Overlap Correction Research Articles

The electron capture decay of 131Ba

The decay of 131Ba has been investigated by means of a 4 π internal source scintillation spectrometer and a Ge(Li) detector. The L/K. and M/L electron capture ratios of the allowed transitions to the 373, 620 and 1048 keV levels in 131Cs have been measured. From these electron capture ratios, the ifQ EC value and the exchange and overlap corrections X L/K and X M/L have been derived.

Application of direct peak analylsis to energy‐dispersive X‐ray fluoescence spectra

AbstractA modified covell method for direct peak analysis has been applied to energy‐dispersiv X‐ray flourescence spectra. The method is background independent and is well‐suited to computerized data reduction. It provides acceptable precision, minimizes errors from instrumental gain shift, and permits peak overlap correction. Peak overlap errors exhibit both positive and negative nodes as a function of peak separation distance, and are corrected using concentration ratios determined from thin, single‐element standards. Peak precisions and overlaps are evaluated as a function of window width to aid in width selection. Least‐square polynomial smoothing prior to peak analysis significantly improves peak area precisions without significantly affecting their accuracies.

Far infrared absorption of diatomic polar molecules in simple liquids and statistical properties of the interactions. I. Spectral theory

A theory of the far infrared spectra of diatomic polar molecules dissolved in simple liquids is presented. The starting point is a basic spectrum of additive Lorentzian lines, whose widths and shifts are expressed up to second order with respect to the interaction. This basic spectrum is distorted by the finite correlation time of the interaction, by the correlation between initial states, and by the overlap between the lines which are not completely resolved for the liquid state. All these deviations, including the overlap correction, which leads to a nonadditivity effect of the lines, are also treated up to second order with respect to the interaction.

Practical Correction of Boundary Overlap

Abstract Boundary overlap has concerned forest samplers acutely since the introduction of horizontal point sampling in the 1950's. Although numerous methods have been proposed to minimize this source of bias, none has done it so neatly as the "mirage method" developed by P. Schmid and published in German in 1969. This article decribes the method for use with point or plot sampling and discusses an alternative for use where the mirage method is inappropriate.

A Scheme for Fully Quantitative Energy Dispersive Microprobe Analysis

A procedure and program are described for rapid, economical and simple production of fully quantitative, multi-element analyses from energy dispersive microprobe data. Methods are outlined for background shaping and scaling, comprehensive overlap correction, and adjustment for instrumental drift. Program facilities include the output of all coefficients required, built-in standard data, the option to use default standards when no working standards have been measured, and the ability to respecify standards during data processing.

Diamagnetic susceptibility for some ionic solids

Diamagnetic susceptibility for several ionic crystals was calculated by using the LCAO method in the free-ion approximation of the basic atomic spin orbitals. The density matrix of the crystal was then expressed as a superposition of diamagnetic crystal ion densities. Consequently, the susceptibility could be written in the form of a power series of the overlap matrix; the first term describing the system of the free ions, and the other ones, linear quadratic etc. overlap contributions. Numerical applications show that the linear overlap corrections to the susceptibility are very significant and cannot be neglected in calculations. The results of the present work were compared with the experimental data and good agreement was found for alkali halide crystals, whereas in the case of the MgO crystal there is a clear discrepancy between theoretical and experimental results, specific reasons for which are suggested.

Ohmic hole mobility in cubic semiconductors

Lattice ohmic mobility of holes in cubic semiconductors has been theoretically evaluated accounting for most fundamental aspects of the physical problem. Solutions sufficently simple for the interpretation of experimental data have been obtained. (1) The deformation potential approach has been used in the description of the hole-acoustic and hole-optical phonon scattering mechanism. (2) The overlap corrections introduced in the scattering rates by the symmetry of the valence band wave functions, which are predominantly p-like, have been taken into account. (3) Intra-band and inter-band transitions within and between the heavy and light mass bands have been considered. (4) Non-parabolicity and warping of equienergetic surfaces has been omitted in favour of spherical parabolic bands. Results show that (2) doubles the mobility with respect to the case in which overlap is omitted, and (3) halves the mobility when the two valence bands have equal effective masses with respect to the case in which inter-band scattering is omitted. Comparison with experimental mobility is good for Ge and fair for Si due to the strong non-parabolicity of its valence bands.

