On the analysis of photo-electron spectra

We analyze Photo-Electron Spectra (PES) for a variety of excitation mechanisms from a simple mono-frequency laser pulse to involved combination of pulses as used, e.g., in attosecond experiments. In the case of simple pulses, the peaks in PES reflect the occupied single-particle levels in combination with the given laser frequency. This usual, simple rule may badly fail in the case of excitation pulses with mixed frequencies and if resonant modes of the system are significantly excited. We thus develop an extension of the usual rule to cover all possible excitation scenarios, including mixed frequencies in the attosecond regime. We find that the spectral distributions of dipole, monopole and quadrupole power for the given excitation taken together and properly shifted by the single-particle energies provide a pertinent picture of the PES in all situations. This leads to the derivation of a generalized relation allowing to understand photo-electron yields even in complex experimental setups.     

On the spectra of gamma-ray bursts

Summary One of the possible interpretations of the spectra of gammaray bursts is in terms of synchrotron emissivity of mildly relativistic electrons. In this case, the shape of the spectra depends on the angle between the magnetic field and the observer. We show here that, although this angle can be important for single events, the statistical properties of gamma-ray bursts are determined essentially by those events for which this angle is near π/2, namely events observed in the direction of maximum emitted flux. Paper presented at the 2° Convegno Nazionale di Fisica Cosmica, held at L'Aquila, 29 May–2 June 1984.     

On the photoelectron spectra of the azanaphthalenes

An iterative extended Hückel-level method is applied to the photoelectron spectra of naphthalene, quinoline, isoquinoline and the ten diazanaphthalenes. The thirteen highest molecular orbital energies of each compound are discussed and compared with the experimental spectra in the region 8–16 eV by means of empirical corrections. The identification of π-bands and nitrogen “lone pair” bands is in perfect agreement with the results of Brogli, Heilbronner and Kobayashi¹ and van den Ham and van der Meer².     

On the nature of the photoproton spectra

Two classes of the proton channels of dipole LAS in the even-even nuclei have been studied: the decay into the “one hole” and “two hole-one particle” states of the residual nucleus. The photoproton spectra for ¹¹⁴Sn and ¹²⁴Sn have been calculated and compared with experiment.     

On thep-complex spectra of the BaH molecule

We report new high resolution measurements on the photoabsorption spectra of BaH in the wavelength region 3,000 Å–3,800 Å using the second order of a 3.4 metre Ebert spectrograph and a High pressure xenon arc as the background source of continuum. Observations include two new electronic transitions of BaH and BaD, denoted asK ² ∑-X ² ∑ at 3,725 Å andL ² Π —X ² ∑ at 3,694 Å, which are forming an p-complex orginating from the 7p atomic state of barium. A rotational analysis of the band systems have been carried out and effective rotational constants are determined.     

On the analysis of complex thermoluminescent spectra

A procedure is proposed for analyzing complex thermoluminescent glow spectra on the ground of the Antonov-Romanoskii and Lushchik kinetic equations. The procedure allows the characterizing of the multiplicity of carrier traps and recombination centres present in thermoluminescent phosphors. A simple example is presented, showing the application to pink quartz thermoluminescent emission.     

On the von Staudt-Clausen theorem for q-Euler numbers

The q-Euler numbers and polynomials were recently constructed [T. Kim, “The Modified q-Euler Numbers and Polynomials,” Adv. Stud. Contemp. Math., 16, 161–170 (2008)]. These q-Euler numbers and polynomials have interesting properties. In this paper, we prove a theorem of the von Staudt-Clausen type for q-Euler numbers; namely, we prove that the q-Euler numbers are p-adic integers. Finally, we prove Kummer-type congruences for the q-Euler numbers.     

On the measurement of luminescence excitation spectra

A method is presented for the unique determination of excitation spectra for non-linear luminescence, assuming only that the non-linearity occurs subsequent to absorption.     

