Density Effect Correction Research Articles

A Note on the Density Effect Correction for the Stopping Power Values of Electrons in Sulfur and Calcium

SHARADA, K. S. A Note on the Density Effect Correction for the Stopping Power Values of Electrons in Sulfur and Calcium. Radiat. Res. 97, 424-433 (1984). The general expression given by Dr. Sternheimer is used to calculate the density effect correction in the stopping power values for electrons in calcium and sulfur for energies 0.75 to 10 MeV to study the linearity of the electron energy response of CaSO4:Dy Teflon disk dosimeters toward higher energies. It is found that up to 10 MeV the stopping power values versus electron energy above 2 MeV tend to be a constant which predicts the linearity of the electron energy response of the dosimeter toward the high-energy region so that it can be used for dose measurements of high-energy machines with no loss of accuracy. The various constants entering into the general expression for density effect correction are calculated and tabulated. The density effect correction is computed and tabulated. The stopping power for electrons in CaSO4:Dy Teflon TLD disk dosimeter is computed and presented. The electron energy response of this material for the energy range 10 keV to 10 MeV is also computed and presented. The stopping power values for electrons in calcium and sulfur with density effect correction are computed and tabulated.

Erratum: Density effect for the ionization loss of charged particles in various substances

The density-effect correction $\ensuremath{\delta}(\ensuremath{\beta})$ for the ionization energy loss of charged particles has been evaluated for 72 substances (34 metallic elements, 26 compounds, 11 gases, and liquid hydrogen), using up-to-date values of the mean excitation potential $I$ and of the atomic absorption edges $h{\ensuremath{\nu}}_{i}$, which were employed as input data for the general equations for $\ensuremath{\delta}(\ensuremath{\beta})$ previously derived by Sternheimer.

Density effect for the ionization loss of charged particles in various substances

The density-effect correction $\ensuremath{\delta}(\ensuremath{\beta})$ for the ionization energy loss of charged particles has been evaluated for 72 substances (34 metallic elements, 26 compounds, 11 gases, and liquid hydrogen), using up-to-date values of the mean excitation potential $I$ and of the atomic absorption edges $h{\ensuremath{\nu}}_{i}$, which were employed as input data for the general equations for $\ensuremath{\delta}(\ensuremath{\beta})$ previously derived by Sternheimer.

Fermi density effect on the stopping power of metallic aluminum

The density-effect correction $\ensuremath{\delta}$ to the Bethe stopping-power formula for fast charged particles is evaluated for metallic aluminum from the dielectric-response function $\ensuremath{\epsilon}(E)$. The latter has been accurately determined over the entire range of excitation energy $E$ by Shiles, Sasaki, Inokuti, and Smith through comprehensive analysis of all pertinent experimental data. The resulting values of $\ensuremath{\delta}$ (which is a function of the particle speed $\ensuremath{\beta}c$) should be the most reliable to date. The present result agrees well with that of Sternheimer, who used a simpler and less rigorous procedure, and thus corroborates the general view that $\ensuremath{\delta}$ is insensitive to fine details of the behavior of $\ensuremath{\epsilon}(E)$. We also present general remarks on the evaluation of $\ensuremath{\delta}$ and on the analytic continuation of $\ensuremath{\epsilon}(E)$ as a function of the complex energy $E$.

General expression for the density effect for the ionization loss of charged particles

The equations for the density-effect correction $\ensuremath{\delta}(X)$ for the ionization loss as given in a previous paper have been extended to the case where $\ensuremath{\delta}({X}_{0})\ensuremath{\equiv}{\ensuremath{\delta}}_{0}g0$. Here ${X}_{0}$ is the lower limit of the range ${X}_{0}lXl{X}_{1}$, where a particularly simple expression for $\ensuremath{\delta}(X)$ applies; $X={log}_{10}(\frac{p}{{m}_{0}c})$, where $p$ is the momentum and ${m}_{0}$ is the mass of the incident particle. The case ${\ensuremath{\delta}}_{0}g0$ applies directly to the calculation of $\ensuremath{\delta}(X)$ for conductors (metals).

Energy loss of relativistic electrons and its fluctuation in gas proportional counters

Absolute measurements of the energy loss and its fluctuation of relativistic electrons in this gas layer over the momentum region of 50–800 MeV/ c have been extensively achieved with high accuracy using a 100 cm proportional counter, operated with a conventional mode or a special mode (the central wire is divided by a small glass bead into two sensitive lengths of 10 cm and 90 cm). The counter is filled with Ar + 10% CH 4 mixture at various pressures between 0.1 and 2.0 atm. The experimental distributions of the energy losses are compared with those predicted by the Landau theory, the Blunck-Leisegang theory, the Chechin-Ermilova theory and the Monte Carlo method (Ispiryan et al., Cobb et al. and Ermilova et al.). The observed fractional widths agree relatively well with those of the Monte Carlo calculations. The observed values of the most probable energy losses for small thickness (≤3 × 10 −2 g/cm 2) of gas layer are 10–25% smaller than those predicted by the Landau-Sternheimer theory and they approach to the theoretical ones with increase of the thickness. A part of such a discrepancy between the theory and the experiment may be explained by the fact that the inner shell electrons of argon atoms in the absorber material do not contribute to the most probable energy loss, when the energy loss is not larger than the binding energy of K-shell electrons. The explanation, however, does not give an understanding for the fact that even when the thickness of gas layer is equal for the short and long counters, the difference in the most probable value between both counters is larger than that predicted by the Landau-Sternheimer theory. This suggests that the density effect correction given by Sternheimer may be insufficient to the thin gas layer. The observed most probable values are also compared with those predicted by the Chechin-Ermilova theory and the Monte Carlo method (Cobb et al. and Ermilova et al.). These predictions do not give a satisfactory explanation for the decrease of the observed values. However, the Monte Carlo results calculated by Ermilova et al. show the tendency close to the observed data.

