Atomic Level Widths Research Articles

Incident-photon energy-distribution effects on radiationless resonant Raman scattering.

In the experimental observation of radiationless resonant Raman scattering, features that differ from the idealized case can arise when the spectral width of the incident photon distribution is comparable to the width of pertinent atomic energy levels. These features include nonlinear dispersion of the peak maxima and changes in the symmetry and width of the ejected-electron lines with changes in the average incident photon energy. Under certain conditions, the electron line shapes can become highly asymmetric or even double peaked. The origin of these features in actual experiments is explored through a model calculation for large spectral widths. Some possible applications of these effects are pointed out.

A note on nuclear excitation by positron annihilation with K-shell electrons

Experimental data for the nuclear excitation of115In by positron annihilation with K-shell electrons have been examined, taking account of the effective thickness of an In target used, and then the cross sectionσres for resonance excitation to the 1078 keV energy level by positron annihilation has been reevaluated. The cross section for the process is induced by the measured effective cross sectionσeff of nuclear excitation of the isomeric level115mIn. In this work the effective thicknesses of the In target for positrons with kinetic energies 83.9 and 470 keV have been estimated. The effective thickness δr has been determined from a relation δr=δE/ ¦dE/dr¦, where δE is the positron energy width at 83.9 or 470 keV, δr is the mean distance traversed by them, and ¦dE/dr¦ the stopping power of indium for them. In the present case,δK, the atomic-level width of the K-level of indium, is used as δE. Neglecting a contribution from the 1464 keV level being much smaller than that from the 1078 keV level, a reevaluated value ofσres has been obtained as 1.7×10−25 cm2.

Radiation decay of atomic states: atomic residue polarization and gauge noninvariant contributions

The problem of the construction of the optimal one-electron representation in the theory of the multielectron atom is reduced to the minimization of the gauge dependent multielectron contribution to the radiation widths of atomic levels. The minimization criterion is numerically tested by calculation of the resonance radiation transition probability in the Na-like ion SVI taking into account the core polarization effects.

Energy shifts and broadening of atomic levels near metal surfaces.

We present calculations of the lifetime broadening and the shifts of hydrogenlike atomic levels (ground and excited states of H, Li, Na, K, Rb, and Cs) near jellium metal surfaces (Al and Na). The energies and widths of the atomic resonances are obtained from the Schr\odinger equation with use of the complex scaling technique; the electron potential in the surface region is calculated with use of density-functional theory. We find that the energy shifts of the atomic levels are influenced mainly by the properties of the surface potential close to the atom. The widths of the atomic levels, on the other hand, depend on the surface potential in the whole surface region. We show that in order to obtain accurate widths of atomic levels it is important to incorporate nonlocal effects, particularly the image potential. We also find that the widths are strongly influenced by hybridization among the near-degenerate atomic levels. The excited atomic levels shift differently with distance from the surface leading to multiple level crossings. At such positions the hybridization can be strongly enhanced, resulting in states that are oriented towards or away from the surface, with very different lifetimes that may vary in a nonexponential manner with distance from the surface.

Lifetimes of excited atoms near metal surfaces

Abstract We present accurate calculations of the lifetimes and energy shifts of hydrogen and alkali atomic levels near a jellium metal surface. “Complex scaling” of the Schrodinger equation is employed to obtain directly the real and imaginary parts of the atomic resonance energies. Excited atomic levels shift differently with distance and there are many possibilities of level crossings. At such positions the hybridization can be strongly enhanced and lead to states that are oriented towards or away from the surface, with very different lifetimes and non-exponential decay of widths with distance from the surface. Previous calculations of the atomic level widths have not included these facts and typically have overestimated the level widths by several orders of magnitude. We discuss the qualitative consequences of our findings of longer lifetimes and extensive hybridization on the interpretation of neutralization processes in ion-surface collisions. Finally, we show that the presence of a weak lateral corrugation in the surface potential has a similar effect on neutralization as an increased surface temperature.