On the evaluation of Bernoulli numbers using binomial coefficients

A new algorithm is presented for calculating the Bernoulli numbers valid for all values of their argument. We introduce a simple, new analytical computer method for calculating the Bernoulli numbers on the basis of their integral expressions. The formula given in this study for the evaluation of Bernoulli numbers shows good rate of convergence and numerical stability with existing formulas.     

On the Doppler distortion of the sea-wave spectra

Discussions on a form of a frequency spectrum of wind-driven sea waves just above the spectral maximum have continued for the last three decades. In 1958 Phillips made a conjecture that wave breaking is the main mechanism responsible for the spectrum formation [O.M. Phillips, J. Fluid Mech. 4 (1958) 426]. That leads to the spectrum decay ∼ω⁻⁵, where ω is the frequency of waves. There is a contradiction between the numerous experimental data and this spectrum. Experiments frequently show decay ∼ω⁻⁴ [Y. Toba, J. Oceanogr. Soc. Japan 29 (1973) 209; M.A. Donelan, J. Hamilton, W.H. Hui, Phil. Trans. R. Soc. London A315 (1985) 509; P.A. Hwang, et al., J. Phys. Oceanogr. 30 (1999) 2753]. There are several ways of the explanation of this phenomenon. One of them (proposed by Banner [M.L. Banner, J. Phys. Oceanogr. 20 (1990) 966]) takes into account the Doppler effect due to surface circular currents generated by underlying waves in the Phillips model.In this article the influence of the Doppler effect on an arbitrary averaged spectrum is considered using both analytic and numerical approaches. Although we mostly concentrated on the very important case of Phillips model, the developed technique and general formula can be used for the analysis of other spectra.For the particular case of Phillips spectra we got analytic asymptotics in the vicinity of spectral maximum and for high frequencies. Results were obtained for two most important angular dependences of the spectra: isotropic and strongly anisotropic. Together with the analytic investigation we performed numerical calculations in a wide range of frequencies. Both high and low frequency asymptotics are in very good agreement with the numerical results.It was shown that at least at low frequencies, the correction to the spectrum due to the Doppler shift is negligible. At high frequencies there is an asymptotic with tail ∼ω⁻³.     

On the fine structure in delayed-proton spectra

The fine structure in delayed-proton spectra is interpreted on the basis of statistical fluctuations associated with the variation of β-decay matrix elements and the relative proton widths of the excited states. Formulae are derived which give the variance of relative proton intensity in terms of the average characteristics of the delayed proton emission and the level density. The experimental data on the variance of the relative proton intensity for ¹¹¹Te and the calculations using these formulae are in satisfactory agreement. The fluctuations predicted for ¹⁰⁹Te considerably exceed the measured ones.     

On the spectra of resonant coherent Raman scattering

The spectra of resonant coherent anti-Stokes and Stokes Raman scattering of excited molecules are calculated and discussed. The interaction of light and molecules is treated semi-classically. The energy level diagram of four energy levels describing the process is used in four modifications possible for excited molecules. It is shown that non-vibrational resonances give extra maxima in some of the spectra. Comparison of the spectral structure in the Stokes and anti-Stokes components gives information on which of the four schemes the interaction is realized by. The influence of the pumping detuning on the Stokes component shape is pointed out.     

On the spectra of randomly perturbed expanding maps

We consider small random perturbations of expanding and piecewise expanding maps and prove the robustness of their invariant densities and rates of mixing. We do this by proving the robustness of the spectra of their Perron-Frobenius operators.V. Baladi started the present work during a postdoctoral fellowship at IBM, T.J. Watson CenterL.-S. Young is partially supported by the National Science Foundation     

On the two frequency spectra of Timoshenko beams

This paper is concerned with the question of whether there are, indeed, two distinct spectra of frequencies for the transverse vibrations of Timoshenko beams as has been claimed by a number of prior authors for the case of the simply supported beam and, more recently, for beams supported in an arbitrary manner. Elementary analysis leads to the conclusion that there is only a single frequency spectrum; in the particular case of the simply supported beam the “two frequency spectra” viewpoint may be expedient as a device to compute frequencies but does not serve otherwise to explain the complex, dynamical behavior of Timoshenko beams.     

