Dissociation energy of diatomic molecules

The dissociation energy of twelve diatomic molecules has been determined by fitting four-parameter potential functionU(r)=D _e[[1−exp{−b(r−r _e)}]/ [1−Cexp{−b(r−r _e)}]]² to the true Rydberg-Klein-Rees (RKR) curves for their fifteen electronic states using the mean square deviation as the criterion for the selection of the best fit. Average deviation ofD _e has been found to be 2.7% as compared to 20.5% obtained with Lippincott’s potential function for these molecules. In addition the anharmonocity constantω _ex_e has also been calculated for the same electronic states yielding average mean deviation 8.9%.     

Wei Hua’s four-parameter potential: Comments and computation of molecular constants αe and εeXe

The value of adjustable parameterC in the four-parameter potentialU(r) =D _e [(1 - exp[-b(r -r _e)])/(1 -C exp[-b(r -r _e)])]² has been expressed in terms of molecular parameters and its significance has been brought out. The potential so constructed, withC derived from the molecular parameters, has been applied to ten electronic states in addition to the states studied by Wei Hua. Average mean deviation for these 25 states has been found to be 3.47 as compared to 6.93, 6.95 and 9.72 obtained from Levine, Varshni and Morse potentials, respectively. Also Dunham’s method has been used to express rotation-vibration interaction constant (α_e) and anharmonicity constant (ω_ex_e) in terms ofC and other molecular constants. These relations have been employed to determine these quantities for 37 electronic states. For α_e, the average mean deviation is 7.2% compared to 19.7% for Lippincott’s potential which is known to be the best to predict these values. Average mean deviation for (ω_ex_e) turns out to be 17.4% which is almost the same as found from Lippincott’s potential function.     

X-ray energy levels: Deviations between experimental and theoretical values

Energy values ofK, L _II andL _III levels calculated by the relativistic self consistent field method have been used to compute the energies ofKα _{1, 2} lines. These values deviate considerably from the experimental values due to Bearden and Burr. The deviations are discussed and given an empirical fit.     

Overtone spectroscopy of benzaldehyde

The vibrational overtone spectra of aryl and alkyl C-H stretch vibrations in benzaldehyde have been studied using conventional IR and thermal lensing technique at room temperature. The stretching vibrational frequencyω _e, anharmonicity constantω _e x _e and the dissociation energies of the two C-H bonds have been calculated. The bond length of C-H bond in aryl position has been estimated.     

Return current instability and its effects on beam-plasma system

The return current induced in a plasma by a relativisitc electron beam generates a new electron-ion two-stream instability (return current instability). Although the effect of these currents on the beam-plasma e-e instability is negligible, there exists a range of wave numbers which is unstable only to return current (RC) instability and not to e-e instability. The electromagnetic waves propagating along the direction of the external magnetic field, in which the plasma is immersed, are stabilized by these currents but the e.m. waves with frequencies,ω ²≪Ω _e ² ≪ω _pe ² (Ω _e andω _pe being cyclotron and plasma frequency for the electrons of the plasma respectively) propagating transverse to the magnetic field get destabilized. Heuristic estimates of plasma heating, due to RC instability and due to decay of ion-acoustic turbulence generated by the return current, are made. The fastest time scale on which the return current delivers energy to the plasma due to the scattering of ion-sound waves by the electrons can be ∼ω _pi ⁻¹ (ω _pi being the plasma frequency for the ions).     

Electron screening in backward elastic scattering

Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θ_lab=165° and E _lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σ_R(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σ_R(E,θ)=(1+U_e/E)⁻¹, where U _e is an atomic screening potential energy. The deduced average value, U _e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998     

Effect of upflowing field-aligned electron beams on the electron cyclotron waves in the auroral magnetosphere

The role of low density upflowing field-aligned electron beams (FEBs) on the growth rate of the electron cyclotron waves at the frequencies ω _r < Ω_e, propagating downward in the direction of the Earth’s magnetic field, has been analysed in the auroral region at ω _e/Ω_e < 1 where ω _e is the plasma frequency and Ω_e is the gyrofrequency. The FEBs with low to high energy (E _b) but with low temperature (T _‖b) have no effect on these waves. The FEBs with E _b < 1 keV and T _‖b (> 1.5 keV) have been found to have significant effect on the growth rate. Analysis has revealed that it is mainly the T _‖b which inhibits the growth rate (magnitude) and the range of frequency (bandwidth) of the instability mainly in the higher frequency spectrum. The inhibition in the growth rate and bandwidth increases with increase in T _‖b. The FEBs with less E _b (giving drift velocity) reduce growth rate more than the beams with larger E _b. The inhibition of growth rate increases with the increase in the ratio ω _e/Ω_e indicating that the beams are more effective at higher altitudes.      

