Calculation Of Transition Rates Research Articles

SUR/FIN 2007: A RousingSuccess!

The calculation of laser-induced radiative transition rates for electric-dipole transitions is reviewed. The effects of laser polarization can only be understood by considering the Zeeman structure of energy levels. In particular, the case of laser coupling of degenerate levels is considered by including the Zeeman structure of the upper and lower energy levels. The interaction of the laser radiation with the atomic or molecular resonance is formulated in terms of the density matrix. The electric-dipole matrix elements are written as the product of a scalar quantity, the reduced density matrix element, and a vector quantity that is a function of the angular momentum quantum numbers J and magnetic quantum numbers M for the upper and lower Zeeman states. The calculation of absorption and stimulated emission rates, absorption coefficients, and susceptibilities for the limiting case of an isotropic medium is reviewed. Polarization effects in laser-induced fluorescence are reviewed, and the theoretical framework for the analysis of these effects is developed. The calculation of polarization spectroscopy signals and of polarization effects in resonant four-wave mixing are discussed. The effects of hyperfine structure in diatomic molecules are discussed.

Relativistic many-body calculations of electric-dipole lifetimes, rates and oscillator strengths of Δn = 0 transitions between 3l−14l′ states in Ni-like ions

Transition rates, oscillator strengths and line strengths are calculated for electric-dipole (E1) transitions between odd-parity 3s23p63d94l1, 3s23p53d104l2 and 3s3p63d104l1 states and even-parity 3s23p63d94l2, 3s23p53d104l1 and 3s3p63d104l2 (with 4l1 = 4p, 4f and 4l2 = 4s, 4d) in Ni-like ions with the nuclear charges ranging from Z = 34 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start from a 1s22s22p63s23p63d10 Dirac–Fock potential. First-order RMBPT is used to obtain intermediate coupling coefficients and second-order RMBPT is used to calculate transition matrix elements. Contributions from negative-energy states are included in the second-order E1 matrix elements to ensure the gauge independence of transition amplitudes. Transition energies used in the calculation of oscillator strengths and transition rates are from second-order RMBPT. Lifetimes of the 3s23p63d94d levels are given for Z = 34–100. These atomic data are important in modelling of M-shell radiation spectra of heavy ions generated in electron beam ion trap experiments and in M-shell diagnostics of plasmas.

An MCHF atomic-structure package for large-scale calculations

An MCHF atomic-structure package for large-scale calculations

The effect of forbidden transitions on cosmological hydrogen and helium recombination

More than half of the atoms in the Universe recombined via forbidden transitions, so that accurate treatment of the forbidden channels is important in order to follow the cosmological recombination process with the level of precision required by future microwave anisotropy experiments. We perform a multilevel calculation of the recombination of hydrogen (H) and helium (He) with the addition of the 2 3 P 1 -1 1 S 0 spin-forbidden transition for neutral helium (He I), plus the nS-1S and nD-1S two-photon transitions for H (up to n = 40) and among singlet states of He I (n ≤ 10 and e ≤ 7). The potential importance of such transitions was first proposed by Dubrovich & Grachev using an effective three-level atom model. Here, we relax the thermal equilibrium assumption among the higher excited states to investigate the effect of these extra forbidden transitions on the ionization fraction Χ e and the cosmic microwave background (CMB) angular power spectrum C e . The spin-forbidden transition brings more than 1 per cent change in Χ e . The two-photon transitions may also give non-negligible effects, but currently accurate rates exist only for n ≤ 3. We find that changes in both Χ e and C e . would be at about the per cent level with the approximate rates given by Dubrovich & Grachev. However, the two-photon rates from 3S to IS and 3D to IS of H appear to have been overestimated, and our best numerical calculation puts the effect on Χ e and C e at below the per cent level. Nevertheless, we do not claim that we have the definite answer, since several issues remain open; sub-per cent level computation of the C e values requires improved calculations of atomic transition rates as well as increasingly complex multilevel atom calculations.

Multiconfiguration Dirac-Hartree-Fock calculations of transition rates and lifetimes of the eight lowest excited levels of radium

The multiconfiguration Dirac-Hartree-Fock (MCDHF) model has been employed to calculate the transition rates between the nine lowest levels of radium. The dominant rates were then used to evaluate the radiative lifetimes. The decay of the metastable $ 7s7p ^3 P_0 $ state through 2-photon E1M1 and hyperfine induced channels is also studied.