On the restricted energy loss of relativistic charged particles in matter

The Bethe-Bloch formula with density effect correction which describes the restricted energy loss of relativistic charged particles in matter is extended to the case when the upper energy transfer in single collisions are of the order or less than the binding energy of atomic inner shell electrons.

Berechnung der elektronen-bremsstrahlspektren in NaJ, CsJ, Si und Ge

Following the method of Zerby and Moran, the bremsstrahlung spectra, the total number of emitted bremsstrahlung photons, and the bremsstrahlung yield resulting from electrons slowing down in NaI, CsI, Si and Ge were calculated. Contrary to the earlier calculations the Sternheimer density-effect corrections, the energy loss by bremsstrahlung, and some corrections of the bremsstrahlung cross-section expressions of the Bethe-Heitler theory were taken into account. The comparison with the earlier calculations neglecting these corrections shows some discrepancies, which underline the necessity of using all corrections available.

Quantum Mechanical Calculation of Neutron Stopping Power

The stopping power of matter is calculated quantum mechanically for the binding of atomic electrons is important) is shown to be insignificant at neutron energies of the order of 420/sup 0.35/ GeV or greater, where Z is the atomic number of the medium traversed. The quantum mechanical result shows a weaker dependence on neutron energy than an earlier semiclassical computation, applicable up to 10 GeV, although the two calculations give comparable numerical values in the range 5-10 GeV. A simple stopping-power formula is given for neutrons with form rtant. A more complicatd formula is given and evaluated numerically to 7000 GeV. The density effect and radiative corrections are not treated.

The rate of ionization loss and intrinsic resolution of cadmium telluride detectors

The values of stopping power and most probable energy loss in CdTe have been calculated for heavy charged particles by taking into account both the shell effect and density effect corrections, in the energy interval 5 MeV to 100 000 MeV. The fluctuations in energy loss have also been discussed and the values of fwhm as percentage of the most probable energy loss are shown graphically as a function of kinetic energy of various particles for different thickness of CdTe detectors.

The density effect and rate of energy loss in common plastic scintillators

The density effect term in the rate of ionization energy loss formula has been determined for common types of plastic scintillator following the well-known dispersion model of Sternheimer. The rate of energy loss and the most probable energy loss in thin detectors made of plastic scintillator have been calculated and tabulated systematically taking into consideration both density effect and shell correction terms. The values of fwhm as percentage of the most probable energy loss in detectors of three different thickness have been calculated and presented graphically covering the range of interest in both high energy physics and cosmic rays.

General Expression for the Density Effect for the Ionization Loss of Charged Particles

The equations for the density-effect correction $\ensuremath{\delta}(X)$ for the ionization loss as given in a previous paper have been extended to the case where $\ensuremath{\delta}({X}_{0})\ensuremath{\equiv}{\ensuremath{\delta}}_{0}g0$. Here ${X}_{0}$ is the lower limit of the range ${X}_{0}lXl{X}_{1}$, where a particularly simple expression for $\ensuremath{\delta}(X)$ applies; $X={log}_{10}(\frac{p}{{m}_{0}c})$, where $p$ is the momentum and ${m}_{0}$ is the mass of the incident particle. The case ${\ensuremath{\delta}}_{0}g0$ applies directly to the calculation of $\ensuremath{\delta}(X)$ for conductors (metals).

The range-energy relation in emulsion

The Bethe-Bloch theory of stopping, including shell corrections and the density-effect correction, is used to calculate theoretical ranges for standard Ilford G.5 emulsion. Only the mean ionization potential is an adjustable parameter. Making corrections for theK shells of all emulsion atoms except hydrogen, and also correcting for theL shells of iodine, silver, and bromine, one can obtain a fit to the measured ranges for protons of 1 to 700 MeV. The mean ionization potential found is (331 ±6) eV, andI/Z has a value of (12.1 ±0.2) eV as an average for all emulsion elements except hydrogen. At low velocities the hydrogenlike atomic model used in the shell-correction calculations appears to over-accentuate the shell effects. A better agreement with the experimental data for proton energies below 40 MeV is obtained semiempirically. A range table for emulsion of standard density is given. A calculated range table for water, useful for adjusting ranges measured under nonstandard density conditions, is also included.

Precision quantameter for high energy X-rays

An ionization chamber has been designed to serve as a standard for measurements of the intensity of beams of high energy photons. The chamber consists of twelve plates of copper, each of one cm thickness, so that nearly all the energy of the photons is absorbed in the chamber. The ionization in the shower is sampled at the twelve gaps between plates, and the gap widths are arranged so that a Simpson's rule integration of the shower curve is automatically made. By making the last gap larger and by making an appropriate gap at the sides of the chamber, a compensation is made for any leakage of energy out of the chamber. The total energy content of a photon beam, U, should be accurately proportional to the ionization charge measured, q, independently of the spectral shape of the beam. An absolute calibration of the chamber has been calculated to an accuracy of a few percent. A density effect correction to the stopping power of copper has been included in the calculation.

Density Effect for the Ionization Loss in Various Materials

The reduction in the ionization loss of charged particles due to the polarization of the medium has been calculated using the mean excitation potentials recently determined by Caldwell. Values of the coefficients of an approximate analytic expression for the density effect correction have been obtained for a number of metals, compounds, and gases.