Perturbation of the radiative lifetimes of rovibronic levels of the nl complex of terms of a diatomic molecule

Within the framework of a sufficiently general nonadiabatic model taking into account the interaction of an arbitrary finite number of electronic states and not requiring the smallness of a perturbation parameter, expressions have been obtained for the radiative lifetimes of the rovibronic levels of states of the nl complex of terms of a diatomic molecule. It is shown that the determination of ratios of the nonadiabatic and adiabatic radiative lifetimes for the rovibronic levels can be reduced to the solution of two independent problems (the determination of ratios of the adiabatic values of radiative lifetimes for the mutually perturbing states and determination of the expansion coefficients of the wave functions of rovibronic states in the Born-Oppenheimer basis set of wave functions) when the rovibronic states are perturbed by only a single rovibrational level of each electronic state or by an arbitrary number of rovibrational states of each electronic state provided that the potential curves of the combining states are similar and the dipole moments of electronic transitions weakly depend on the internuclear separation (which is quite a case for highly excited electronic states). To illustrate the efficiency of using the expressions obtained, the perturbations of the radiative lifetimes of rovibrational levels of the I ¹Π _g ^? and J ¹Δ _g ^? states of the 3d complex of terms of the H₂ molecule were considered.     

Electronic branching ratios of spontaneous emission for transitions between states of the 3d and 2p singlet complexes of terms of H2

The ratios of probabilities (the electronic branching ratios) for the rovibronic spontaneous transitions are for the first time measured for transitions from the rotational levels with J′≤6 of the I ¹Π _g ^? , v′=0–2 and J ¹Δ _g ^? , v′=0 states to the vibrational-rotational levels of different low-lying electronic states B ¹Σ _u ⁺ , v″, J′ and C ¹Π _u ^? , v?, J′?1 of the H₂ molecule (for the vibrational quantum numbers v″≤4 and v?≤2). Values of these quantities provide a new channel of information on the internal structure of the hydrogen molecule thus far unused and should be particularly sensitive to the adiabatic values of the electronic transition dipole moments. In studying the entire set of rovibronic radiative transitions, they may significantly add to the experimental data on rovibronic terms, radiative lifetimes, and vibrational and rotational branching ratios used before. The experimental data obtained are compared to the corresponding values derived from the results of an earlier semiempirical determination and ab initio calculation of the absolute transition probabilities. Our experimental data are in remarkable agreement with the semiempirical results and significantly differ from the ab initio results. This fact directly suggests the necessity of performing more accurate ab initio calculations of the rovibronic transition probabilities for the given systems of bands.     

Semiempirical investigation of perturbations of the g factors of electronic-vibrational-rotational levels of hydrogen: III. The r 3Π g − and s 3Δ g − states of the H2 and D2 molecules

The g factors of rovibrational levels of the (4d)r ³Π _g ^? and (4d)s ³Δ _g ^? states of the H₂ and D₂ molecules have been obtained for the first time. These values were found within the nonadiabatic model taking into account the interaction of the 4dπ³Π_g and 4dδ³Δ_g states in the pure precession approximation using semiempirical values of the expansion coefficients of the wave function in an adiabatic basis, which was obtained for the first time for the states of the triplet 4d complex of terms of the hydrogen molecules, and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. It is established that the interference effects of the interaction between the 4dπ³Π _g ^? and 4dδ³Δ _g ^? states lead to significant (up to 7 times for the r ³Π _g ^? state of the H₂ and D₂ molecules and 70 and 8 times for the s ³Δ _g ^? state of the H₂ and D₂ molecules, respectively) differences between the nonadiabatic values of the g factors and the corresponding adiabatic values. It is found that the perturbed values of the g factors are much closer to the values corresponding to the case of Hund’s d coupling of angular momenta than to the values corresponding to the b coupling. It is established that the perturbations of the g factors of rovibrational levels of the states of the 4d complex of terms are much greater (up to 2 times for the ³Π _g ^? states and 350 times for the ³Δ _g ^? states) than the perturbations of the same characteristics for the 3d complex of terms of the hydrogen molecule with the same vibrational and rotational quantum numbers.     