Shell model method for Gamow-Teller transitions in heavy, deformed nuclei

A method for calculation of Gamow-Teller transition rates is developed by using the concept of the Projected Shell Model (PSM). The shell model basis is constructed by superimposing angular-momentum-projected multiquasiparticle configurations, and nuclear wave functions are obtained by diagonalizing the two-body interactions in these projected states. Calculation of transition matrix elements in the PSM framework is discussed in detail, and the effects caused by the Gamow-Teller residual forces and by configuration-mixing are studied. With this method, it may become possible to perform a state-by-state calculation for beta-decay and electron-capture rates in heavy, deformed nuclei at finite temperatures. Our first example indicates that, while experimentally known Gamow-Teller transition rates from the ground state of the parent nucleus are reproduced, stronger transitions from some low-lying excited states are predicted to occur, which may considerably enhance the total decay rates once these nuclei are exposed to hot stellar environments.

Electron-impact excitation of neutral oxygen

Aims.Our goal was to calculate transition rates from ground and excited states in neutral oxygen atoms due to electron collisions for non-LTE modelling of oxygen in late-type stellar atmospheres, thus enabling the reliable interpretation of oxygen lines in stellar spectra.

Ti ii] and [Ni ii] emission from the strontium filament of η Carinae

We study the nature of the [Ti II] and [Ni II] emission from the so-called strontium filament found in the ejecta of eta Carinae. To this purpose we employ multilevel models of the Ti II and Ni II systems which are used to investigate the physical condition of the filament and the excitation mechanisms of the observed lines. For the Ti II ion, for which no atomic data was previously available, we carry out ab initio calculations of radiative transition rates and electron impact excitation rate coefficients. It is found that the observed spectrum is consistent with the lines being excited in a mostly neutral region with an electron density of the order of 10(exp 7) per cubic centimeter and a temperature around 6000 K. In analyzing three observations with different slit orientations recorded between March 2000 and November 2001 we find line ratios that change among various observations, in a way consistent with changes of up to an order of magnitude in the strength of the continuum radiation field. These changes result from different samplings of the extended filament, due to the different slit orientations used for each observation, and yield clues on the spatial extent and optical depth of the filament. The observed emission indicates a large Ti/Ni abundance ratio relative to solar abundances. It is suggested that the observed high Ti/Ni ratio in gas is caused by dust-gas fractionation processes and does not reflect the absolute Ti/Ni ratio in the ejecta of eta Carinae. We study the condensation chemistry of Ti, Ni and Fe within the filament and suggest that the observed gas phase overabundance of Ti is likely the result of selective photo-evaporation of Ti-bearing grains. Some mechanisms for such a scenario are proposed.

Cross sections forOHtransitions due to electron impact on water molecules

We have measured absolute cross sections for electrons $(9--700\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ incident on water molecules. By fitting synthetic vibrational bands to the experimental emission spectra, we measured the emission cross sections for the $\mathrm{OH}$ $A\phantom{\rule{0.2em}{0ex}}^{2}\ensuremath{\Sigma}^{+}--X\phantom{\rule{0.2em}{0ex}}^{2}\ensuremath{\Pi}$ $(0,0)$, $(0,1)$, $(1,0)$, $(1,1)$, $(2,1)$, $(2,2)$, $(3,2)$, and $(3,3)$ bands. The branching fractions from our cross sections are consistent with those we measured in the emission of a rf discharge and with our calculated transition rates. We have also calculated apparent level cross sections for the $A\phantom{\rule{0.2em}{0ex}}^{2}\ensuremath{\Sigma}^{+}{v}^{\ensuremath{'}}=0$, 1, 2, and 3 vibrational levels where the effects of predissociation are obvious.

Oscillator Strengths of Near‐Infrared Lines of Feii

We present extensive configuration interaction calculations of oscillator strengths and transition rates of certain near-infrared emission lines of Fe II observed in the BD Weigelt blobs of η Carinae. Comparison is made between our work and results available in existing databases. We offer arguments in favor of our results being the most accurate, where differences occur.

Electron–ion interactions for trapped highly charged Ge ions

A theoretical simulation of complex K X-ray spectra including those from dielectronic recombination and excitation processes is presented for trapped highly charged germanium ions ( Geq+, q = 27–30) interacting with a dense electron beam. We carried out numerical calculations of transition rates, level energies, transition wavelengths, resonance and collision strengths, and satellite intensity factors. Analytical results related to cross sections of B- through He-like Ge ions were obtained as well. The simulated spectra, including the contribution from different charge states of Ge27+–Ge30+, show good overall agreement over a wide electron energy range with the available X-ray measurements from the Heidelberg electron beam ion trap (EBIT). We have also predicted the electron impact excitation cross-section ratios for different transitions of Ge29+ and Ge30+ ions. It should be emphasized that the present analysis can also provide new information and clues of possible temperature measurements for EBIT and other plasma diagnostics.PACS No.: 32.30.Rj

