Measured Stopping Cross Sections Research Articles

Stopping cross-sections of various gases for alpha particles in the energy region 0.2 to 5.5 MeV

A single experimental apparatus has been designed to allow measurements of stopping cross-sections of materials in liquid and vapour phase, for alpha particles, using an indirect method. The method in which residual energies for increasing absorber thicknesses are obtained and differentiated, has been used in a number of investigations of phase effects in stopping power. As a set of preliminary experiments, the stopping cross-sections of He, N2, Ar, CH4 and air for alpha particles have been measured, to allow overall assessment of measurement and data analysis procedures by comparison with other published results. Such comparison suggests that the absolute uncertainty of the techniques employed is unlikely to exceed 4 or 5%. Some of the problems associated with indirect measurements of stopping power are discussed.

Stopping cross sections for α particles from 1.0 to 8.5 MeV in H 2, He, N 2, O 2, Ne, Kr and Xe

Stopping cross sections for α particles from 1.0 to 8.5 MeV in H 2, He, N 2, O 2, Ne, Kr and Xe are presented. Natural α particles were used from the decay of 212Bi and 212Po, and the energy loss measurements were made by varying the source-to-detector distance in a differentially pumped gas-cell system. Measured values including Lewis and multiple scattering corrections are fitted to a semi-empirical range-energy function with three parameters. Deviations for all the data points from the fitted curves are shown, and the stopping power results are determined with an accuracy from 0.3 to 5%. Comparisons are made with previous stopping cross section measurements and the agreements are briefly discussed.

Binary-encounter stopping cross sections. III. Straggling and screening

A previously developed binary-encounter model describing the slowing down of energetic heavy charged particles over a broad range of incident-particle energies is employed to calculate energy straggling as a function of target ${Z}_{2}$ for incident helium and hydrogen. This model seriously overestimates the measured stopping cross sections at high incident-particle energy for helium on heavy target atoms, but appears to yield more reasonable results for energy straggling. The large results in the stopping calculation are attributed to the neglect of the distortion of the electron charge cloud during the collision. A screened interaction, based on screening in a free-electron gas, is employed to estimate the size of the effect on both the stopping and straggling results for 10-MeV incident ${\mathrm{He}}^{++}$ on target atoms $1\ensuremath{\le}{Z}_{2}\ensuremath{\le}36$, and for equilibrium-charge-state beams of hydrogen at energies 1 keV to 1 MeV on a number of targets. It was found that the neglect of distortion may result in errors equivalent to or greater than those due to the neglect of the long-range dipole interactions when estimating $S$, particularly at higher energies. For the straggling calculation both of these effects result in considerably smaller correction to the binary-encounter method.

Stopping cross section measurements with thin supported films

Elemental stopping cross sections, ϵ, can be determined by Rutherford backscattering either with thin-film or bulk targets. Both methods rely on approximations, which are met well for heavy elements. We present a modification of thin-film method which eliminates the need for approximations, but at the cost of precision. Results obtained for both light and heavy elements agree with those obtained by traditional methods. For Al, ϵ values are obtained which deviate from most published results, but agree with previously unexplained AlSi and AlAl 2O 3 yield ratios.

Stopping cross section measurements with heavy ions in the keV energy range in gases by time-of-flight spectroscopy

Energy loss measurements of ions in gases are reported which have been performed by time-of-flight spectroscopy. This new method is especially applicable to ions in the keV energy range, where isotope separators are ideal for providing the ion beams. Theoretically the low energy range is of special interest because in this region the slowing down process is mainly due to elastic collisions. Experimental data are rare and more investigations are needed for a better understanding. The time-of-flight technique is demonstrated by the measurement of twelve stopping cross sections of 208Pb-ions in H 2-gas in the energy interval 20 keV ≤ E ≤ 156 keV. The data are compared with theoretical nuclear stopping cross sections which were calculated by Lindhard, Nielsen and Scharff for three different screened Coulomb potentials. They are also compared with the measurements of Sidenius and of Hvelplund which were performed by a different method.