Experimental determination of the electron density at the nucleus as a function of the chemical state of ruthenium

The effect of the chemical state on the electron capture rate has been measured for the first time at an element suitable for Mössbauer work (Ru). Changes of the electron densities at the nucleus are deduced with (as well as without) overlap and exchange corrections.

Electron energy relaxation time in Si and Ge

The electron energy relaxation time τ ϵ has been analytically evaluated as a function of lattice temperature taking into account the electron-lattice scattering mechanisms for Si and Ge. Calculations have been carried on in the deformation potential approach including nonparabolicity and overlap corrections with a Maxwell-Boltzmann distribution function, and have been limited to the warm electron range. Since theoretical results agree only qualitatively, even accounting for different approaches, with available data, τ ϵ has been related to β a physical quantity given by a wealth of experimental data. Theoretical results agree satisfactorily with β and seem to indicate that the present theory is essentially sound. A comparative study of lattice scattering for Si and Ge evidences the different effects of the various electron-phonon scattering mechanisms upon τ ϵ .

Spectral and total emissivity of water vapor and carbon dioxide

Data on the infrared radiation characteristics of carbon dioxide and water vapor in the form of absorption coefficients and line spacings averaged over narrow spectral intervals have been compiled from various sources. These data are to be used in heat transfer calculations from hot gases. In order to investigate the accuracy of the data, the simplest case possible is chosen: a comparison with the total emissivity charts of water vapor and carbon dioxide. It appears however that the charts are not entirely reliable as standards for comparison: it seems probable that Hottel's chart for water vapor gives too low values at temperatures above 900°C and that the partial pressure correction is temperature dependent. With the exception of some regions where judgment is difficult, the calculations using spectral data seem to represent total emissivities with a maximum error which is estimated to around 10%. Sources of error in the spectral data and in Hottel's total emissivity charts are discussed. Total emissivity charts, pressure and overlap corrections based on calculations with spectral data are presented.

Radiative Electron Capture inBe7

The continuous spectrum of photons accompanying the electron-capture transition from $^{7}\mathrm{Be}$ to the first excited state in $^{7}\mathrm{Li}$ has been measured in coincidence with the nuclear $\ensuremath{\gamma}$ rays from the deexcitation of this state. The end-point energy of the photon spectrum was determined to be 388 \ifmmode\pm\else\textpm\fi{} 8 keV, in good agreement with accepted mass differences. The probability of $1s+2s$ radiative capture giving a photon energy greater than 50 keV per nuclear $\ensuremath{\gamma}$ ray was determined to be (10.3 \ifmmode\pm\else\textpm\fi{} 0.6) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$. This result should be compared with the value 9.2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$ predicted by the theory of Martin and Glauber. At energies higher than 120 keV the shape of the spectrum agrees with the predictions of theory. At energies lower than 120 keV the intensity falls off faster than expected from the theory. Exchange and overlap corrections to the radiative-capture theory have been calculated and shown to be too small to account for the observed discrepancy.

FIGATOM: a new graphic program for stereoscopic crystal structure illustrations

This paper describes an original Fortran program for drawing stereoscopic Views of any type of crystal structure with a graphic plotter or a 35 mm film visualization unit. Very few input cards – without format – are required since the program contains all symmetry elements for every Wyckoff position of the 230 space groups, and can perform bond length and compacity calculation, atom-intersection testing, chemical and coordination bond drawing, as well as overlap correction for spherical atoms, so that the first treatment of any problem delivers illustrations which may be used, without retouching, for scientific publication purposes.

X-ray scattering factors for ionic crystals with complete electron shells

X-ray scattering factors for the NaF, NaCl, LiCl, LiBr, and KBr crystals were computed using the Hartree-Fock wave functions of the free ions given by Clementi [3]. The corrections, due to the overlap between the free ions in crystals, were evaluated by means of the formulae presented in our previous paper. The results show that these overlap corrections are small and, in practice, independent on direction for all alkali halides with the NaCl structure. The theoretical values obtained agree well with recent experimental data.