On the energy spectra of one-dimensional anharmonic oscillators

In this paper we present explicit and simple analytical formulae for the energy eigenvaluesE _n (λ) of one-dimensional anharmonic oscillators characterized by the potentials 1/2mω ² x ²+λx ^2α withα=2, 3 and 4. A simple intuitive criterion supplemented by the requirement of correct asymptotic behaviour, has been employed in arriving at the formulae. Our energy values over a wide range ofn andλ are in good agreement with the numerical values computed by earlier workers through very elaborate techniques. To our knowledge this is the first time that formulae of such wide validity have been given. The results for pure power oscillators are trivially obtained by going over to theω→0 limit. Approximate analytic expressions for the low order even moments ofx are also given.     

On the spectra luminescence properties of charoite silicate

Charoite is a hydrous alkali calcium silicate mineral [K₄NaCa₇Ba_0.75Mn_0.2Fe_0.05(Si₆O₁₅)₂(Si₂O₇)Si₄O₉(OH)·3(H₂O)] exhibiting an intense lilac colour related to Mn²⁺ and Fe³⁺ colour centres. These ions also contribute to a strong luminescence at ∼585 and 705 nm. This work studies the thermal dependence of these luminescent centres by (i) thermoluminescence (TL) of pre-heated and pre-irradiated charoite aliquots, (ii) by time-resolved cathodoluminescence (TRS-CL) at room and cryogenic temperatures (RT and CT), (iii) by spatially resolved spectra CL under scanning electron microscopy (SRS-CL-SEM) and (iv) by ion beam spectra luminescence (IBL) with H⁺, H₂⁺ and ⁴He⁺ ions at RT and LT. The main peak, ∼585 nm, is linked to a transition ⁴T_1,2 (G)→⁶A₇(S) in Mn²⁺ ions in distorted six-fold coordination and the emission at ∼705 nm with Fe²⁺→Fe³⁺ oxidation in Si⁴⁺ lattice sites. Less intense UV-blue emissions at 340 and 390 nm show multi-order kinetic TL glow curves involving continuous processes of electron trapping and de-trapping along with an irreversible phase transition of charoite by de-hydroxylation and lattice shortening of Δa=0.219 Å, Δb=0.182 Å; Δc=0.739 Å. The Si-O stressed lattice of charoite has non-bridging oxygen or silicon vacancy-hole centres, and Si-O bonding defects which seem to be responsible for the 340 nm emission. Extrinsic defects such as the alkali (or hydrogen)—compensated [AlO₄/M⁺] centres could be linked with the 390 nm emission. Large variations in 585 and 705 nm intensities are strongly temperature dependent, modifying local Fe-O and Mn-O bond distances, short-range-order luminescence centres being very resistant under the action of the heavy ion beam of ⁴He⁺. The SRS-CL demonstrates strong spatial heterogeneity in the luminescence of the charoite.     

On the photoelectron spectra of HBr and DBr

The photoelectron spectra of HBr and DBr with He I (58.4 nm) are discussed. The photoelectron spectrum of DBr confirms the predissociation of the A²Σ⁺ electronic state. A rough estimate of the predissociation rate is calculated.     

On developed hydrodynamic turbulence spectra

New results in the theory of the developed hydrodynamic turbulence spectra are reviewed. Within the limits of the hypothesis of interaction locality it is shown that the series of equations for the moments has a scale-invariant solution with the Kolmogorov index values. With the help of the Wyld diagram technique the equations in the Direct Interaction Approximation are formulated which accurately take into account the transfer effect and have the precise solution in the form of the Kolmogorov spectrum. In the framework of these equations the corrections to the Kolmogorov spectrum due to gyrotropy and compressibility are found.