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The present status of the field of fluorescence yields, radiationless (Auger and Coster-Kronig) and radiative transition probabilities is summarized. Tables of experimental and theoretical results are included, and tables of "best values" of important quantities are presented.

The electronic dipole moment functions of Browne are used in calculations of the individual radiative transition probabilities for all the bands of the Lyman system of molecular hydrogen. The resulting lifetimes of the vibrational levels of the upper electronic state are in harmony with the experimental data of Hesser, and an apparent discrepancy between two experiments is resolved.

The effects of the electronic correlations on the radiative transition matrix elements are investigated theoretically. The calculation shows that the effective electronic configurations are drastically reduced by utilizing the modified H-F operator.

The effect of external heavy-atom perturbation is examined for each of the three spin subcomponents of the π,π * triplet state. It is shown that the radiative decay rate from the subcomponent whose spin wavefunction is within the molecular plane is most effectively enhanced. The main perturbing singlet state is the charge-transfer state arising from the excitation of an electron from a π orbital of the molecule to the σ * orbital of the perturber.

High resolution Si(Li)-Si(Li) and Si(Li)-Ge(Li) detector arrangements have been used to studyL x-ray spectra in coincidence withL-shell internal conversion electrons, gamma rays, andK x-rays emitted in249Cf decay. TheL1 subshell fluorescence and Coster-Kronig yields determined forZ=96 from these spectra are ω1=0.25±0.06,f12≦0.10, andf13=0.69 ±0.08. The presence of theL1-L3 radiative transition is also further confirmed in this work.

Fluorescence quantum yields and lifetimes have been measured as a function of temperature for anthracene and 9,10‐dichloroanthracene in hexane and ethanol. It was found that the radiative transition probabilities are very slightly temperature dependent. However, for the nonradiative processes, 9,10‐dichloroanthracene shows a strong temperature dependence, whereas anthracene shows none.

The energy for the ground state and the three first excited states for one F center perturbed by a negative interstitial halide ion in KC1, KF, K1 and KBr is given. Using this results an approximate calculation was made for the ratio of the non-radiative to radiative transition of F center at room temperature. It is founded that in an approximate way an F center is not stable if a negative interstitial halide ion is within six lattice sites of the vacancy.

We use calculated Auger and radiative transition rates to compute $K$-shell fluorescence yields for $18\ensuremath{\le}Z\ensuremath{\le}54$. The calculated fluorescence yields are generally higher than the most recent measurements (by as much as 8%). In addition we compare the calculated Auger rates with measured $\mathrm{KLL}$ and $\mathrm{KLM}$ intensities, the calculated $\mathrm{KLL}$ total yield with other calculations, and the calculated $\frac{\mathrm{KLX}}{\mathrm{KLL}}$ and $\frac{\mathrm{KXY}}{\mathrm{KLL}}$ ratios with measurements.

Decays of the donor-acceptor pair luminescence have been measured as a function of the pair distance R at liquid He temperatures using a pulsed laser beam excitation and applying gated integration techniques to display the decays. The decay time constants were derived from the exponential decays below R ≈ 20 A (on the resolved pair lines) and from the major components of the non-exponential decays at larger R. The decay time depends exponentially on R, the dependence increasing in the “green” pair sequence (S-C), (S-Zn) and (S-Cd) with the characteristic lengths 9.1 A, 7.7 A and 7.0 A. For the “red-orange” pairs (S-Si) no such length could be derived owning to the strong phonon replication. The radiative transition probabilities extrapolated to zero R are ≈ 5 × 105 sec-1 for the “green” pairs and ≈ 105 sec-1 (rough estimate) for the “red-orange” pairs. The zero-phonon transition probabilities were found to be ≈ 4 × 105 sec-1 and ≈ 3 × 103 sec-1 respectively. Possible causes of decay distortion above R ≈ 20 A are discussed as well as thermal effects.

The systematics of the excitation energies of the non-normal parity states of the scandium isotopes are interpreted in terms of the formation of a quartet of 1f7/2 nucleons. Calculation of theB(E2) value for a typical radiative transition between non-normal parity states in43Sc, using this model, shows that the transition must involve more than the single quartet formed in the 1f7/2 shell; that is, that core polarization is an important factor in determining theB(E2) value.

