Energy shift in (dtμ)e due to the finite size of the muonic molecular ion (dtμ)+

The energy shift due to the presence of the extended (dtμ)₁₁ pseudonucleus (in its first excited state with one unit of angular momentum) in the quasihydrogenlike system (dtμ)₁₁ e _1s is estimated using perturbation theory up to second order with two choices of zeroth order electron wavefunctions. The energy shift is found to be 0.50 meV using pure Coulomb electron wavefunctions and 0.58 meV using electron wavefunctions calculated with a potential modified to take partial account of the finite size of (dtμ)₁₁. In both cases, the perturbation Hamiltonian is expanded in multipoles, retaining terms up to and including octupole terms.     

Excited-state energy eigenvalue and wave-function evaluation of the Gaussian asymmetric double-well potential problem via numerical shooting method 2

This project aims at computation excited-state energy eigenvalues and wave-function of a particle under Gaussian asymmetric double-well potential using numerical shooting method and perturbation theory a method to deal with discrete-eigenvalue problems. We also compare the energy eigenvalue and wave-function with those obtained from other typical means popular among physics students, namely the numerical shooting method and perturbation theory. Show that the idea of program of the numerical shooting method and perturbation theory of this problem (see Sects. 2.1 and 4) The numerical shooting method is generally regarded as one of the most efficient methods that give very accurate results because it integrates the Schr?dinger equation directly, though in the numerical sense. The n = even case is shown in Figs. 4, 5 and 6. In this case, the wave-function has split up on asymmetric nodes under Gaussian asymmetric double-well potential. The n = odd case is shown in Fig. 7. In this case, the wave-function has not split up on asymmetric nodes under Gaussian asymmetric double-well potential.     

Second-order perturbation theory for the angular pair correlation function in molecular fluids

Second-order perturbation theory is used to calculate spherical harmonic coefficients of the angular pair correlation function g(rω₁ω₂) for a liquid in which the molecules interact with a pair potential that is the sum of Lennard-Jones and quadrupole-quadrupole parts. The theory is compared with both molecular dynamics results and with the predictions of the GMF ≡ LHNC, QHNC and first-order perturbation theories. Second-order perturbation theory gives excellent results for the harmonic coefficient g(224,r), but is poorer for g(222,r) and g(202,r).     

The infrared spectrum of cyclohexane adsorbed on Pt(111)

The reflection—absorption infrared spectrum of cyclohexane adsorbed on Pt(111) has been recorded using a Fourier Transform spectrometer. The spectrum at 150 K shows the broad, low-frequency CH stretching band previously revealed by electron energy loss spectroscopy and also three sharper bands attributed to vibrational modes involving the relatively unperturbed hydrogens. At 95 K a second adsorbed phase is formed in which the perturbation of the molecule is reduced. Continued exposure leads to multilayer formation. Spectra of adsorbed monolayers of the related compounds n-hexane, cyclopentane and 2,2-dimethylpropane (neopentane) showed much less evidence for perturbation of CH bonds.     

The non-additive ligand field

The semi-empirical ligand field is a perturbation operator whose consequences are taken to first order using a basis set ofl functions. Since the basis spans an irreducible representation of the 3-dimensional rotation-inversion groupR _3i it is useful to express the operator as a sum of components of irreducible tensor operators with respect to this group. IfR _3i is reduced with respect to the molecular subgroup the electronic factor of each term in the sum must be totally symmetrical within this group. This choice of operator leads to thecrystal field parameterization without implying an electrostatic model. Alternatively a shift operator withinl space may be chosen as the essential part of the perturbation operator. This leads to theligand field parameterization. Between the two parameterizations there exists a one to one relationship, whose coefficients are proportional to 3l symbols. This relationship is given together with a brief discussion of the reasons for the proposed parameterizations.     

A theoretical study of the dielectric solvent effect on vicinal spin coupling constants

The dielectric solvent effect on HCCH, HCNH and HCNC spin coupling constants in ethane, tetrachloroethane and trans N-methylformamide has been calculated by finite perturbation theory based on the INDO and CNDO/2 approximations incorporating solvaton theory. The available experimental data are interpreted using the calculated variations of spin coupling constants. The effect of dielectric constant on the general form of the Karplus relation is included in the finite perturbation calculations.     

