possible to calculate the polarizability of a few-body bound complex directly based on solving integral equations for the wave function of the ground bound state and the transition matrix at negative energy, both of them being real functions of momenta. A formula for the multipole polarizabilities of a two-body bound complex formed by a central interaction potential has been derived and studied. To test, the developed t-matrix formalism has been applied to the calculation of the dipole, quadrupole and octupole polarizabilities of the hydrogen atom.

Blackbody radiation shift of the B+clock transition

A calculation of the blackbody radiation shift of the B$^+$ clock transition is performed. The polarizabilities of the B$^+$ $2s^2$ $^1$S$^e$, $2s2p$ $^1$P$^o$, and $2s2p$ $^3$P$^o$ states are computed using the configuration interaction method with an underlying semi-empirical core potential. The recommended dipole polarizabilities are 9.64(3) $a_0^3$, 7.78(3) $a_0^3$ and 16.55(5) $a_0^3$ respectively. The derived frequency shift for the $2s^2$ $^1$S$^e$ $\to$ $2s2p$ $^3$P$^o_0$ transition at 300 K is 0.0160(5) Hz. The dipole polarizabilities agree with an earlier relativistic calculation (Safronova {\em et al.} Phys. Rev. Lett. {\bf 107} 143006 (2011)) to better than 0.2%. Quadrupole and octupole polarizabilities and non-adiabatic multipole polarizabilities are also reported.

Dispersion coefficients for interactions among H, Li, Na, K atoms with Debye–Hückel potentials

The effect of Debye–Hückel screening on the dispersion coefficients C6, C8, C10 for interactions among H, Li, Na and K atoms has been investigated using the symplectic algorithm. The C6, C8, C10 coefficients for interactions among alkali-metal atoms along with the dipole, quadrupole and octupole polarizabilities of K atom for various screening parameters are reported for the first time in the literature. In free-atomic cases, our results are comparable with available theoretical and experimental results.

Polarizabilities of Li and Na in Debye plasmas

We have carried out calculations to investigate the effect of Debye plasmas on the dipole, quadrupole, octupole polarizabilities of lithium and sodium atoms using the symplectic algorithm in the framework of the pseudo-state summation technique. The polarizabilities of alkali-metal atoms for various Debye lengths are reported for the first time in the literature. The behavior of the transition energies and oscillator strengths for Li and Na in plasma environments is also presented. In free atomic cases, our calculated results are in good agreement with the reported theoretical and experimental results.

Polarizabilities of two-electron positive ions with screened Coulomb potentials

We have carried out calculations of the polarizabilities of the two-electron positive ions Li${}^{+}$, Be${}^{2+}$, ${\mathrm{B}}^{3+}$, ${\mathrm{C}}^{4+}$, ${\mathrm{N}}^{5+}$, and ${\mathrm{O}}^{6+}$ interacting with screened Coulomb potentials. Highly accurate correlated exponential wave functions are used to represent correlation effects on the charged particles. The dipole, quadrupole, and octupole polarizabilities for the screening parameters in the range 0--$1{a}_{0}^{\ensuremath{-}1}$ are reported. Reported results for the unscreened case are comparable with the available results and for the screened case show some interesting behavior with increasing nuclear charge.

Multipole polarizabilities of helium and the hydrogen negative ion with Coulomb and screened Coulomb potentials

We have carried out calculations of multipole polarizabilities of helium and the hydrogen negative ion interacting with pure Coulomb and screened Coulomb potentials using highly accurate correlated exponential wave functions with exponent generated by a quasirandom process. The dipole, quadrupole, and octupole polarizabilities for the ground $1{s}^{2}$ ${^{1}S}^{\text{e}}$ state for different screening parameters starting from infinity (pure Coulomb case) to small values of the screening parameters, are reported. The octupole polarizability of the hydrogen negative ion is reported for the first time in the literature. The bound $4\text{ }^{1}F$ state energy of helium for different screening parameters are also reported.