The radiative transition probability from the 3 2 + state at 16.7 MeV to the 3 2 − ground state in 5He is calculated using cluster-model wave functions. The excited state is assumed to have a triton-deuteron cluster structure and the ground state an alpha-particle-neutron structure. The result is found to be in quite close agreement with the experimental value, indicating that the cluster-model wave functions provide a good description of the 5He nucleus.

— The radiative fluorescence lifetimes of the all-trans, 9 cis and 13 cis retinol, have been measured at various temperatures, and in various solvents. The comparison of these results and of the data calculated from the absorption spectra using the Strickler and Berg equation shows that the transition probabilities are at least one hundred times lower for the radiative emission than for the absorption. Such a discrepancy, which is a general property of the polyenic structure, is closely related to the magnitude of the shift between absorption and fluorescence spectra. We interpret the observed elongation of the radiative fluorescence lifetimes and the temperature dependence of the radiative transitions in the case of all trans retinol as being due to the fact that only the lowest vibrorotational sublevels of 1S1, have a reasonable radiative transition probability: the temperature dependence of the radiationless transitions is considered to be due to the existence of a non radiative decay pathway at 550cal/mole above the ‘0’ level.

The use of a spin-forbidden transition enhancer as dimethylmercury allows one to measure phosphorescence spectra in a fluid medium at room temperature. As an example, the T 1 → S 0 radiative transition of octahelicene, 1,2-benzanthracene, 1,2,5,6-dibenzanthracene and 3,4-benzophenanthrene have been studied.

The Hylleraas-Scherr-Knight variation-perturbation method is applied to the calculation of oscillator strengths for the dominant transitions from the metastable $2p3p^{3}P$ and $2p3d^{1,3}D$ states of helium and the heliumlike ions. The results explain the absence of the $1s2p^{3}P\ensuremath{-}2p3p^{3}P$ transition of He i from recent beam-foil excitation spectra.

The pressure broadening at high temperatures and the radiative transition probabilities for some of the carbon monoxide vibration‐rotation transitions, Δν = 1, have been measured by the absorption of laser light in shock heated CO. The results are compared with other experimental data, and formulas for pressure broadening and the dipole moment function of CO are deduced.

The lifetime of the 3p54p1-3p54s2 transitions of argon has been determined experimentally to be 22.8±0.8 x 10-9 sec. Absolute transition probabilities for 16 argon I lines between the 3p54p and 3p54s configurations have been obtained by combining the lifetime measurement with relative transition probabilities obtained from an absorption experiment and an emission experiment.