Lifetimes of excited atoms near metal surfaces

We present accurate calculations of the lifetimes and energy shifts of hydrogen and alkali atomic levels near a jellium metal surface. “Complex scaling” of the Schrödinger equation is employed to obtain directly the real and imaginary parts of the atomic resonance energies. Excited atomic levels shift differently with distance and there are many possibilities of level crossings. At such positions the hybridization can be strongly enhanced and lead to states that are oriented towards or away from the surface, with very different lifetimes and non-exponential decay of widths with distance from the surface. Previous calculations of the atomic level widths have not included these facts and typically have overestimated the level widths by several orders of magnitude. We discuss the qualitative consequences of our findings of longer lifetimes and extensive hybridization on the interpretation of neutralization processes in ion-surface collisions. Finally, we show that the presence of a weak lateral corrugation in the surface potential has a similar effect on neutralization as an increased surface temperature.

Measurements of atomic level widths in thulium: Effect on the measurement of neutrino mass from tritium beta decay spectra.

Measurements have been made with curved crystal x-ray spectrometers of the natural line widths of the L/sub 1/M/sub 2/ (GAMMA = 12.1 +- 2 eV), L/sub 1/M/sub 3/ (GAMMA = 12.7 +- 1 eV), and M/sub 1/N/sub 3/ (GAMMA = 19 +- 3 eV) atomic transitions in Tm. These results are combined with published results to determine M/sub 1/, M/sub 2/, and M/sub 3/ internal conversion line widths for /sup 169/Tm. These lines have been used in the calibration of a beta spectrometer for recent measurements of the electron antineutrino mass from the tritium beta decay spectrum. A reanalysis of these results suggests that there is no conclusive evidence for a finite mass for the electron antineutrino.

A relativistic program for optical response in atoms using a time-dependent local density approximation

The so-called elementary theory of the atomic photoeffect is presented in a form that is suited for practical numerical calculation of subshell cross sections and angular distributions of emitted photoelectrons. Atomic states are described within the independent-electron approximation, with bound and free one-electron orbitals that are solutions of the Dirac equation with the Dirac–Hartree–Fock–Slater self-consistent potential of the ground-state configuration. Detailed derivations are given of subshell cross sections for both excitation to discrete bound levels and ionization. In the case of ionization, the cross section differential in the direction of the photoelectron is obtained for partially polarized photons, with the polarization specified by means of the Stokes parameters. The theoretical formulas have been implemented in a computer program named photacs that calculates tables of excitation and ionization cross sections for any element and subshell. Numerical calculations are practicable for excitations to final states with the principal quantum number up to about 20 and for ionization by photons with energy up to about 2 MeV. Elaborate extrapolation schemes for determining the subshell cross section for excitation to bound levels with larger principal quantum numbers and for ionization by photons with higher energies are described. The effect of the finite width of atomic energy levels is accounted for by convolving the calculated subshell cross-section with a Lorentzian profile.

S-matrix approach to hadronic atom level shifts

It is shown that once the hadron-nucleus scattering problem has been solved, the hadronic atom level shifts and widths can be extracted by continuing the $S$ matrix below threshold.NUCLEAR REACTIONS $S$-matrix theory, hadronic atom complex level shift calculated and correlated with scattering parameters.

Low-energy kaon-nucleus interaction

Low-energy kaon-nucleus interaction has been considered in the framework of multiple scattering theory as formulated by Watson and by Kerman, McManus, and Thaler. A kaon-nucleus optical potential of the shape of nuclear density is shown to follow from theory under the assumption that the nuclear excited states may be neglected and that the range of the underlying microscopic $\overline{K}N$ interaction is small in comparison with the nuclear radius. The depth of the effective potential is a nonlinear function of the $\overline{K}N$ scattering lengths and depends upon a single parameter related to the unknown range of the $\overline{K}N$ interaction. This parameter has been adjusted to the available kaonic atom data. The resulting potential has been used to evaluate the kaonic atom level shifts and widths and the calculated quantities are compared with experiment.NUCLEAR REACTIONS Optical potential derived and applied to evaluate kaonic atoms level shifts.

