Variation-perturbation Approach Research Articles

Variational perturbation approach to resonance-state wave functions

The variational perturbation theory for wave functions, which has been shown to work well for bound states of the anharmonic oscillator, is applied to resonance states of the anharmonic oscillator with negative coupling constant. We obtain uniformly accurate wave functions starting from the bound states.

Variation-perturbation method in time-dependent density-functional theory

We develop the variation-perturbation approach for periodic time-dependent perturbations within the Kohn-Sham method of density-functional theory. Our formulation parallels a similar formulation developed by Gonze for static perturbations. The theory is demonstrated by calculating the dynamic polarizability and hyperpolarizability for the helium atom.

Confined exciton-polaritons in parabolic and Gaussian quantum wells

In order to study the confined polaritons in gradual quantum structures we have calculated the exciton binding energies of parabolic and Gaussian quantum wells using a variational perturbative approach. In the linear regime, we have established, by means of the semi-classical theory, the dispersion modes of a polariton confined in quantum wells, where the confining potentials are parabolic and Gaussian. In fact, we have evaluated the oscillator strength of each quantum well in order to get an idea about the confinement size and we have concluded that the polariton is more confined in a Gaussian quantum well than in a parabolic quantum well. To make a complete description of the confined polariton we have taken into account the electron - hole exchange energy. Numerical results show that the largest effect arising from the exciton - radiation interaction is the ZT and LT splittings, which strongly depend on the quantum confinement.

Retardation long-range potentials between two helium atoms.

The retardation long-range potentials between two 1${\mathrm{}}^{1}$S (or 2${\mathrm{}}^{3}$S) helium atoms are calculated. The complex dynamic multipole polarizabilities of 1${\mathrm{}}^{1}$S and 2${\mathrm{}}^{3}$S states of helium are obtained through a variation-perturbation approach with B-spline and Slater-type basis functions in a configuration-interaction scheme. They are used to calculate the retardation long-range potentials. The retardation coefficients are examined. Their relative magnitudes are different for different systems. The possibility of an excited state of helium dimer from the 1${\mathrm{}}^{1}$S--2${\mathrm{}}^{3}$S ${\mathrm{He}}_{2}$ state is estimated. \textcopyright{} 1996 The American Physical Society.

Vibrational behaviour of the carbon–muonium bond in the muonated ethyl radical

Using a variation-perturbation approach, harmonic and anharmonic corrections to some stationary point properties of the ethyl radical are computed for deuterium and muonium isotopomers. The anharmonic corrections in the muonated radical are found to be highly significant. The fundamental frequency for the C—Mu bond is calculated as 7877 cm–1. The effect upon the muon–electron β-hyperfine coupling constant of excitation of the muonated radical to higher vibrational states is investigated.

Dispersion coefficients for 1, 21S and 23S helium dimers

Dynamic multipole polarizabilities of 1, 2 1S and 2 3S states of helium are calculated through a variation-perturbation approach. They are used to calculate the dispersion coefficients, C6, C8, and C10, using 32-point and 64-point Gauss-Legendre integrations. The dispersion coefficients govern the interaction energy for the long-range electronic interaction between two helium atoms. The present numerical results are compared with other calculations.

Dipole polarizabilities of the 1, 21S and 23S states of the helium sequence

The dipole polarizabilities of the 1, 21S and 23S states of helium-like ions (2<or=Z<or=10) are calculated through a variation-perturbation approach. The polarized wavefunctions are constructed by using selecting B-spline basis functions in a CI scheme. The values of alpha d are converged to an accuracy of at least 0.01% and are in excellent agreement with those obtained from explicitly correlated wavefunctions and with experiment (Leonard and Barker, 1975).

Static Multipole Polarizabilities and Shielding Factors for the S‐Electron Moving in the Screened Coulomb Potential

AbstractThe variational perturbation approach of Rivail and Rinaldi as generalized by Shukla and Easa is utilized to derive a 2L‐pole static polarizability and a shielding factor for the electron in the ground state moving in a screened Coulomb potential of Debye form. The final formulas are reduced to power series of the screening parameter D in the asymptotic region. The special cases discussed by Fowler can readily be obtained from the present generalized form by direct substitution of the corresponding L values.