Rapid X-Ray Fluorescence Determination of Phosphorus in Geologic Samples

Calcium and Kβ1 and Kβ5 both have second order (II) lines that interfere spectrally with the phosphorus Kα1 first order (I) analytical line in the x-ray fluorescence determination. By combining maximum pulse height discrimination with a mathematical correction for peak overlap, phosphorus can be accurately determined in a wide variety of geologic samples.

On the exchange and overlap corrections in electron capture

Abstract The approximations made in the calculations of the exchange and overlap correction coefficients were investigated. It is shown that the one-electron wave functions of the final state cannot be replaced by those of the unexcited daughter atom, and that the overlap of all inner s, p and d electrons is to be taken into consideration. The new approximation gives a better agreement with the experimental K/β + , L/K and M/L capture ratios than the old approximation.

Occupied Band Structure of Cu: Soft-X-Ray Spectrum and Comparison with Other Deep-Band-Probe Studies

We report a new measurement of the soft-x-ray ${M}_{2,3}$ emission spectrum of Cu, using improved experimental techniques. Previously unreported fine structure was observed in the spectrum. Although exact correction for satellite and subband overlap and self-absorption effects is not yet possible, careful consideration has been given to them, with the result that the ${M}_{3}$ band profile can be resolved from the accompanying structure in a plausible way. Its features can be taken with reasonable confidence to be characteristic of the true ${M}_{3}$ profile. Comparison is made with the complementary ${L}_{3}$ soft-x-ray profile, with band-theoretical estimates of both experimental x-ray profiles, and with the results of ultraviolet-photoemission, x-ray-photoemission, and ion-neutralization measurements. These comparisons favor a single-particle description of the occupied bands of Cu.

Resonance Overlap Effect on Effective Cross Section in Unresolved Resonance Region

The effect of resonance overlap on the effective cross section was studied in the unresolved resonance region. The sequential overlap between resonances belonging to the same sequence of an isotope was studied by a method that approaches Method A at higher energies and Method B at lower energies. The accidental overlap effect between different sequences was studied in reference to factors for overlap correction and flux correction. Numerical studies indicate that in large fast reactors, when an average is taken over the distribution of level spacing, a greater influence is provided on the effective cross section by the sequential as compared with the accidental overlap.

Resonance Overlap Effect on Effective Cross Section in Unresolved Resonance Region

The effect of resonance overlap on the effective cross section was studied in the unresolved resonance region. The sequential overlap between resonances belonging to the same sequence of an isotope was studied by a method that approaches Method A at higher energies and Method B at lower energies. The accidental overlap effect between different sequences was studied in reference to factors for overlap correction and flux correction. Numerical studies indicate that in large fast reactors, when an average is taken over the distribution of level spacing, a greater influence is provided on the effective cross section by the sequential as compared with the accidental overlap.

Stereology, or the quantitative evaluation of microstructures

SUMMARYA general survey is presented of the basic equations of stereology, that is, the quantitative relationships that exist between quantities measured on the two‐dimensional plane of polish or section and the magnitudes of microstructural features that occur in three‐dimensional space. A new and important branch of stereology concerns the quantitative relationships between structures in a thin foil and their projected images. Basic equations are given in the absence of overlap and truncation; then overlap and truncation corrections are indicated for simple cases. The methods of determining the size distribution of particles or grains are outlined. Finally, other important parameters are described, such as the mean free distance and the mean intercept length.The subject of stereology is not completely new to some, but there are still many experiments to be run and methods to be perfected. It is hoped that microscopists dealing with microstructures will be encouraged to apply quantitative methods in their work in order to advance our knowledge in this fascinating field.

Effect of the ligand charge distribution on the crystalline electric field of rare-earth ions

The effect of the overlap between the magnetic electron wave function of the central Pr3+ ion and the electronic wave function of the nearest Cl- ions on the crystal-field parameters of the Pr3+ ion in a PrCl3 crystal has been estimated. The Coulomb part of the overlap contribution, which always opposes the point-charge contribution, to A60 and A66 is nearly double the point-charge contribution, while for A40 and A20 it is 89% and 23%, respectively, of the point-charge contributions. The effect of the overlap correction to the parameters calculated by Hutchings and Ray on the basis of the point-electric-moment model of the ligands has been estimated. The calculation emphasizes the need for a detailed molecular-orbital treatment of crystal-field splitting of the energy levels of rare-earth ions, possibly allowing for the covalency.