High-resolution Ge(Li) and Si(Li) x-ray spectrometers and a wall-less anticoincidence multiwire proportional counter were used for coincidence measurements between various $K$ and $L$ x rays and $M$ x rays of Np (Z=93) and Cm ($Z=96$) following $\ensuremath{\alpha}$ decay of ${\mathrm{Am}}^{241}$ and ${\mathrm{Cf}}^{249}$, respectively. The effect of multiple vacancies in the $M$ shell was taken into account in the determination of the following mean $M$-subshell fluorescence yields: ${\ensuremath{\nu}}_{1}^{M}=0.065\ifmmode\pm\else\textpm\fi{}0.014$, ${\ensuremath{\nu}}_{2}^{M}=0.080\ifmmode\pm\else\textpm\fi{}0.029$, ${\ensuremath{\nu}}_{4}^{M}=0.062\ifmmode\pm\else\textpm\fi{}0.005$, ${\ensuremath{\nu}}_{4,5}^{M}=0.065\ifmmode\pm\else\textpm\fi{}0.012\ensuremath{\approx}{\ensuremath{\omega}}_{5}^{M}$ at $Z=93$; and ${\ensuremath{\nu}}_{1}^{M}=0.081\ifmmode\pm\else\textpm\fi{}0.016$, ${\ensuremath{\nu}}_{2}^{M}=0.068\ifmmode\pm\else\textpm\fi{}0.023$, ${\ensuremath{\nu}}_{3}^{M}=0.062\ifmmode\pm\else\textpm\fi{}0.019$, ${\ensuremath{\nu}}_{4}^{M}=0.080\ifmmode\pm\else\textpm\fi{}0.006$, and ${\ensuremath{\nu}}_{4,5}^{M}=0.075\ifmmode\pm\else\textpm\fi{}0.012\ensuremath{\approx}{\ensuremath{\omega}}_{5}^{M}$ at $Z=96$. The close agreement of the various mean $M$-subshell fluorescence yields with that of the ${M}_{4,5}$ subshells for each element indicates that Coster-Kronig transitions are very strong in the $M$ shell. Including earlier measurements of mean $M$-shell fluorescence yields at lower $Z$, corrected for multiple vacancies, and accepting Bhalla's theoretical calculations of radiative ${M}_{4,5}$-subshell widths, one concludes that the nonradiative widths of the ${M}_{4,5}$ subshells are essentially constant from $Z=76 \mathrm{to} 96$. Comparison of fluorescence yields of the $K$ shell and the ${L}_{3}$ and ${M}_{4,5}$ subshells at the same energy of the principal radiative transition (i. e., at different values of $Z$ indicates that the ratio of radiative to Auger widths decreases from the $1{s}_{\frac{1}{2}}$ to $2{p}_{\frac{3}{2}}$ state, but remains constant from $2{p}_{\frac{3}{2}}$ to $3{d}_{\frac{5}{2}}$. The resolution of the Si(Li) detector was sufficient to separate the radiative transitions from fillings of the ${M}_{1,2}$- and ${M}_{3,4,5}$-subshell groups, so that from $K$ and $L$ x-ray coincidences with the ${M}_{1,2}$ group of x rays, it was possible to determine the following quantities: ${\ensuremath{\omega}}_{1}^{M}+{f}_{12}^{M}{\ensuremath{\omega}}_{2}^{M}=({2.0}_{\ensuremath{-}2.0}^{+3.1})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3} \mathrm{and} ({7.5}_{\ensuremath{-}7.5}^{+8.9})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ at $Z=93 \mathrm{and} 96$, respectively, and ${\ensuremath{\omega}}_{2}^{M}=({4.6}_{\ensuremath{-}4.6}^{+5.1})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ at $Z=96$. Thus, about 94% of ${M}_{2}$-subshell vacancies undergo Coster-Kronig shifts to higher subshells before filling from $N$ and higher major shells occurs. Observation of the radiative ${L}_{1}\ensuremath{-}{L}_{3}$ transition was made for the first time in the high-$Z$ region, and its intensity is in reasonable agreement with extrapolated theoretical predictions (6-7% of x rays filling ${L}_{1}$-subshell vacancies). The radiative fraction ${\ensuremath{\omega}}_{13}^{L}$ in the Coster-Kronig yield ${f}_{13}^{L}$ is found to be about 2% in the region of $Z=93\ensuremath{-}96$, and ${\ensuremath{\omega}}_{13}^{L}=0.011\ifmmode\pm\else\textpm\fi{}0.005 \mathrm{and} 0.009\ifmmode\pm\else\textpm\fi{}0.005$ at $Z=93 \mathrm{and} 96$, respectively. The absolute emission rate of $M$ x rays from ${\mathrm{Am}}^{241}$ was measured with multiwire and single-wire proportional counters, and values are found of (6.35 \ifmmode\pm\else\textpm\fi{} 0.60) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}2}$ $M$ x rays per $\ensuremath{\alpha}$ decay and 0.470 \ifmmode\pm\else\textpm\fi{} 0.045 $M$ x rays per ${L}_{\ensuremath{\alpha}}$ x ray. These intensities were used in determinations of efficiency at 3.25 keV of the semiconductor x-ray detectors.

By means of a highly sensitive detecting device the radiative transition from the lowest triplet level of anthracene single crystals to the ground level and several of its vibrational levels are observed at 4.2, 77.4, and 293 °K. Most of these vibrational levels correspond to the levels deduced from fluorescence and solid-solution phosphorescence studies. At 4.2 °K the radiative triplet lifetime is much larger than at 77.4 °K. The dependence of the phosphorescence intensity on the exciting laser intensity and on crystal temperature is studied. Mit Hilfe eines hochempfindlichen Nachweisgerates werden der strahlende Ubergang vom untersten Triplettzustand von Anthrazenkristallen in den Grundzustand sowie einige Schwingungsterme dieses Grundzustandes bei 4,2, 77,4 und 293 °K beobachtet. Die meisten dieser Schwingungsterme entsprechen Termen, die bereits aus Kristallfluoreszenz- und Festlosungsphosphoreszenz-Spektren bekannt. sind. Bei 4,2 °K ist die strahlende Triplettlebensdauer wesentlich groser als bei 77,4 °K. Die Abhangigkeit der Phosphoreszenzemission von der Temperatur und der Intensitat der Anregung wird gemessen.