Time-dependent gauge-invariant approach to the calculation of dynamic hyperpolarizabilities: Application to FH and LiH

The variation-perturbation approach with a time-dependent electric field is used in order to obtain the third-order energy and to find the first hyperpolarizability with the first-order perturbed function. The function used is the same as the one described in a previous paper [M. R\'erat, M. Merawa, and C. Pouchan, Phys. Rev. A 45, 6263 (1992)] relative to dynamic-polarizability calculation from a time-dependent gauge-invariant method. Static-hyperpolarizability components are given for FH and LiH and discussed in comparison with previous calculations. Dynamic components are calculated for the electro-optic Pockels effect up to the first resonances.

Electron-hole quantum-confined states affected by point charge in semiconductor crystallite

The effects of a point charge inside a semiconductor crystallite on the electron, hole and electron-hole (e-h) pair ground quantum-confined states have been studied under the effective-mass approximation by means of the variational-perturbation approach. The electron, hole and e-h pair ground quantum-confined state energy as functions of the crystallite radius, the charge position inside the crystallite have been obtained. The validity of the variational-perturbation method is presented. Effects of this point charge on the optical properties of the crystallite have also been discussed.

Zero-point vibrational corrections for the geometry, electric dipole moment and 17O nuclear quadrupole coupling constant calculated for the muonium isotopomers, MuOH and Mu2O, of the water molecule

A variation–perturbation approach is applied to investigate isotope-dependent zero-point vibrational corrections to one-electron properties of a muonium-substituted water molecule in its ground electronic state. The corrections for MuOH and Mu2O indicate that the root-mean-square displacement involving the OMu internuclear distance is ca. 11 pm with a root-mean-square displacement in the internuclear angle for MuOH of 12.73° and Mu2O of 14.71°.As a consequence, the muonium-substituted species sample points on a property surface well distant from the equilibrium position. It is found that this behaviour alters the electric dipole moment and produces significant isotope effects on vibrational transition frequencies and the 17O nuclear quadrupole coupling constant. Single muonium substitution of H2O produces a 2% increase in the zz-component of the quadrupole coupling constant rising to a 16% increase in the xx-component with respect to the vibrationally averaged values of H2O in its ground vibrational state.

Vibrationally averaged β-hyperfine coupling constants for the muonium-substituted ethyl radical

A variation-perturbation approach is applied to compute isotope-dependent zero-point vibrational corrections to the β-hyperfine coupling constant of the ethyl radical. The corrections increase the coupling by ca. 5, 7 and 23% for the deuterium-, protium- and muonium-substituted radicals, respectively. The large vibrational correction to the muon β-hyperfine coupling constant could explain the ‘residual’ isotope effect observed experimentally.

Surface optical phonon effects on surface impurity states in isotropic semiconductors InP, InAs and InSb

The surface optical phonon effects on the low lying energy states of the surface impurities in isotropic semiconductors are studied by a variational perturbative approach proposed recently. The ground state and the first excited state energies of the surface polaron are calculated. Numerical results for III–V compounds InP, InAs and InSb are obtained. It is found that the surface phonon effects on the energy levels of the surface impurity atom in these semiconductors are small. To make an explicit comparison we also apply our approach to calculate the ground polaron state energy of GaAs. The result shown in the contribution of the electron-SO phonon interaction is not so large as obtained in the previous conventional variational method.

Effect of surface optical phonon on the surface impurity states of GaAs and CdS

The effect of the surface optical phonon on the low lying surface impurity states of isotropic semiconductors GaAs and CdS are studied by a variational perturbative approach. The electron-surface phonon coupling constants for these two semiconductors are relatively small and thus can be treated as a perturbation. The ground and the first excited state energies of the surface polaron are calculated and compared with the previous work.