Energy levels and probabilities of radiative transitions in the Kr IX ion

The energy levels of the 3d ⁹4l (l = 1–3) and 3p ⁵3d ¹⁰4l (l = 0, 1) configurations in the Kr IX ion and the probabilities of radiative transitions to the ground state from these excited states have been calculated within the relativistic perturbation theory using a zero-approximation model potential. The results are shown to be stable within this approximation. The well-known problem of anomalously low accuracy of the calculations of some higher lying singlet levels is considered.     

Comparison of semiempirical and ab initio absolute probabilities of rovibronic transitions for the I 1Π g − , J 1Δ g − →C 1Π u ± system of bands of the H2 molecule

The absolute values of probabilities of the I ¹Π _g ^? , v′, J′; J ¹ Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ spontaneous transitions in the H₂ molecule (for the vibrational and rotational quantum numbers v′=v″=0–3, J′=1–6, and J″=J′, J′ ±1) are calculated by using ab initio and semiempirical data on the dipole moments of the 3dπ ¹Π_g, 3dδ¹Δ_g→2pπ¹Π_u electronic transitions. In both cases, the calculations are performed both in the adiabatic approximation and with an allowance for the nonadiabatic effect of electronic-rotational interaction. The coefficients of expansion of the wave functions of perturbed rovibronic states in the Born-Oppenheimer basis functions used in the calculations were obtained in the approximation of pure precession from experimental values of the terms. It was found that the values of transition probabilities based on the ab initio calculations systematically exceed the corresponding semiempirical data by a factor of 1.2–1.9 for the I ¹Π_g→C ¹Π _u ^± transition and by a factor of 1.4–1.6 for the J ¹Δ _g ^? →C ¹Π _u ^± transition. It was established that the difference between the ab initio and semiempirical values of electronic transition moments virtually has no effect on the dependence of the transition probabilities on the vibrational quantum numbers. The discrepancies between the results of adiabatic and nonadiabatic calculations are significant and reach two orders of magnitude, which is indicative of the important role of perturbations in the probabilities of the transitions considered.     

Observation of perturbations in the rovibronic transition probabilities for the (4d)r 3Π g − , (4d) s 3 Δ g − → (2p) c 3Π u ± band systems of the H2 molecule

The ratios of the radiative transition probabilities for the lines of the P, Q, and R branches of the (4d)r ³Π _g ^? , (4d)s ³Δ _g ^? → (2p) c ³Π _u ^± band systems of the H₂ molecule have been measured for the first time. Significant (to two orders of magnitudes) differences are found between the experimental values and the adiabatic theory predictions. It is established that the results of the nonadiabatic calculation performed by us in the pure-precession approximation taking into account the electronic-rotational interaction of the 4d ³Π_g and 4d ³Δ_g states are in agreement with the experimental data. The optimal energies of rovibronic levels of the r ³Π _g ^? , s ³Δ _g ^? , c ³Π _u ^? , and c ³Π _u ⁺ states have been found and reidentification of 11 from 54 spectral lines, assigned previously to the (0-0) and (1-1) bands, was performed.     

Probabilities of rovibronic transitions in the I 1Π g − , J 1Δ g − →C 1Π ± u systems of bands of the deuterium molecule

Probabilities of spontaneous rovibronic transitions I ¹Π _g ^? , v′ J′, J ¹Δ _g ^? , v′, J′→C ¹Π _u ^± , v″, J″ of the D₂ molecule (for vibrational and rotational quantum numbers v′=v″=0–3 and J′=1–9, J″=J′±1) have been obtained for the first time. They were determined using (1) the previously proposed nonadiabatic model, which takes into account the electron-rotational interaction of the upper levels; (2) the coefficients of expansion of wave functions of perturbed states in the Born-Oppenheimer basis, which were found from the experimental data on rovibronic terms; and (3) semiempirical b initio data on electronic transition dipole moments of the 3dπ¹Π_g→2pπ¹Π_u and 3dπδ¹Δ_g→2pπ¹Π_u transitions. The dependences of the transition probabilities on J′ for the same bands of both hydrogen isotopomers H₂ and D₂ were found to be identical. They represent monotone functions for R and P branches and functions with a maximum (minimum) for Q branches. The ratios of transition probabilities of different isotopomers for different branches of the same systems of bands and for the same branches of different systems of bands were found to be correlated. The semiempirical values obtained in the paper agree with the experimental values within the limits of the errors of their determination. The nonempirical values of transition probabilities agree with the experiment considerably worse.     