The reactive two-body part of the pion-nucleus optical potential

We calculate the reactive component of the two-body contribution to the pion-nucleus optical potential from a two-nucleon pion absorption mechanism that predicts the total cross section and angular distributions for π +d → pp very well. At threshold the calculated absorptive parts explain most of the values obtained from pionic atom level widths, whereas the dispersive parts, which are very sensitive to wave function correlations are considerably more attractive than what the conventional phenomenological parameters would suggest.

The absorptive P-wave pion-nucleus optical potential

We derive the absorptive part of the P-wave pion-nucleus optical potential from a two-body model for the absorption mechanism which involves rescattering of a pion and ϱ-meson through a Δ 33 resonant state. The model gives an adequate explanation for the fundamental π +d → pp reaction cross section and leads to values for the optical potential parameter which are in fair agreement with those obtained from pionic atom level widths.

Kaon-nucleus interaction at low energies

A kaon-nucleus absorptive potential is derived by folding the $\overline{K}N$ finite range complex potential into the nuclear density distribution. The strengths of the $\overline{K}p$ and $\overline{K}n$ potentials have been adjusted to the corresponding scattering length values and the range of the $\overline{K}N$ forces has been obtained by fitting the $\overline{K}\ensuremath{-}^{4}\mathrm{He}$ scattering data. The resulting $\overline{K}N$ potential with no free parameters has been used to calculate kaonic atom level shifts and widths. Within the experimental uncertainties all kaonic data can be fitted in a consistent manner.

Effect of Atomic Level Width on Ge(Li) X-ray Spectra

The shapes of x-ray and γ-ray peaks have been studied with the use of a high resolution Ge(Li) spectrometer. The Kα x-ray peaks of high Z elements have been found to exhibit larger width compared to the width of γ-ray peaks of same energy. This excess width has been assigned to the natural energy width of characteristic x-ray lines. An analytical study of the variation of the observed width with the natural width of the incident radiation has been made. The computed results are in excellent agreement with the experimental observation.

Theory of resonant multiphoton processes

The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order ${10}^{8}$ W/${\mathrm{cm}}^{2}$) is determined by the intensity-dependent level width ($6f$ configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order ${10}^{12}$ W/${\mathrm{cm}}^{2}$) are determined by both the intensity-dependent widths and shifts a$\stackrel{\mathrm{`}}{\mathrm{s}}$ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.

Nuclear transition properties and atomic level widths in Sm 151

Internal conversion electron lines in Sm 151 resulting from Pm 151 decay have been studied in an iron-free double focussing spectrometer at an instrumental resolution setting of 0.1% in momentum. The use of post acceleration techniques has made possible the study of the shapes and relative intensities of the M subshell conversion lines of the low energy transition feeding the ground state. The transition energy is found to be 4.821±0.003 keV. The relative M subshell conversion line intensities indicate that the transition multipolarity is dominantly M1 with a very small admixture of E2. From a detailed analysis of the shapes of the internal conversion electron lines the natural widths of the atomic levels in Sm characterized by a K, an M I, M II and an M III electron vacancy are found to be 17±3, 14±3, 4.7±1 and 7.7±1.5 eV, respectively. These widths are compared with those of other atoms ( Z ≧ 47) for which M level widths are presently available.

Differences in natural widths of conversion lines

A folding procedure was applied to K- and L-conversion line pairs due to gamma-ray transitions in Hg- and Bi-isotopes, measured with an ironfree double focussing beta-ray spectrometer. Apart from yielding an accurate determination of the Bϱ-ratio of corresponding K- and L-lines this procedure indicated the difference of the atomic level widths to be 49±5 eV in Bi and 54±5 eV in Hg, in fair agreement with X-ray data.