High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C 6, C 8, and C 10 for alkaline-earth dimers

The static and dynamic electric dipole, quadrupole, and octupole polarizabilities of the alkaline- earth atoms (beryllium, magnesium, calcium, strontium, and barium) in the ground state were calculated. The dynamic polarizabilities obtained were used to calculate the van der Waals coefficients C 6 , C 8 , and C 10 of alka- line-earth metal dimers for the interaction of two like atoms in the ground state. The results are compared with other theoretical and experimental data.

Quadrupole and octupole polarizabilities for the ground states of lithiumlike systems from Z=3 to 20.

The quadrupole and octupole polarizabilities for the ground states of lithiumlike systems from Z=3 to 20 are calculated with the full-core plus correlation method. For the neutral lithium atom, the typical patterns of convergence of the quadrupole and octupole polarizabilities are analyzed. The calculated quadrupole and octupole polarizabilities of the ground state for lithium atom are compared with the previous theoretical results obtained by other methods; our predictions agree with the most accurate reports in the literature very well. For lithiumlike ions, our prediction may provide valuable reference data for other accurate theoretical calculations in future.

Polarizabilities of helium in high-angular-momentumstates

The static dipole, quadrupole, and octupole polarizabilities ofhelium are calculated for the n 1L and n 3L states withn up to 10 and L up to 9, using variational wavefunctionsin Hylleraas coordinates.

Polarizabilities of the Rydberg states of helium

The static dipole, quadrupole, and octupole polarizabilities of helium are calculated for the four Rydberg series $1sns{}^{1}S,$ $1sns{}^{3}S,$ $1snp{}^{1}P,$ and $1snp{}^{3}P$ with n up to 10, using variational wave functions in Hylleraas coordinates. The large-$n$ expansions for polarizabilities are presented for these series.

Polarizabilities of heliumlike ions in the1s2p1Pand1s2p3Pstates

The static dipole, quadrupole, and octupole polarizabilities of heliumlike ions are calculated for the $1s2p{}^{1}P$ and $1s2p{}^{3}P$ states with $Z$ up to 10, using variational wave functions in Hylleraas coordinates. A general sum rule for the ${2}^{l}$-pole oscillator strengths is derived.

Long-range interactions of metastable helium atoms

The electric dipole, quadrupole, and octupole polarizabilities of a helium atom and the associated dispersion coefficients for the interaction of two helium atoms are calculated for the atomic $n=2$ singlet and triplet states, respectively, $\mathrm{He}(2{}^{1}S)$ and $\mathrm{He}(2{}^{3}S)$. The calculations utilize highly accurate, variationally determined, wave functions composed of doubled basis sets. The effects of retardation due to the finite speed of light are calculated for the dispersion potentials of two $\mathrm{He}(2{}^{1}S)$ or two $\mathrm{He}(2{}^{3}S)$ atoms and for the atom-surface interaction potentials of a $\mathrm{He}(2{}^{1}S)$ or a $\mathrm{He}(2{}^{3}S)$ atom with a perfectly conducting or a dielectric wall.

Torsional dependence of molecular electrical properties and long-range interactions: CH3OH–rare gas systems