Radiative constants in the spectra of ions of the krypton isoelectronic sequence

The probabilities of the 4p ⁶,4p ⁵5p→4p ⁵(4d+5s) radiative transitions and the radiative lifetimes of the 4p ⁵4d,4p ⁵5s, and 4p ⁵5p levels are calculated semiempirically for the RbII-MoVII isoelectronic sequence.     

The mass yield distribution of fragments studied with improved antisymmetrized molecular dynamics

The radiative decays of 4.7 d^119m Te and 16 h^119g Te have been re-investigated. Compared to previous investigations, almost twice more transitions have been observed. Revised decay schemes are proposed in which most of the observed transitions are attributed. The half lives of the levels at 270.45 keV (g 7/2), 644.01 keV (s 1/2), 1212.69 keV (9/2⁺) and 1366.15 keV (h 11/2) have been measured by means of the delayed coincidence method and found to be 35±10ps, <10ps, <10 ps and 112±15 ps respectively. The states are discussed in the framework of current models.     

Features of the Emission Spectra of Ni-Like Ions. Application to Calculating the Wavelengths of Self-Photo-Pumped X-Ray Lasers

The energy levels and probabilities of radiative transitions to the ground state of Ni-like ions with Z = 36–51 are calculated. The energies of the upper working level 3d_3/24f_5/2 [J = 1] and the lower working level 3d_3/24d_3/2 [J = 1] of self-photo-pumped X-ray lasers along the sequence of Ni-like ions are studied. It is shown that, at the points of intersection of levels of the same parity, a strong interaction of these levels takes place, which leads to a redistribution of the oscillator strengths of the radiative transitions from these levels. Near the intersection points, the emission spectra change abruptly with variation in the nuclear charge Z.     

Luminescence study of the 4f5d configuration of Nd in LiYF4, LiLuF4 and BaY2F8 crystals

Ultraviolet fluorescence of Nd³⁺ ions induced by triphotonic excitation process was studied in Nd-doped LiYF₄, LiLuF₄ and BaY₂F₈ crystals using a technique of time-resolved spectroscopy. The observed ultraviolet luminescence was due to transitions between the bottom of 4f²5d configuration and 4f³ states of Nd³⁺ ions. Narrow emission lines superposed to the broadband emissions were observed. A detailed analysis of luminescence spectrum revealed that the narrow emissions are due to parity and spin allowed radiative transitions from the Stark levels of ⁴K_11/2(5d) state created by the electrostatic interaction between the 5d electron and the two electrons of the 4f² configuration. The narrow emissions are related to the high spin state (S=3/2) which gives f-f characteristics to the f-d broadband emissions. The narrow emissions superposed to the wide emission correspond to 18%, 34% and 43% of the integrated broadband emission at 262 nm observed in LiYF₄, LiLuF₄ and BaY₂F₈ crystals, respectively. Although the 5d-4f² interaction is observed to be weaker than 5d-crystal field interaction, it is stronger enough to select only the radiative transitions from 4f²5d configuration to 4f³ states that preserves the total spin S=3/2.     

The probabilities of radiative transitions and lifetimes of levels in the spectra of Cu XX,La IV

The probabilities of radiative electric dipole transitions 2p ⁵3p, 2p ⁶–2p ⁵3s, and 2p ⁵3d in the spectrum of neon-like copper Cu XX and 5p ⁵6p, 5p ⁶–5p ⁵6s, 5p ⁵7s, and 5p ⁵5d in the spectrum of xenon-like lanthanum La IV are calculated. The wave functions of the intermediate coupling were found from the wellknown experimental energy levels by the least-squares method (LSM). To transfer to an absolute scale the radial integrals for the transitions calculated in the form of a length on the Hartree–Fock functions have been used. By summing the calculated probabilities of the transitions, the lifetimes of the levels of configurations 2p ⁵3s, 2p ⁵3p, and 2p ⁵3d in the spectrum of Cu XX and levels of configurations 5p ⁵6s, 5p ⁵6p, and 5p ⁵7s in the spectrum of La IV have been obtained.     

Stochastic autoionization of a relativistic two-electron atom

On the basis of the analysis of absorption spectra of Er³⁺:PbMoO₄ crystals made for the transitions from the ground ⁴ I _15/2 state to excited states of Er³⁺ ions by the Judd-Ofelt method, the main spectroscopic characteristics of the crystals were obtained, including the transition probabilities and the radiative lifetimes.     