Relativistic many-body calculations of energies, E2, and M1 transition rates of 4s 24p states in Ga-like ions

Ionization energies, fine-structure splitting of 4s 24p states, and magnetic-dipole and electric-quadrupole transition rates for the 4s 24p 2P 1/2–4s 24p 2P 3/2 transition are calculated for Ga-like ions with nuclear charge Z ranging from 31 to 100. First-, second-, third-order, and all-order Coulomb energies and first- and second-order Coulomb–Breit energies are calculated. Electric-quadrupole and magnetic-dipole matrix elements are evaluated to calculate the lifetime of the 4s 24p 2P 3/2 state. The matrix elements are calculated using both relativistic many-body perturbation theory, complete through third order, and the relativistic all-order method restricted to single and double excitations. These calculations provide a theoretical benchmark for comparison with experiment and theory.

A phase-space approach to the T1⇝S radiationless decay in benzene: The effect of deuteration

The influence of full deuteration on the T1 right arrow-wavy S0 intersystem crossing in benzene is studied by a phase space approach. A full treatment of all the vibrational modes in the molecule leads to a ratio of the rate between the two isotopomers which is very close to the experimental value. Several aspects of the results are compared to previous estimates, and the effects of anharmonicity on the rates and accepting modes are examined. This first successful application of the method to a real physical system encourages the possibility of establishing a routine procedure for simple calculations of transition rates even for relatively large molecules.

Relativistic many-body calculations of excitation energies, line strengths, transition rates, and oscillator strengths in Pd-like ions

Excitation energies, line strengths, oscillator strengths, and transition probabilities are calculated for 4d–14f, 4d–15p, 4d–15f, and 4d–16p hole–particle states in Pd-like ions with nuclear charges Z ranging from 49 to 100. Relativistic many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start from a [Kr] 4d10 closed-shell Dirac–Hartree–Fock (DHF) potential and include second- and third-order Coulomb corrections and second-order Breit–Coulomb corrections. First-order perturbation theory is used to obtain intermediate-coupling coefficients and second-order MBPT is used to determine matrix elements. Contributions from negative-energy states are included in the second-order electric-dipole matrix elements. The resulting transition energies, line strengths, and transition rates are compared with experimental values and with other recent calculations. Trends of oscillator strengths as functions of nuclear charge Z are shown graphically for all transitions from the 4d–14f, 4d–15p, 4d–15f, and 4d–16p states to the ground state. PACS Nos.: 31.15.Ar, 31.15.Md, 32.70.Cs, 32.30.Rj, 31.25.Jf

Relativistic many-body calculations of electric-dipole lifetimes, transition rates and oscillator strengths for 2l−13l′ states in Ne-like ions

Transition rates, oscillator strengths and line strengths are calculated for electric-dipole (E1) transitions between odd-parity 2s22p53s, 2s22p53d and 2s2p63p states and even-parity 2s22p53p, 2s2p63s and 2s2p63d states in Ne-like ions with the nuclear charges ranging from Z = 14 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded E1 matrix elements in length and velocity forms. The calculations start from a 1s22s22p6 Dirac–Fock potential. First-order RMBPT is used to obtain intermediate coupling coefficients and second-order RMBPT is used to calculate transition matrix elements. Contributions from negative-energy states are included in the second-order E1 matrix elements to ensure the gauge independence of transition amplitudes. Transition energies used in the calculation of oscillator strengths and transition rates are from second-order RMBPT. Lifetimes of the 16 even-parity and 18 odd-parity levels are given for Z = 14–100. Transition rates, line strengths and oscillator strengths are compared with critically evaluated experimental values and with results from other recent calculations. These atomic data are important in the modelling of L-shell radiation spectra of heavy ions generated in electron beam ion trap experiments and in L-shell diagnostics of plasmas.

Radiative emission probabilities of Dy 3+-doped alkali borate and fluoroborate glasses

Optical absorption and photoluminescence properties of Dy 3+-doped alkali borate: 59 H 3BO 3 + 30 Li 2CO 3 + 10 Al 2O 3 + 1 Dy 2O 3 (Glass-A) and alkali fluoroborate: 59 H 3BO 3 + 30 LiF + 10 Al 2O 3 + 1 Dy 2O 3 (Glass-B) glasses have been investigated. From the measured absorption spectra, the oscillator strengths are determined from the area under the absorption bands. Judd-Ofelt analysis was applied and the intensity parameters (×10 −20 cm 2) Ω 2 = 4.620, Ω 4 = 2.706, Ω 6 = 2.087 and Ω 2 = 5.306, Ω 4 = 2.027, Ω 6 = 1.511 for glasses A and B, respectively were evaluated with a reasonable agreement between the measured and calculated f-values. These parameters were used for the calculation of radiative transition rates ( A R), branching ratios ( β R), radiative lifetimes ( τ R) and integrated absorption cross-sections ( Σ) for the 4F 9/2, 6H 5/2, 6H 9/2, 6F 11/2, 6H 11/2 and 6H 13/2 electronic excited states and are compared with those of other glasses reported in the literature. From the radiative spectroscopic parameters, it is predicted that these Dy 3+-doped glasses A and B are found to be more attractive for blue–green solid-state laser devices.