Self-consistent-field (SCF) values are reported for all Cartesian tensor components of the dipole, quadrupole, and octupole moments (μ,Θ,Ω) and polarizabilities α and A of the methanol molecule in its staggered, eclipsed, and three intermediate conformations. The methanol geometry was held rigid except for a single internal rotation angle γ, describing the relative orientation of the methyl rotor and the hydroxyl framework. Three different basis sets were used, including a 110 contracted Gaussian set based on the electrical properties (ELP) basis of Dykstra et al. [Adv. Chem. Phys. 75, 37 (1989), and references therein]. It was found that the tensor components Ωxxx, Ωxyy, Axxx, Axyy, and Ayxy vary as cos 3γ, while the components Ωyyy, Ωyxx, Ayyy, Ayxx, and Axyx vary as sin 3γ. All other components of Ω and A, as well as all components of μ, Θ, show little variation with γ. This dependence was explained using a simple model that treats each property as a sum of a constant, hydroxyl framework contribution and a conformation-dependent, methyl rotor contribution. Torsional averages of these properties were computed from torsional wave functions obtained by diagonalization of the internal axis method (IAM) Hamiltonian. It was found that the large amplitude internal rotation in methanol gives rise to large vibrational effects on the Axxx, Axyy, and Ayxy polarizability components. The conformational dependence of the electrical properties was used to describe the conformational dependence of long-range interactions involving a near-symmetric, nonrigid molecule such as methanol. The leading γ-dependent interaction term was shown to vary as R−8 and R−7 for the induction and dispersion interactions (respectively) between a methanol molecule and a structureless atom. Cartesian tensor expressions are given for the long-range dispersion interaction within second-order perturbation theory, and the leading torsionally dependent interaction is shown to vary as sin3 θ cos 3(φ−γ), where θ,φ are the spherical coordinates of the atom.

Dipole, quadrupole, octupole, and dipole–octupole polarizabilities at real and imaginary frequencies for H, HE, and H2 and the dispersion‐energy coefficients for interactions between them

AbstractWe have calculated certain dynamic polarizabilities (for both real and imaginary frequencies) for H, He, and H2 and the dispersion‐energy coefficients for long‐range interactions between them. We have done so in a sum‐over‐states formalism with explicitly electron‐correlated wave functions to describe the states. To be precise, we have determined the dipole (α1), quadrupole (α2), and octupole (α3) polarizabilities of H and He for real frequencies (ω) in a range between zero and the first electronic‐transition frequency and for imaginary frequencies (iω) on a 32‐point Gauss‐Legendre grid running from zero to ħω = 20 Eh, and for H2, we have found the dipole (α), quadrupole (C), and dipole–octupole (E) polarizability tensors for the same real and imaginary frequencies. The dispersion‐energy coefficients, obtained by combining the sum‐over‐states for‐malism for the polarizabilities with analytic integration over ω, gave values of C6, C8, and C10 for the atom–atom systems; C, C, C, C, and C for the atom–diatom systems; and C6, C and C for the H2H2 system. Nearly all the results are considered to be more reliable than those hitherto published and some have been obtained for the first time, e.g., C(iω), E(ω), and E(iω) for H2 and C, C, and C for the HH2 system. © 1993 John Wiley & Sons, Inc.

Dynamic multipole polarizabilities and Rydberg states of the beryllium isoelectronic sequence.

Dynamic dipole, quadrupole, and octupole polarizabilities of the beryllium isoelectronic sequence up to Z=10 are calculated using time-dependent linear-response theory. Excitation energies and analytic representations of the singly excited Rydberg states of s, p, d, and f symmetries in their singlet configurations are also obtained for excitations up to principal quantum number n=8. The (\ensuremath{\omega}${)}_{\mathrm{\ensuremath{\omega}}\ensuremath{\rightarrow}0}$ obtained compare well with existing static results. Excitation energies compare favorably with the available spectroscopic values. The oscillator strengths for the dipolar and quadrupolar transitions are calculated and the effective quantum numbers are estimated using the complete screening model. Agreement is reasonably good with existing data wherever available.

The electronic and vibrational energies of the 5Σ g+ state of He 2 which corresponds asymptotically to the interaction of two 1s2s 3S He atoms

A reliable adiabatic potential curve for the 5Σ g + state of He 2 which corresponds to the interaction of a pair of 1s2s 3S atoms is determined by configuration interaction (CI) calculations comprising single and double excitations from a 31-configuration multireference base. It has a van der Waals well nearly 900 cm −1 deep which supports at least 17 bound vibrational energy levels. Reliable values for the dipole, quadrupole, and octupole polarizabilities of the triplet atom were calculated at the CI level in the course of developing our basis set.