The short-wavelength series of the edge emission of CdS single crystals is studied in the temperature range 18 to 150 °K with respect to (i) band shape, (ii) dependence of the half-width of the components on temperature and excitation intensity, (iii) temperature dependence of the peak position of the zero-phonon component, (iv) of the polarization ratio, and (v) of the luminescent intensity. It is concluded that this emission is due to an internal electronic transition occurring in nearest-neighbour donor-acceptor associates. The half-width of the components is ascribed to 5 meV-phonon and centre-centre interaction. The polarization ratio IE⊥c/IE∥c is interpreted as due to a temperature dependent distribution of the associates over the possible directions of orientation in the crystal. Die kurzwellige Serie der Kantenemission von CdS-Einkristallen wurde im Temperaturbereich von 18 bis 150 °K untersucht in bezug auf: Bandenform, Abhangigkeit der Halbwertsbreite der Teilbanden von Temperatur und Anregungsintensitat; Temperaturabhangigkeit der Lage des Maximums der Null-Phonon-Teilbande, des Polarisationsverhaltnisses und der Lumineszenzintensitat. Aus den Ergebnissen wird geschlossen, das diese Emission durch einen inneren Elektronenubergang in Donator-Akzeptor-Assoziaten bedingt ist, wobei Donator und Akzeptor sich auf nachstbenachbarten Gitterplatzen befinden. Die Halbwertsbreite der Teilbanden wird der Wechselwirkung mit 5 meV-Phononen und einer Zentrum-Zentrum-Wechselwirkung zugeschrieben. Das Polarisationsverhaltnis IE⊥c/IE∥c wird als Folge einer temperaturabhangigen Verteilung der Assoziate uber die im Kristall moglichen Orientierungsrichtungen interpretiert.

The nuclei ${\mathrm{Sr}}^{88}$ and ${\mathrm{Y}}^{89}$ have been studied by observing the inelastic scattering of 65- and 70-MeV electrons through angles 70\ifmmode^\circ\else\textdegree\fi{}-150\ifmmode^\circ\else\textdegree\fi{}, with an over-all energy resolution of 200 keV. Strongly excited states were found in ${\mathrm{Sr}}^{88}$ at 1.84 MeV (${2}^{+}$), 2.74 MeV (${3}^{\ensuremath{-}}$), 4.0, 6.5, and 7.8 MeV; and in ${\mathrm{Y}}^{89}$ at 1.50 MeV (${\frac{3}{2}}^{\ensuremath{-}}$), 1.73 MeV (${\frac{5}{2}}^{\ensuremath{-}}$), 2.21 MeV (${\frac{5}{2}}^{+}$), 2.52 MeV (${\frac{7}{2}}^{+}$), 2.86 MeV (($\frac{5}{2}, {\frac{7}{2}}^{+}$), 3.1, 3.72, 4.0, and 4.16 MeV. The data were analyzed by a distorted-wave calculation to determine multipolarities and reduced nuclear radiative transition probabilities. The results show that the excited states in ${\mathrm{Y}}^{89}$ cannot be described by a weak coupling of the $2{p}_{\frac{1}{2}}$ proton to core-excited states of ${\mathrm{Sr}}^{88}$. The sum of the $B(E2)'\mathrm{s}$ of the low-lying quadrupole states in ${\mathrm{Y}}^{89}$ is found to be about 30% of the $B(E2)$ of the 1.84-MeV state of ${\mathrm{Sr}}^{88}$, and three strong octupole states are excited in ${\mathrm{Y}}^{89}$, where only two are expected from the weak-coupling model. No detailed information on the single-particle structure of the levels could be obtained at these momentum transfers.

Electromagnetic transitions in isomeric nuclei are investigated. Radiative transition probabilities for isomeric nuclei are compared with theoretical estimates. The comparison is made for allowed and j- andl -forbidden transitions in spherical nuclei (and also for transitions between levels of a single rotational band), and for single-particle and K-forbidden transitions in deformed nuclei. Experimental data for electromagnetic radiation and quantum characteristics of isomeric nuclei agree with contemporary pictures of the atomic nucleus.

In this note we report the observation of emission of the azulene molecule in the region of 13 200 cm−1, characterized by a quantum yield of 10−7, which is assigned to the 1A1(2) → 1B1(1) radiative transition between excited electronic states of a large molecule.

Evidence is presented which indicates that the direct spin—orbit coupling between low-lying ππ* states is largely responsible for the efficient S1 → T1 intersystem crossing and T1 → S0 radiative transition in non-planar aromatic amines.