Measurement of the stopping cross sections for protons and 4He ions in erbium and erbium oxide: A test of Bragg's rule

Measurements of absolute stopping cross sections of erbium and erbium oxide for 250 keV to 2.5 MeV protons and 4He ions have been made by ion backscattering. Contamination of the erbium films was minimized by in situ deposition of the reactive metal onto the target substrate in an ultra-high vacuum chamber attached to the beam line of a 2.5 MeV Van de Graaff accelerator. Oxidation was accomplished by in situ annealing in an oxygen atmosphere. The oxidation state of the film was determined by both X-ray diffraction and elastic proton scattering. A stringent test of Bragg's Rule was made for erbium oxide by measuring the energy loss of the ion beam in an erbium film before and after oxidation. The measurements confirmed Bragg's Rule at the highest velocities of this experiment (21 × 10 8 cm/s), the rule was in error by 13%. This is believed to be the first stringent test of Bragg's Rule in solids using absolute cross sections in which significant disagreement was observed between experiment and theory. The measured cross sections were also used to determine the parameters of the electronic stopping cross section formula developed by Brice.

Relative measurements of stopping cross section factors by back-scattering

From international conference on ion beam surface layer analysis; Yorktown Heights, NY (18 Jun 1973). A procedure for evaluating relative stopping cross section factors from the ratios of two heights in a single back-scattering spectrum is described. The method, which requires a two-layered target, is used to test the stopping cross sections of 1 to 2 MeV /sup 4/He/sup +/ ions incident on Au, Ag, Cu, Si and Al. The ratios of the heights of Au, Ag and Cu are consistent with published stopping cross section data. The Au--Al height ratio is within the errors quoted for the Au and Al stopping cross section measurements. The Al-- Si height ratio differs significantly from the expected value. It is also shown that the height ratio changes slightly as a function of the thickness of the surface layer. (auth)

Z1 oscillations in stopping of atomic particles

The measured stopping cross sections for atomic projectiles in various materials show Z1 oscillations, a more or less periodic dependence of the stopping on Z1, the atomic number of the projectile.These oscillations have a larger amplitude when the projectiles are channeled in single crystals than when they are not.In this paper it is shown that the oscillations are a size effect, i.e., the larger an atom the more it is ionized and the greater is the stopping. Calculation of stopping of low [Formula: see text] channeled particles in tungsten and silicon give qualitative agreement with experiment: the maxima and minima are in the right places, and vary in the right way, but the calculated amplitude of oscillation is too small. Possible explanations for the amplitude discrepancy are suggested.

Stopping cross-section measurements in carbon using recoil ions from radioactive decay

An experiment is described for measuring the stopping cross section of fast heavy ions colliding with stationary atoms. The heavy ions are obtained by recoil from alpha disintegration, and their energy loss in passing through thin absorber foils is measured by a time-of-flight method. Using this technique the mean stopping cross section of 169 kev lead ions in carbon has been shown to have the value 32·7 × 10−14 ev cm2 (±5%).

Lifetime of the First Excited State ofLi7

The ${\mathrm{Li}}^{7}(p, {p}^{\ensuremath{'}}){\mathrm{Li}}^{7*}$ reaction was used as the source of Doppler-broadened 478-kev gamma rays to determine the mean life of the first excited state of ${\mathrm{Li}}^{7}$ by the nuclear resonance fluorescence technique. Both scattering and self-absorption experiments using both LiF and Li as the scattering and absorbing materials were performed.The resonance scattering gives a mean life of (1.09\ifmmode\pm\else\textpm\fi{}0.07)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ sec after a 2% correction for slowing down of the ${\mathrm{Li}}^{7*}$ nuclei has been made. This correction follows from the measured stopping cross sections for lithium ions. An additional correction, for the effect of collisions in which the ${\mathrm{Li}}^{7*}$ nuclei lose a large fraction of their energy, is found difficult to estimate, although it is certainly not more than a few percent. For this reason, the scattering measurement is regarded as giving a lower limit for the mean life.The self-absorption measurements give a mean life of (1.15\ifmmode\pm\else\textpm\fi{}0.14)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ sec. Debye temperatures of 400\ifmmode^\circ\else\textdegree\fi{}K and 700\ifmmode^\circ\else\textdegree\fi{}K were used for Li and LiF, respectively. The error given, about twice the statistical error of the data, includes estimates of the effect of other experimental uncertainties.