On the variational perturbation approach to the Dirac equation

A relativistic version of the variational perturbation method is extended to apply to excited states of the Dirac equation. It is proved that the value of the Hylleraas functional is an upper bound to the exact second-order (proportional to c−4) correction to the energy. In order to demonstrate the usefulness of this approach to the problem of optimising non-linear parameters the method is applied to the special case of hydrogen-like atoms. The first-order relativistic corrections to the wavefunctions for some s, p and d states have been approximated in terms of expontential functions.

Relativistic perturbation theory. third order variational perturbation calculations for H2+

A variation perturbation approach is presented for the Dirac equation of linear molecules. The method is tested on the lowest S1/2 state of H and σ1/2 state of H2+.

The atomic polarisability of krypton and xenon

Mean static dipole polarisabilities are calculated for the ground states of atomic krypton and xenon using a variation-perturbation approach with a configuration interaction formalism. The values obtained are 16.79 and 27.78 a30 for krypton and xenon, respectively.

Exciton binding energy in a quantum well with inclusion of valence-band coupling and nonparabolicity.

Binding energies of excitons associated with several transitions between different subbands in undoped quantum wells are calculated for different well widths using a novel perturbational approach. The degeneracy of the valence band, the nonparabolicity of the conduction band, and the matching of the wave function at the interfaces are taken into account. The zeroth-order wave function is taken to be the product of the envelope functions in the z direction (perpendicular to the layers) for the electron and the hole and a purely two-dimensional (2D) exciton wave function. The difference between the 2D and 3D interaction between the electron and the hole is included in a variational-perturbational approach. The effect of the valence-band degeneracy on the properties of the holes is described with the use of the 4\ifmmode\times\else\texttimes\fi{}4 Luttinger Hamiltonian. We include the off-diagonal elements of this matrix in perturbation theory up to second order. This involves summations over the bound exciton states and integrals over the continuum states, which are found to be important. These off-diagonal elements in some cases modify the results considerably and improve the agreement with recent experimental results.

Evaluation of atomic polarisabilities using the variational perturbation approach: the first transition series

Using the variational perturbation approach, mean static dipole polarisabilities for the first transition series, resulting from the contribution to the total polarisability of the polarisation of the 4s shell, are calculated. Two different sets of calculations are performed. With the exception of zinc, the polarisabilities calculated using a 4p polarising function, determined by minimising the second-order energy functional and representing the zero-order wavefunction by the Hartree-Fock configuration 3dn(2S+1L)4s2 and each component of the perturbed function by the configurational function 3dn(2S+1L)4s(2SL)4p, are within 2% of that obtained from the theoretically more correct calculation, consisting of a 4p correlating function, determined to describe the important near-degeneracy effect 4s2 to 4p2, and a 5p polarising function, determined by optimising the second-order functional. In the latter optimisation the unperturbed wavefunction is represented by the Hartree-Fock single configuration 3dn4s2, augmented by the near-degenerate configuration 3dn4p2, and each component of the perturbed function consists of the most important polarising and configurational functions. In addition, it is shown that the configurations 3dn-14s24p and 3dn-14p3, from the 3d to 4p replacement, can be eliminated from the perturbed-states expansion, as their inclusion in the configuration interaction expansion of the perturbed states causes less than a 1% change in the polarisability.

Effect of coupling between heavy and light holes on the binding energy of an exciton in a quantum well

The binding energy of excitons belonging to the different subbands in a quantum well has been calculated for different well widths and barrier heights. The degeneracy of the valence band, the non-parabolicity of the conduction band and the matching of the wave function at the interfaces are taken into account. The zeroth order wave function is taken to be the product of the envelope functions in the z-direction (perpendicular to the layers) for the electron and the hole and a purely two-dimensional (2D) exciton wave function. The difference between the 2D and 3D interaction between the electron and the hole is included in a variational-perturbational approach. The effect of the valence band degeneracy on the properties of the holes is described with the use of the 4 × 4 Luttinger Hamiltonian. Most previous authors have only considered the diagonal elements of this matrix, which are included in our zeroth order Hamiltonian. We include the off-diagonal elements in perturbation theory up to second order. This involves summations over bound exciton states and integrals over the continuum states, which are found to be important. These off-diagonal elements in some cases modify the results considerably and improve the agreement with recent experimental results.