Electronic transition dipole moment functions for NaK

Phase-consistent electronic transition dipole moment functions were calculated (as a function of internuclear separation) for the 80 dipole selection rule allowed transitions in the manifold of states of NaK treated previously [W. J. Stevens, D. D. Konowalow, and L. B. Ratcliff, (1984) J. Chem. Phys. 80, 1215–1224]. Agreement was found with experimental determinations of the 2¹Π-1¹Σ⁺ transition. Agreement of the asymptotic values with experimental and previous theoretical determinations of corresponding atomic transition moments suggests that the present computations may be relatively reliable. The positions of a number of satellite bands are predicted from the potential energy difference curves.     

Electronic transition dipole moment functions and difference potentials for transitions among low-lying states of Li2 and Na2

Electronic transition dipole moment functions based on ab initio multiconfiguration self-consistent field wavefunctions are computed for the transitions ¹Σ_u⁺-¹Σ_g⁺, ³Σ_g⁺-³Σ_u⁺, ¹Π_u-¹Σ_g⁺, ³Π_g-³Σ_u⁺, ¹Σ_u⁺-¹Π_g, ³Σ_g⁺-³Π_u, ¹Π_u-¹Π_g, and ³Π_g-³Π_u in Li₂ and Na₂. (In each case the states are the lowest lying of their symmetry.) We also calculate the matrix element 〈³Σ_u⁺|i(L_x - iL_y)|³Π_u〉 for the predissociation of the ³Π_u state by the ³Σ_u⁺ state. Several unobserved spectral features are predicted.     

Conical quantum dot: Electronic states and dipole moment

The electronic states in a conical quantum dot in the framework of the adiabatic approximation as well as the combined approach with the perturbation theory have been considered. The obtained results have been compared with the results of numerical methods–the finite element and the Arnoldi methods. The interpolation formula for the energy correction and its dependence on the geometric parameters of the conical quantum dot have been obtained. The comparing of the wave functions obtained by different methods and the range of applicability of different methods have been defined. The dependence of the z-component of the dipole moment on the geometric parameters of the structure has been considered.     

Effective dipole moment of rotational transitions of X 2 Y molecules

Contributions determining the rotational dependence of the effective dipole moment of molecules are calculated for the ground state of H₂S and H₂O molecules. The calculation is carried out in various ordering algorithms of perturbation theory. It is shown that the convergence of the effective dipole moment for the ground state of an H₂O molecule in the polynomial representation is rather slow in the rotational operator J _z (the convergence radius is K*≤17). Nonpolynomial forms of the dipole moment as a function of rotational operators are discussed.     

Ab initio calculation of transition dipole moments for transitions between valence states in oxygen molecules

Results of ab initio calculations of potential-energy curves for 20 singlet and 20 triplet valence states of oxygen with configuration interaction taken into account in the 6-31G basis are presented. Transition dipole moments of triplet-triplet (1³Π_g ← B ³Σ _u ^? , 1³Π_g ← A ³Σ _u ⁺ , 1³Π_g ← A′ ³Δ_u, B ³Σ _u ^? ← X ³Σ _g ^? , 2³Π_u ← 1³Π _g, 2³Σ _g ^? ← B ³Σ _u ^? , 1³Π_u ← X ³Σ _g ^? , 2³Π_u ← X ³Σ _g ^? , 2³Π _g ← A′³Δ_u, 3³Π_g ← A′ ³Δ _u, 2³Δ_u ← 2³Π_g, 3³Π_g ← B ³Σ _u ^? , and 2³Π_g ← A ³Σ _u ⁺ ) and singlet-singlet (2¹Σ _g ⁺ ← 2¹Π_u, 2¹Π_u ← 1¹Π ^g, ¹Π_u ← 2¹Δ_g, 1¹Π_g ← c ¹Σ _u ^? , ¹Π_u ← b ¹Σ _g ⁺ , 1¹Δ _u ← a ¹Δ_g, 2¹Π_u ← a ¹Δ_g, 2¹Δ_g ← 1¹Δ_u, ¹Π _u ← a ¹Δ _g, 1¹Π_u ← b ¹Σ _g ⁺ , 2¹Π_g ← 1¹Π_u, 2¹Π _g ← c ¹Σ _u ^? , 1¹Δ _u ← 1¹Π _g, f′Σ _u ⁺ ← b ¹Σ _g ⁺ , 2¹Σ _g ⁺ ← f ′¹Σ _u ⁺ , 3¹Π_g ← 1¹Δ_u) radiative transitions are calculated as functions of internuclear separation. The possibility of observing these transitions under experimental conditions is discussed.     

Dipole moment functions for electronic transitions from ion-pair states of the second tier of molecular iodine

The emission spectra caused by the transitions from the ion-pair states and f0 _g ⁺ and G1_g of the I₂ molecule are obtained by excitation of individual rovibronic levels of the molecule by the method of optical-optical double resonance. The emission spectra from the state F0 _u ⁺ populated due to collisions I₂(f) + I₂(X) are also measured. By modeling the experimental emission spectra, the dipole moment functions for the electronic transitions f _g ⁺ -B0 _u ⁺ , A0 _u ⁺ , and B″0 _u ⁺ ; G1_g-A0 _u ⁺ and B″0 _u ⁺ ; and F0 _u ⁺ -X0 _g ⁺ and a′0 _g ⁺ of the iodine molecule are reconstructed.     