Analysis of transitions from autoionization states of the Bi III, Bi IV, and Bi V ions

The spectra of transitions from the autoionization states of bismuth ions are studied in the wavelength region from 170 to 500 Å. More than twenty transitions from the levels of configurations accompanied by excitation of the inner 5d subshell in the Bi V, Bi IV, and Bi III ions are identified and their autoionization widths are measured. In addition, transitions from the highly excited 5d ¹⁰ np levels (n=8–11) in the Bi V ion are identified and the ionization potential is refined.     

Theoretical calculation of transition probabilities and lifetimes of levels of the 4d 95p configuration of CdIII

The configuration superposition method realized in the basis of Hartree-Fock functions and transformed radial orbitals with variable parameters is applied to ab initio calculation of electronic transition probabilities from levels of the 4d ⁹5p configuration of the CdIII ion. Relativistic corrections in the energy spectra are calculated within the framework of the Hartree-Fock-Pauli approximation, i.e., in the second order in the fine structure constant. The inclusion of correlation and relativistic corrections makes it possible to achieve a good coincidence of the values of electric dipole transition probabilities calculated with the use of two forms of the operator—the form of length and the form of velocity—for both strong and weak transitions. Using the transition probabilities obtained, radiative lifetimes of levels of the configuration indicated are determined. They are in a good agreement with the currently available experimental data.     

Calculation of collisional and radiative transition probabilities between excited argon levels

Average radiative transition probabilities for argon atoms have been calculated for transitions between 24 levels in two groups characterized by the atomic core terms ²P_1/2 and ²P_3/2 by using the method of Bates and Damgaard. The results are compared with data in the NBS tables (Wiese et al.) and with those of Katsonis and Drawin. We find satisfactory agreement for the order of magnitude, even for transitions between lower lying levels. Parameters, which appear in Drawin's semiempirical cross-section expressions for electronic excitation of optically allowed and parity-forbidden transitions, are determined with the multipole expansion method proposed by Sobel'man for transitions between the specified levels. Most of these are easily obtained, but the method must be improved for transitions between levels having the same azimuthal quantum number because the summation over the constituent terms does not converge.     

Adiabatic Energies of Excited Σu States of the Hydrogen Molecule

Accurate Born-Oppenheimer potential energy curves and adiabatic corrections are computed for the six lowest ¹Σ_u states of the hydrogen molecule. For the 4¹Σ_u-6¹Σ_u states adiabatic term values of the vibrational levels supported by the potentials and the corresponding rotational constants are given. For the outer potential well of the 6¹Σ_u state, Franck-Condon factors are listed for the possible transitions to the HH?¹Σ_g state.     

Proton pick-up from nuclei in the middle of the 1p shell

The (d,³He) reaction has been used to excite proton hole states in⁸Li,⁹Be and¹⁰Be. Angular distributions have been measured and have been analyzed in terms of the DWBA to get spectroscopic factors for the considered transitions. Excitation energies and transition strengths are compared with the results of Cohen and Kurath's intermediate coupling shell model calculations, where the two models of the effective interaction produce different results especially for transitions to final states in mass 8 and 10 nuclei. The experimental results are clearly in favour of the (6–16) 2 BME interaction. A positive parity state in¹⁰Be predicted by the calculations has been looked for and found at 9.60 MeV.     

Radiative lifetimes of some excited states of Hg+ and Hg2+

A delayed-coincidence method with pulsed electron excitation was used to measure the radiative lifetimes of some 5d⁹6snl states of Hg⁺. Radiative lifetimes of five long lived 5d⁸6s² states of Hg²⁺ and some Hg²⁺ spectral line transition probabilities are also reported. The data are obtained for the first time.     

Multiphoton mass spectra of Xe2 molecules in the range of excited Xe*(6p, 5d) atoms

The (2 + 1) photoionization mass spectra of Xe₂ molecules are studied in a supersonic jet upon excitation by laser radiation in the energy range 80321.3–77821 cm^?1, corresponding to the dissociation of the Xe₂ molecule into atoms Xe(¹ S ₀) + Xe*(6p, 5d). Several vibrational progressions are observed, which are attributed to two-photon transitions of Xe₂ from the ground state to the excited states of the O ⁺ _g, 1_g, and 2_g symmetries. Based on the analysis of these progressions, the molecular constants of a number of excited states of Xe₂ are estimated.