The rate of spontaneous emission of radiation by a loosely bound composite system is calculated from quantum electrodynamics correct through terms of relative order α2Z2. Recent criticisms by Feinberg and Sucher of the semiclassical method of deriving the higher-order radiation coupling terms are discussed. It is proved that the Breit interaction remains valid in the presence of radiation emission and that the semiclassical and quantum-electrodynamic methods of deriving the higher-order coupling terms always yield the same results to relative order α2Z2. We discuss in particular relativistic corrections to allowed and spin-forbidden electric dipole transitions and the 1s2s S13-1s2 S01 magnetic dipole transition. © 1972 The American Physical Society.

Newly calculated radiative transition probabilities for the A 1Σ+→X 1Σ+ (v′–v″) emission bands of 7LiH (preceding paper) are used to calculate the radiative lifetime of the various vibrational levels (0⩽v′⩽26) of A 1Σ+ LiH. For higher levels an estimate of the bound‐to‐free emission probability is also needed and included. For the highest two levels, A 1Σ+→B 1Π emission is possible and has been included, but makes a negligible contribution to the radiative lifetime. The calculated radiative lifetimes increase with v′ from 28.9 nsec at v′=0 to 36.1 nsec at v′=16 and then decrease to 27.1 nsec at v′=26. They are found to be in good agreement with measured total lifetimes, implying the nonradiative (predissociative) lifetime for the measured levels is ≳10−7 sec, in accord with simple theoretical expectations.

We report the first direct observation of radiative no-phonon and acoustic phonon-assisted transitions, determination of relative rates of radiative and non-radiative phonon-assisted decay for centres of various types in semiconductors. We also have suggested improvement of experimental approach to get a form of the distribution function for non-equilibrium acoustic phonons in crystals.

Weak emission lines are observed at the energies far lower than the energies of edge emissions in TlCl and TlBr. They are explained as due to the radiative decay of two indirect X+6 × R−6 excitons, both at the same M-point, by leaving one direct X+6 × X−6 excitons through zero-phonon process.

In an experiment to measure emission line intensities from the Belike ion Ne VII (Lang 1983), the intensity ratio I(2s3s3S−2s3p3P)/I(2p23P−2s3p3P) was found to be a factor six larger than predicted from the ratio of the theoretical spontaneous radiative transition probabilities (A values). Indeed, to reconcile the Ne VII experiment and theory in several respects it was suggested also that in Be-like C III the theoretical ratios I(2s3s1 S−2s3p1P)/I(2p21D−2s3p1P) was about a factor three too low.The same apparatus was used to measure A value ratios in Be-like N IV and 0 V. Briefly the 40 kJ θ-pinch plasma source was viewed radially using a m Ebert and a l m grazing incidence photoelectric spectrometer. The m Ebert was intensity calibrated from 7300 Å to 3600 Å using a tungsten filament lamp, and from 3800 Å to 2500 Å using a deuterium lamp, both lamps having been calibrated by NPL. As described fully by Lang (1983), the branching-ratios method was used to calibrate the front exit slit of the grazing incidence instrument in the wavelength range 88 Å to 500 Å. Only Li-like line pairs of those listed in that paper were used with the addition of the C IV doublets 2s2S−3p2P (312.4 Å) and 3s2S−3p2P (5801.33 Å, 5811.98 Å). The H-like ion He II 1–4 transition (243.0 Å) and 3–4 transition (4685.7 Å) were used to cross-check the calibration. As shown in the figure, the He II result agrees excellently with the calibration as defined from the Li-like lines.

Radiative transition probabilities for electric dipole transitions from excited states of Nd 3+ and Er 3+ in POCl 3 :ZrCl 4 are calculated using eigenstates in the intermediate coupling scheme and intensity parameters determined from experimental absorption spectra in terms of the Judd—Ofelt method. The results are compared with experimental data.

Quantum yields and mean lifetimes of fluorescence have been measured of 5-phenyltetrazole and its three methyl derivatives, para-, meta- and ortho-methyl-5-phenyltetrazole. The rate constants, kF, of the radiative transition S1 → S0 have been deduced from these measurements. The mean lifetimes, τF, the quantum yields of fluorescence and the rate constants have been found to be clearly dependent on the position of the methyl substituent in the ring and could be arranged as follows: τp F>τm F>τ0 F and k0 F>km F>kp F

The zero-phonon luminescence associated with the 0.78 eV band from gold in silicon [Mazzaschi et al . (1981)] is observed at high resolution. It corresponds to an internal transition at the defect. The interpretation as a radiative transition from shallow “hydrogen-like” states towards the deep donor state is coherent with the known experimental results. It would imply a reduced symmetry of the site.