The calculation of ionization energies by perturbation,configuration interaction and approximate coupled pair techniques and comparisons with green's function methods for Ne,H2O and N2

The vertical valence ionization potentials of Ne, H₂O and N₂ have been calculated by Rayleigh-Schrödinger perturbation and configuration interaction methods. The calculations were carried out in the space of a single determinant reference state and its single and double excitations, using both the N and N - 1 electron Hartree-Fock orbitals as hole/particle bases. The perturbation series for the ion state were generally found to converge fairly slowly in the N electron Hartree-Fock (frozen) orbital basis, but considerably faster in the appropriate N - 1 electron RHF (relaxed) orbital basis. In certain cases, however, due to near-degeneracy effects, partial, and even complete, breakdown of the (non-degenerate) perturbation treatment was observed. The effects of higher excitations on the ionization potentials were estimated by the approximate coupled pair techniques CPA′ and CPA″ as well as by a Davidson type correction formula. The final, fully converged CPA″ results are generally in good agreement with those from PNO-CEPA and Green's function calculations as well as experiment.     

Improvement of the RKR procedure obtained by semi-classical calculations

In this letter we present a new technique to improve RKR molecular potential curve calculations. The potential curve obtained gives calculated G(ν) and B(ν) values extremely close to the measured ones. The aim of these calculations is the same as that of the inverted perturbation approach of Vidal and Sheingraber, but the potential-well corrections are calculated by using Watson's semi-classical inversion procedure.     

Semiclassical exponential perturbation theory. An adiabatic approach for rotationally inelastic scattering

The exponential perturbation approximation is tested in the semiclassical perturbed stationary states frame, using spline functions for interpolation of the non-adiabatic couplings. An application is realized for the p-H₂ + ⁴He rotational cross sections.     

Evaluation of the toxicity of ZnO nanoparticles to Chlorella vulgaris by use of the chiral perturbation approach

The toxicity of ZnO nanoparticles (NPs) has been widely investigated because of their extensive use in consumer products. The mechanism of the toxicity of ZnO NPs to algae is unclear, however, and it is difficult to differentiate between particle-induced toxicity and the effect of dissolved Zn²⁺. In the work discussed in this paper we investigated particle-induced toxicity and the effects of dissolved Zn²⁺ by using the chiral perturbation approach with dichlorprop (DCPP) as chiral perturbation factor. The results indicated that intracellular zinc is important in the toxicity of ZnO NPs, and that ZnO NPs cause oxidative damage. According to dose–response curves for DCPP and the combination of ZnO NPs with (R)-DCPP or (S)-DCPP, the toxicity of DCPP was too low to perturb the toxicity of ZnO NPs, so DCPP was suitable for use as chiral perturbation factor. The different glutathione (GSH) content of algal cells exposed to (R)-DCPP or (S)-DCPP correlated well with different production of reactive oxygen species (ROS) after exposure to the two enantiomers. Treatment of algae with ZnO NPs and (R)-DCPP resulted in reduced levels of GSH and the glutathione/oxidized glutathione (GSH/GSSG) ratio in the cells compared with the control. Treatment of algae with ZnO NPs and (S)-DCPP, however, resulted in no significant changes in GSH and GSH/GSSG. Moreover, trends of variation of GSH and GSH/GSSG were different when algae were treated with ZnSO₄·7H₂O and the two enantiomers. Overall, the chiral perturbation approach revealed that NPs aggravated generation of ROS and that released Zn²⁺ and NPs both contribute to the toxicity of ZnO NPs.

Perturbed hard-sphere equations of state of real fluids. II. Effective hard-sphere diameters and residual properties

Effective hard-sphere diameters for argon, krypton and xenon have been calculated from the currently most accurate perturbation theories using accurate pair-potential models. Based on the theoretical diameters and on pressure—volumes—temperature data for the real fluids, the van der Waals parameter a_p is examined and two conjectures generalizing the behavior of a_p are formulated. These conjectures make it possible to evaluate the effective hard-sphere diameters of simple liquids at the triple-point temperature from data for a few low-temperature pressure—volume isotherms. This fact, together with a corresponding-states principle that emerges from results for the theoretical diameters, forms the basis of a simple method which we propose for evaluating temperature-dependent effective hard-sphere diameters of a perturbed hard-sphere equation of state, independently of any pair-potential model and any perturbation theory. The applicability of the method is demonstrated for methane and its extension to nonsimple liquids is discussed. It is also shown that the use of an approximate theory and/or approximate pair-potential model may often result in a qualitatively misleading picture of a_p behavior.     

A variational principle for weak stimulated absorptions with energy minimizing fields

Optimal time-dependent perturbations in agreement with the Bohr condition for spectroscopic transitions are obtained variationally for two-level systems via the first-order perturbation model. The criterion of optimality is that specified weak absorptions are achieved with minimal applied energy. Results obtain for fixed perturbation intervals of arbitrary length.     