Total electron scattering cross-sections for O atoms: O2 and O3 molecules

Total (elastic+inelastic) cross sections fore ⁻-O,e ⁻-O₂ ande ⁻-O₃ scattering have been calculated at sample energies between 100 and 1000eV. The basice ⁻-O atom scattering amplitudes are obtained from the partial wave analysis with a complex optical potential. Thee ⁻-O₂ ande ⁻-O₃ cross-sections are obtained through the independent atom model. Oure ⁻-O₂ cross-sections reproduce the experimental data quite well. Adequate comparisons are made in all the three cases.     

Fractionally charged non-leaking dyons and fermions in a bag

We consider a fermion of chargee confined to a spherical bag with a Dirac monopole of strengthg at its centre. We find that the boundary conditions making the lowest angular momentum hamiltonian self-adjoint are characterized by a unitary matrixU, and the corresponding vacuum charge has a fractional part 2|eg|α/π where detU = -exp (2iα). Boundary conditions for conservation of helicity,CP, CT andPT are displayed. We demonstrate the possibility of a fractionally charged dyon whose interaction with a fermion conserves helicity. We also show thatthe simultaneous validity of helicity, CP, CT and PT requires integer vacuum charge.     

Spin-orbit coupling in the ground and low-lying excited states of HF<Superscript>+</Superscript> and HF<Superscript>-</Superscript>

Electronic structure and spectroscopic properties B _e, ω_e, ω_e x _e, α_e, T _e of ground state and the low-lying excited states of HF⁺ and HF^- molecular ions were investigated within scalar relativistic multireference configuration interaction with single and double excitations framework using the GAMESS-US program package. All potential energy curves (PECs) were calculated using the relativistic complete active space self-consistent field/spin-orbit multi-configuration quasi-degenerate perturbation theory (CASSCF/SO-MCQDPT). The curves are all fitted to the analytical potential energy function (APEF), from which accurate spectroscopic constants are derived. The spin-orbit splitting was also been studied, the split value of X²P^{2}{\rm \Pi} state of HF⁺ is determined to be 288.38 cm^-1. The calculated properties are in good agreement with the available experimental value. Spectroscopic constants of the ground states of HF^- that have never been observed in experiment are obtained. These curves provide an interpretation of the known experimental observations on this system and suggest a number of further experiments which possible provide a critical test of this data.     

Resonant and surface polaritons in quantum wells

Summary We show how the breaking of the translational invariance in a quantum well modifies the concept of polariton with respect to that defined for bulk material. Polaritons in quantum wells result from the combination of the exciton states with the radiation field. They are here obtained as the solutions of Maxwell equations with retardation, provided an appropriate nonlocal response function is used for the electric susceptibility, and Maxwell boundary conditions are imposed. We find two types of polaritons depending on the values of the in-plane wavevectork _II: those atk _II<ω/v (wherev=c/n is the velocity of light in the sample) are resonant with the radiation field in the barrier and those atk _II>ω/v cannot be coupled to waves in the barrier. In both cases explicit expressions are given for radiative shifts and radiative broadenings as functions ofk _II. Numerical results are obtained for GaAs-Ga_1−x Al _x As and for CuCl quantum wells and new experiments are suggested. The existence of resonant and surface polaritons justifies an interpretation of the temperature dependence of the radiative lifetime suggested by the same authors. It also decreases the radiative efficiency in the direction perpendicular to the planes and increases the radiative efficiency parallel to the planes with increasing temperature. Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.     

Comment on: “Universal relation between spectroscopic constants”

Kaur and Mahajan [1] have claimed to derive a universal relation InG = 1.91578(±0.09727) + 0.97111(±0.03809) In Δ between the Sutherland parameter Δ(=ω _er _e ² /2D_e) and the dimensionless parameterG(= 8ω _ex_e/B_e) for the ground as well as excited electronic states of diatomic molecules. Validity of this relation is checked and we find that the relation is not correct. Next, we checked the validity of the relation Δ = 2.2r_e for the alkali group diatomic molecules. This relation is also found not to be correct.     

Influences on the pseudospin symmetry from the different fields of mesons in deformed nuclei

Influences from different fields of mesons on the pseudospin symmetry are investigated for deformed nuclei. The energy splitting between pseudospin partners are extracted from the relativistic mean field calculations. The results show that the σ-field contribution to the pseudospin energy splitting has nearly the same magnitude as the one obtained by the ω-field, but with opposite signs. The pseudospin energy splittings either for neutron or for protons are almost the same if the σ-field (V _σ ) and the ω-field (V _ω ) change at the same scale. The pseudospin energy splitting depends in the same way as the nucleus binding energy of the cancellation of these two potentials, and is controlled by the same nuclear physics scale as the potential sum V _ω + V _σ In comparison with the σ- and ω-fields, it is seen that the ρ meson field produces a minor influence on the pseudospin symmetry.     