CH and CD molecule predissociation probabilities measured directly and compared with radiative transition probability

The 4F5/2 → 4I9/2 fluorescence group of the Nd3+ ion in the CaWO4 matrix occurring at 8200 A was studied and analyzed. From the intensity measurements versus temperature, it was concluded that the radiative transition from the 4F5/2 state to the ground competes with a nonradiative relaxation to the 4F3/2 state. The value of the nonradiative transition probability W was determined to be ∼ 106 sec−1.

A type of solution of the time-dependent Schrodinger equation is suggested which intuitively corresponds to the system being midway through a radiative transition. This type of solution gives probability amplitudes and certain expectation values which oscillate in time. Some features of these oscillations closely resemble the comparable classical radiating system, and this correspondence seems useful in teaching the introductory quantum-mechanical theory of radiation.

Radiative transition probabilities for fluorescence bands extending from 0.523µ to 13µ of Er3+ in phosphate, germanate and tellurite glasses were calculated using the Judd-Ofelt approach. Multi-phonon relaxation rates from these levels were also calculated using the phenomenological parameters of multiphonon relaxation theory in glasses. Possible laser transitions of Er3+ in those glasses are discussed.

Radiative transition probabilities, oscillator strengths, radiative lifetimes and branching ratios of Nd3+ in GLS and ALS glasses were calculated for levels ranging between 160cm−l − 18,000cm−l. The matrix elements for the transitions were calculated in the intermediate coupling scheme using the measured energies in the glasses. The intensity parameters were obtained from these matrix elements and experimentally obtained oscillator strengths. The cross sections of the 4F3/2→4I9/2, 4I11/2 and 4F3/2→4I13/2 were calculated and compared to the equivalent quantities in oxide glass. The similarity and difference in the radiative characteristics of Nd3+ between oxide and chalcogenide glasses will be discussed.

A highly influential paper by DOUGLAS [1] in 1966 called attention to the fact that reported lifetimes for certain states of CS2, NO2 and SO2 were significantly longer than predicted from absorption measurements of oscillator strengths. He proposed that interactions with nearby states having little or no radiative transition probabilities resulted in mixed levels with lengthened lifetimes. Since that time the use of lasers to excite fluorescence from these molecules has revealed features more complex and interesting than previously suspected. The two principal findings are: 1) the fluor-esence decays are multiexponential showing short as well as long-lived components; 2) the frequency resolved spectra reveal both discrete and continuous features.

The factors affecting radiative and nonradiative processes on transition metal ions in solid materials are discussed; these determine the quantum efficiency of the material. The effect of lattice vibrations on the shape of radiative transitions and on the quantum efficiency is considered.

Spectral investigation of Tm3+ in thulium nitrate has been carried out. For the first time, the second derivative spectrum of this complex has been recorded. The results of a least squares fit of the energy levels and oscillator strengths of the bands are reported in terms of interaction parameters and Judd-Ofelt parameters. Radiative transition probabilities for fluorescence levels3P0,1I6,1D2 and1G4 of Tm3+ in thulium nitrate are estimated.

Spontaneous emission is usually regarded as a fundamental property of matter. An excited atom in empty space inevitably decays to its ground state, the decay rate depending on the nature of the particular radiative transition. The transition rate is given by the Einstein A coefficient, and can be expressed in terms of the “Golden Rule” $$ A = {\hbar ^{ - 2}}{\left| { } \right|^2}\rho \left( \nu \right) $$ where |i> is the initial state (excited atom, no photon), |f> is the final state (ground state atom, l photon), H is the interaction Hamiltonian, and ρ(υ) is the frequency density of final photon states. In free space, ρ0(υ)=4πυ2/c3.

The computer codes currently available to calculate the energy levels and radiative transition probabilities of highly ionized atoms taking some account of relativistic effects are compared and discussed. Some attempt is made to assess the relative quality of the various predictions.

Electromagnetic form factors and radiative transition amplitudes of hadrons are calculated in lattice QCD formalism. Calculated results for the charge radii of pi‐ and rho‐mesons are compared with experimental results. Also, the calcualted transition strength for radiative−decay of vector−mesons is compared with experimental results. (AIP)