The segment-cloud model of the second virial coefficient of polymer solutions: effects of chain length and branching

The segment-cloud model for polymer molecules has been used, and the second virial coefficient A₂ obtained as a function of the interaction parameter z for linear and branched chains having different values of n. It is observed that the chain length effect, though much smaller than in the perturbation theory, increases as the degree of branching increases. Also, the branching parameter g is found to be a better correlating parameter than the segment density distribution for A₂. This is in contrast to earlier results for the perturbation theory of the excluded volume.     

Calculations of hydrogen—fluorine and fluorine—fluorine nuclear magnetic spinspin coupling anisotropies for fluorinated ethenes and benzenes oriented in liqiud crystal solvents

Spinspin coupling tensors are calculated using self-consistent perturbation theory and INDO wavefunctions, in order to estimate whether neglect of their anisotropy influences molecular dimensions deduced from the NMR spectra of partially oriented solutes. It is found that anisotropy of cis and trans and many aromatic HF couplings can be neglected but that trans FF couplings are markedly anisotropic. Comparisons are made with the limited experimental results.     

Three-electron approach of HgH using relativistic effective core,core polarization and spin-orbit operators: the low-lying states

The lowest states of HgH are calculated using a non-empirical relativistic effective core potential considering the mercury atom as a two-electron system. The configuration interaction is done within the CIPSI algorithm. Core-valence polarization and correlation energy are included through a perturbation treatment. The spin-orbit coupling is introduced through an effective hamiltonian in a basis of LS states. Results obtained for the lowest states of HgH are in fair accordance with experimental results. The “atom in molecule” approximation for SO coupling is discussed.     

Lasing without inversion III: microwave coupling induced atomic coherence

We consider the nondegenerateA quantum beat laser, and investigate the possibility of lasing without population inversion when coherence is established, between the lower levels, by applying a strong microwave field. For a specific example we calculate how much coherence may be established between the lower levels using microwave coupling. Analytical calculations are presented for both the open and closed three level atomic systems, using perturbation theory up to third order in the optical fields. Taking the linear equations, we show numerically how gain may be achieved.     

Quantitative aspects of 119Sn-CIDNP

Enhancement factors of the ¹¹⁹Sn-CIDNP signals observed in hexamethylditin — the recombination product of trimethyltin radicals — are determined. The enhanced absorption in the main ¹¹⁹Sn signal, which cannot be explained by Kaptein's rules based on a first order perturbation treatment of the radical pair theory, can be described by applying the high field approximation of the radical pair model if second order perturbation theory is used. The A/E type multiplet effect in the satellites arising from coupling with ¹¹⁷Sn nuclei which is in accordance with Kaptein's rules is not affected by the second order treatment. Pedersen's analytical expressions derived from the three-dimensional diffusion model describe the ¹¹⁹Sn-CIDNP effects using p = 0.32 and Λ = 1 or p = 0.5 and Λ = 0.56. During the photochemical decomposition of hexamethylditin and octamethyltritin, the main ¹¹⁹Sn signals show enhanced absorption. Enhancement factors found experimentally are compared with values calculated using the second order treatment. It follows that both compounds mainly decompose from triplet states.     

Fatigue propagation path of 3D plane cracks under mode I loading

The fatigue growth path of an arbitrary plane crack, loaded by some remote tensile uniform stress, is computed using a perturbation method derived from the three-dimensional weight-function theory of Rice (1985, 1989). First, the stress intensity factor and the weight function of the initial front are calculated. Then, the crack advance is determined by applying Paris' law. One advantage of the method is that only the meshing of the initial front is needed, allowing for the study of propagation on a large scale.     

Multipole polarizabilities of Ar

The four lowest multipole polarizabilities of Ar have been calculated by using the complete fourth-order many-body perturbation theory approach and a large GTO/CGTO basis set including a number of diffuse and polarization functions. The present results for the dipole polarizability (α =11.23 au), quadrupole polarizability (C= 26.79 au), dipole-quadrupole polarizability (B = -164.3), and the dipole hyperpolarizability (γ =1329 au) are compared with other theoretical data and experimental values.     

Thermodynamic perturbation theory of simple liquids

It was proven that after averaging over the canonical Gibbs ensemble, the mean perturbation energy was singled out of the classical partition function before the expansion in a series of perturbation theory. Therefore, the term that formally coincides with first order perturbation theory in a decomposition of the Helmholtz free energy bears no relationship to perturbation theory. Then the proper series of the thermodynamic perturbation theory always starts with a second order infinitesimal. Therefore, the wellknown condition of applicability of the thermodynamic perturbation theory, “...the requirement that the perturbation energy per particle be small compared with T...” (L. D. Landau and E. M. Livshits, Statistical Physics, Vol. V, Pt. I), can be substantially weakened. The most important factor for applicability of thermodynamic perturbation theory is the value of many-particle correlations in an unperturbed system, but not the smallness of the perturbation potential.