Stopping of Low-EnergyH+andHe+Ions in Plastics

The stopping cross scctions of polystyrenes, polyethylene, and Pliolite S--5A for 40- to 340-kev H/sup +/ and He/sup +/ ions were measured. A nearly monoencrgetic analyzed beam of ions of known energy was deflected 90 in the field of a magnetic spectrometer. A thin film of the stopping material was placed in the beam path at thc spectrometer entrance. The energy loss of the beam was determined by measuring the decrease in magnetic field necessary to restore the beam to the 90 deflection angle. The film thickness was obtained by weighing a known area of film. The probable errors in the measurements are 2.3--2.8% for H/sup +/ and 3--4% for He/sup +/. Proton stopping cross-section measurements on gold with this equipment agree with the resuits obtained by Bader, Pixley, Mozers and Whaling. Above 75 kev the He/sup +/ cross sections vary linearly with the ion velocity. (auth)

Stopping Cross Section of Solids for Protons, 50-600 kev

The stopping cross sections of Li, Cu, LiF, CaF2, Pb, and Au for protons have been measured over the energy range Ep=50-600 kev; the stopping cross section of Be for protons has been measured for Ep=50-2600 kev. An electrostatic analyzer and magnetic spectrometer were used to measure the energy loss of protons in a thin film of the stopping material. The density of the stopping film was determined by weighing, or by quantitative chemical analysis of, a known area. The ratio of the stopping cross section of Al, Cu, Mn, Ta, and Pb to that of Au was measured by observing the yield of elastically scattered protons from these targets for Ep=200-600 kev. The ratio of stopping cross section of Ca, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn, to that of Mn was measured for Ep=200-600 kev by the same method. In the region Z=23-29, the stopping cross section decreases as the atomic number of the stopping material increases. The probable error of absolute stopping cross section measurements in this experiment is 3%.

The Stopping Cross Section of Gases for Protons, 30-600 kev

The stopping cross section of ${\mathrm{H}}_{2}$, He, ${\mathrm{O}}_{2}$, air, ${\mathrm{N}}_{2}$, Ne, A, Kr, Xe, ${\mathrm{H}}_{2}$O, N${\mathrm{H}}_{3}$, NO, ${\mathrm{N}}_{2}$O, C${\mathrm{H}}_{4}$, ${\mathrm{C}}_{2}$${\mathrm{H}}_{2}$, ${\mathrm{C}}_{2}$${\mathrm{H}}_{4}$, and ${\mathrm{C}}_{6}$${\mathrm{H}}_{6}$ for protons has been measured over the energy range ${E}_{p}=30\ensuremath{-}600$ kev. An electrostatic analyzer measures the energy of protons incident on a gas cell, and the transmitted beam energy is measured with a magnetic spectrometer. The gas cell is closed off with thin aluminum windows. Comparison of the molecular stopping cross section of the compounds with the values obtained by summing the constituent atomic cross sections shows that Bragg's rule does not hold for any of these compounds below ${E}_{p}=150$ kev; for NO the additive rule does not hold at any energy studied. Above 150 kev the stopping cross section of carbon is obtained by subtracting the hydrogen contribution from the values measured for the hydrocarbons. Average ionization potentials are calculated from these measurements. A range energy relation for protons in air is included. Sources of error are discussed; the probable error of the stopping cross section measurements varies between 2-4 percent.