“Quasi-Planck” spectra of capillary turbulence on the surface of liquid hydrogen

We report the first observation of “quasi-Planck” spectra of capillary turbulence on the surface of liquid hydrogen in the dissipation domain. Capillary waves have been driven by low-frequency random force. We have observed that the frequency spectrum of surface elevation changes its dependence from power-like 〈|η_ω²|〉 ∼ ω^−2,8 at middle-frequency domain to “quasi-Planck” distribution ∼e ^ω/ω _d at higher frequencies. The frequency ω _d is proportional to the boundary frequency between inertial interval and dissipation domain and it is scaled up with the increase of driving force.     

New analysis of the Douglas-Herzberg system (A1Π- X1Σ+) in the CH+ ion radical

Three bands of the A¹Π- X¹Σ⁺ system in the ¹²CH⁺ ion radical have been rephotographed under high resolution as an emission spectra using a Geissler-type discharge tube. The conventional technique of spectroscopy has been implemented. Using the Th lines as a standards, as well as an interferometric comparator equipped with a photoelectric scanning device, the 0-0 , 0-1 and 2-1 bands have been reanalyzed. By means of much longer bands (J_max = 17 in the Q(J) branch of the 0-0 band; J_max = 16 in the R(J) branch of the 0-1 band; J_max = 14 in the P(J) and Q(J) branches of the 2-1 band), than have been observed so far, as well as the merged calculations, using another five bands given by Carrington et al. [A. Carrington, D.A. Ramsay, Phys. Scripta 25, 272 (1982)] additionally, more accurate molecular constants for the X¹Σ⁺ state, the improved reduced band system origin T_e = 24118.726 (14) cm^-1 as well as for the first time the equilibrium molecular constants with their one standard deviation for the A¹Π state in the CH⁺ molecule have been computed: ω_e'=1864.402(22), ω_ex_e'=115.832(14), ω_ey_e'= 2.6301(24), B_e'=11.88677(72), α_e'= 0.9163(18), γ_e'= -2.29(12)×10^-2, ε_e'= 4.95(20)×10^-3, D_e'=1.92960(31)×10^-3, β_e'= 1.0733(50)×10^-4, δ_e'= -1.312(16)×10^-5, , α_qe'= -3.14(16)×10^-3, and q_De'= -2.20(14)×10^-5 cm^-1. Only in our research the addition to the zero-point energy Y'₀₀=-1.9430 cm^-1 and cm^-1 have been calculated. The equilibrium bond lengths of r'_e=1.235053(37) ? and ? for the A¹Π and X¹Σ⁺ states, respectively have been computed. Full quantum-mechanics characteristic of the A-X bands system in the ¹²CH⁺ molecule, i.e. RKR turning points, the Franck-Condon factors and r-centroids have been obtained. Dissociation energies D_e^{X1 Σ+}=(38470± 3503) cm^-1 and D_e^{A1 Π}= (14415 ±3509) cm^-1 for the molecule under consideration have been estimated.     

Dispersion of electromagnetic waves in the presence of magnetic monopoles of electron mass in a uniform magnetic field

The dispersion relation of electromagnetic waves in the presence of magnetic monopoles of electron mass in a uniform magnetic field is obtained. The waves of the frequencyω in the range ω_ϱi<Ω_i<ω<Ω _e <ω_ϱa are analysed. It is shown that the monopole charges lead to observable effects. Finally, the results are applied to a typical pulsar.     

Effective thermal conductivity of granulated two-phase systems at interstitial air pressures

Considering the htermal conduction through molecular collisions an expression for the effective thermal conductivityλ _e of loose and granular two-phase materials at different interstitial air pressure has been derived. The dependence ofλ _e on pore and particle sizes, characteristic pressure and radiative heat transfer is also discussed. Calculated values ofλ _e of glass beads and loose building materials are compared with reported results.     

Estimation of rotational and vibrational constants for diatomic molecules using Mattera's potential function

Summary The potential function suggested by Mattera, Salvo, Terreni and Tommasini is investigated further and the expressions for rotational constant α_e and anharmonicity constantw _e x _e are obtained. The α_e andw _e x _e values of twentyseven diatomic molecules are calculated using those expressions and they are compared with their experimental values.     

New approach in theory of Clebsch-Gordan coefficients foru(n) andU q(u(n))

A new method for calculation of Clebsch-Gordan coefficients (CGCs) of the Lie algebrau(n) and its quantum analogU _q(u(n)) is developed. The method is based on the projection operator method in combination with the Wigner-Racah calculus for the subalgebrau(n−1) (U _q(u(n−1))). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form of the projection operator ofu(n) andU _q(u(n)). It is shown that theU _q(u(n)) CGCs can be presented in terms of theU _q(u)(n−1)) q−9j-symbols. Presented at the 9th International Colloquium: “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000. Supported by Russian Foundation for Fundamental Research, grant 99-01-01163. Supported in part by the U.S. National Science Foundation under Grant PHY-9970769 and Cooperative Agreement EPS-9720652 that includes matching from the Louisiana Board of Regents Support Fund.