Matter wave interferometry for measuring a molecular transition dipole moment

We consider localized states of both single- and two-component Bose-Einstein condensates (BECs) confined in a potential resulting from the superposition of linear and nonlinear optical lattices and make use of Vakhitov-Kolokolov criterion to investigate the effect of nonlinear lattice on the stability of the soliton solutions in the linear optical lattice (LOL). For the single-component case we show that a weak nonlinear lattice has very little effect on the stability of such solitons while sufficiently strong nonlinear optical lattice (NOL) squeezes them to produce narrow bound states. For two-component condensates we find that when the strength of the NOL (γ ₁) is less than that of the LOL (V ₀) a relatively weak intra-atomic interaction (IAI) has little effect on the stability of the component solitons. This is true for both attractive and repulsive IAI. A strong attractive IAI, however, squeezes the BEC solitons while a similar repulsive IAI makes the component solitons wider. For γ ₁ > V ₀, only a strong attractive IAI squeezes the BEC solitons but the squeezing effect is less prominent than that found for γ ₁ < V ₀. We make useful checks on the results of our semianalytical stability analysis by solving the appropriate Gross-Pitaevskii equations numerically.     

Radiative strength functions for dipole transitions in 90Zr

Partial cross sections for the (p, γ) reaction on the ⁸⁹Y nucleus that were measured previously at proton energies between 2.17 and 5.00 MeV and which were averaged over resonances were used to determine the absolute values and the energy distribution of the strength of dipole transitions from compound-nucleus states to low-lying levels of the ⁹⁰Zr nucleus. The data obtained in this way were compared with the predictions of various models.     

Electric dipole transitions for highly excited states in helium-like sulphur

We have calculated relativistic energies, weighted oscillator strengths and transition probabilities for electric dipole (E1) transitions among the terms belonging to 1snl (n?9, l?3) configurations in helium-like sulphur. The calculations are based upon the multiconfiguration Hartree-Fock method within the framework of Breit-Pauli relativistic corrections. Our calculated values are also compared with other experimental and theoretical results.     

On the finite-field transition dipole moment calculations by effective Hamiltonian methods

A simple finite-field scheme of calculations on electronic transition dipole moments in molecules by effective Hamiltonian methods is presented and discussed. The reliability of underlying approximations is analyzed by means of the quasidegenerate perturbation theory and corroborated by the results of pilot numerical applications. Received: 11 May 1998 / Revised and Accepted: 20 July 1998     

Unique definitions for the band strength and the electronic-vibrational dipole moment of diatomic molecular radiative transitions

Unique definitions of the band strength and the electronic-vibrational dipole moment are inferred from a recently published fundamental discussion on the line strength of rotational transitions in diatomic molecules. In addition, consistent relations between these quantities and the transition probability or oscillator strength are presented.     

Radiative strength functions for dipole transitions in 57, 59Co

Data on the (p, γ) reactions on ^{56, 58}Fe that were taken at proton energies of E _p =1.5–3.0 MeV and which were averaged over resonances are used to determine the absolute values of the radiative strength function at energies below 10 MeV. The results obtained in this way are compared with the results of the calculations that rely on the statistical approach and which take into account the temperature of the nucleus and its shell structure. Good agreement with experimental data is achieved without any variation of parameters.     

Equilibrium states and dynamics of the dipole moment of square arrays of dipoles

The dipole lattices in the form of 3 × 3–8 × 8 dipole square arrays have been considered. It has been shown that, after turning off the external field orienting dipoles along the edges of the array, two types of equilibrium configurations of dipole moments can exist depending on the size of the system, namely, the state symmetric with respect to the diagonal of the array and the state with the total dipole moment directed along the edges of the array. It has been found that there are differences in these types of configurations with respect to the alternating-field-induced oscillation modes of the total dipole moment of the system. The dependence of the oscillation modes on the direction of linear polarization of the alternating field has been investigated.     

Forbidden transitions in homopolar isotopically unsymmetric diatomic molecules and the dipole moment of HD

The theoretical expressions for the intensities of forbidden rotational and rotation-vibration spectra of homopolar isotopically unsymmetric diatomic molecules, made allowed by the breakdown of the Born-Oppenheimer approximation, are derived. The results are applied to HD and it is shown that among the previously overlooked contributions to the dipole moment of the molecule there is one with a very significant value in the direction H^?D⁺. A rotationally dependent contribution arising from centrifugal distortion is extremely small. The intensities of the fundamental and overtone bands of HD are also considered.     

Observations of the collision-induced dipole transitions and of a quadrupole transition for barium in krypton

For Ba perturbed by Kr, collision-induced dipole transitions 6s²¹S₀ – 6snd¹D₂ (8?n?10) have been observed. The effective oscillator strength per unit Kr density was found to be 1.8–1.0 x 10^-23 cm³. For the electric-quadrupole transition 6s²¹S₀ -6s6d¹D₂, the oscillator strength is (2.0±0.4) x 10^-6.     

Adequate representation of the dipole moment function for diatomic molecules and the matrices of vibration-rotation transition moments

An exponential representation of perturbations is used as a basis of the perturbed Morse oscillator approach which is applied, in a matrix form, for calculating the radial matrix elements for diatomic molecules. An analytic procedure is developed to deduce an exponential-power series expansion for the dipole moment function M(r) from experimental spectral intensities. It is shown that for real anharmonic molecules, the series expansion in powers of e^ar (α being the Morse parameter) is an adequate form for representing transition operators, just as the usual series expansion in powers of internuclear distance r is adequate for the case of a harmonic oscillator, and it is equivalent to a series expansion in vibrational wavefunctions. An exponential-power series expansion is derived as well for a model dipole moment function which has a correct long-range dependence and limit. To exemplify the accuracy and efficiency of the technique proposed, the (40 × 40) matrices of vibration-rotation transition moments 〈vJ|M(r)|v′J′〉(v, v′ = 0, 1, …, 39) have been calculated for the ground state of CO. Typical results of these computations are presented (up to v = 35, J = 100, and v′ ? v = 1–4) to illustrate the dependence of vibration-rotation interaction functions on the vibrational and rotational quantum numbers.