General calculation of 4f-5d transition rates for rare-earth ions using many-body perturbation theory

The 4f-5d transition rates for rare-earth ions in crystals can be calculated with an effective transition operator acting between model 4f(N) and 4f(N-1)5d states calculated with effective Hamiltonian, such as semiempirical crystal Hamiltonian. The difference of the effective transition operator from the original transition operator is the corrections due to mixing in transition initial and final states of excited configurations from both the center ion and the ligand ions. These corrections are calculated using many-body perturbation theory. For free ions, there are important one-body and two-body corrections. The one-body correction is proportional to the original electric dipole operator with magnitude of approximately 40% of the uncorrected electric dipole moment. Its effect is equivalent to scaling down the radial integral (5d/r/4f) to about 60% of the uncorrected HF value. The two-body correction has magnitude of approximately 25% relative to the uncorrected electric dipole moment. For ions in crystals, there is an additional one-body correction due to ligand polarization, whose magnitude is shown to be about 10% of the uncorrected electric dipole moment.

Relativistic many-body calculations of E1, E2, M1, and M2 transitions rates for the 1 s 2 l′ 2 l′ ′ – 1 s 2 2 l lines in Li-like ions

Reduced matrix elements, oscillator strengths, and transition rates are calculated for all allowed and forbidden 1s2l′ 2l′ ′ – 1s 22l electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions in lithiumlike ions with nuclear charges ranging from Z = 6 to 100. Relativistic many-body perturbation theory (RMBPT), including the Breit interaction, is used to evaluate retarded E1, M1, E2, and M2 matrix elements. The calculations start with a Dirac potential and include all possible 1s2l′ 2l′ ′ configurations, leading to seven odd-parity and nine even-parity states. First-order perturbation theory is used to obtain intermediate coupling coefficients. Second-order RMBPT is used to determine the matrix elements, which are evaluated for the 22, 20, 16, and 18 possible E1, M1, E2, and M2 transitions, respectively. A detailed discussion of the various contributions to the energy levels and E1, M1, E2, and M2 matrix elements is given for lithiumlike iron, Z = 26. The transition energies used in the calculation of oscillator strengths and transition rates are evaluated using second-order RMBPT. Trends of E1, M1, E2, and M2 transition rates as functions of nuclear charge Z are shown graphically for 1s2l′ 2l′ ′ – 1s 22l transitions.

Heterogeneity of solid neutron-star matter: transport coefficients and neutrino emissivity

Calculations of weak-interaction transition rates and of nuclear formation enthalpies show that in isolated neutron stars, the solid phase, above the neutron-drip threshold, is amorphous and heterogeneous in nuclear charge. The neutrino emissivities obtained are very dependent on the effects of proton shell structure but may be several orders of magnitude larger than the electron bremsstrahlung neutrino-pair emissivity at temperatures of 10^9 K. In this phase, electrical and thermal conductivities are much smaller than for a homogeneous bcc lattice. In particular, the reduced electrical conductivity, which is also temperature-independent, must have significant consequences for the evolution of high-multipole magnetic fields in neutron stars.

Low-temperature dynamics of weakly localized Frenkel excitons in disordered linear chains.

We calculate the temperature dependence of the fluorescence Stokes shift and the fluorescence decay time in linear Frenkel exciton systems resulting from the thermal redistribution of exciton population over the band states. The following factors, relevant to common experimental conditions, are accounted for in our kinetic model: (weak) localization of the exciton states by static disorder, coupling of the localized excitons to vibrations in the host medium, a possible nonequilibrium of the subsystem of localized Frenkel excitons on the time scale of the emission process, and different excitation conditions (resonant or nonresonant). A Pauli master equation, with microscopically calculated transition rates, is used to describe the redistribution of the exciton population over the manifold of localized exciton states. We find a counterintuitive nonmonotonic temperature dependence of the Stokes shift. In addition, we show that depending on experimental conditions, the observed fluorescence decay time may be determined by vibration-induced intraband relaxation, rather than radiative relaxation to the ground state. The model considered has relevance to a wide variety of materials, such as linear molecular aggregates, conjugated polymers, and polysilanes.