Total Elastic Scattering Cross Sections Research Articles

Scattering of Slow Electrons by Neon and Argon

Total elastic scattering cross sections have been computed for the scattering of electrons by neutral neon and argon in the energy range 0-1 Ry. These results were obtained by the polarized-orbital method wherein a polarization potential accounts for the distortion of the atomic electron distribution by the scattering electron. The polarization potentials are determined using perturbed orbitals obtained by the Sternheimer and Hartree-Fock-Slater (HFS) approximations. Dipole polarizabilities are also calculated. The results are used to evaluate total scattering cross sections by the two approximations and evaluate their capabilities by comparison with experimental data. The HFS-based approximation works very well for neon giving substantially improved cross sections over earlier Sternheimer-based calculations by Thompson. However, little improvement is obtained in either case for argon.

Production of neutral alkali dimers by sputtering; total elastic cross sections of potassium dimers on the noble gases

It has been observed that polycrystalline alkali targets, bombarded by Ar + ions of about 11 keV, eject not only atoms but also dimers. The dimer fraction has been measured as well as the energy spectrum. A discussion is given in terms of the thermal spike model. These measurements explain a discrepancy in the total elastic-scattering cross sections of K on the noble gases, measured by Politiek et al.. In combination with their measurements the total elastic cross sections of K 2 on the noble gases could be determined in a limited velocity range.

Molecular ramsauer-townsend effect in very low energy 4He- 4He scattering

It is shown that a Ramsauer-Townsend effect is possible in very low energy (≈ 2°K) collisions of 4He- 4He - i.e., a deep minimum in the total elastic scattering cross section occurs at this collision energy. It is seen that no such minimum is possible for the other isotopic variants, 3He- 3He and 3He- 4He.

Elastic Scattering of Positrons by Hydrogen Molecules

Elastic positron–hydrogen molecule collisions are considered below the first electronic excitation threshold. The interaction of the incoming positron with the hydrogen molecule is represented by a superposition of single center static and nonspherical polarization potentials. The static potential is expanded to second degree in Legendre polynomials. The Chebyshev polynomials are used to improve the truncated Legendre series approximation and the effect of including the fourth degree contribution is shown to be slight. Positronium formation effects are neglected. Two semiphenomenological polarization potentials are used, and it is shown that the parameters can be suitably adjusted to reproduce the results obtained if the Henry and Lane polarization potential is used. It is shown that the partial Ramsauer–Townsend effect is useful in determining the values of polarization potential parameters. Total elastic scattering cross sections are given for incoming positron energies between about 0.4 and 14 eV while the positron annihilation coefficient is given to about 60 eV.

Total Elastic Cross-Section Measurements for Argon on Argon

Total elastic scattering cross sections for argon on argon are presented as a function of the relative velocity of collision. The “glory” extrema predicted to be present as well as the correct velocity dependence for a potential with long-range 1 / r6 behavior are observed. The data, while not of sufficient quality to be inverted directly, yield constraints on the shape and position of the argon potential well.

A phase-shift analysis of electron-helium scattering: I - Elastic scattering below the 2S resonance

A phase-shift analysis of electron-helium elastic scattering in the energy range 31 to 191 ev has been made. s- and p-wave phase shifts consistent with the dispersion relation and with experimental information on the total elastic scattering cross section, the diffusion cross section and recent measurements of the differential cross section, to within 5% are obtained. The Gibson-Dolder measurements of the differential scattering cross section are shown to be theoretically preferable to the earlier measurements of Ramsauer and Kollath. The d-wave phase shift cannot be determined to better than 25% by available experimental information. The phase shifts obtained are consistent with, but do not distinguish between, recent non-adiabatic theoretical calculations, but exclude the simple polarized orbital model. They satisfy Spruch bounds based on the experimental polarizability and yield a scattering length of 11a0 in agreement with other determinations.

Calculated total elastic scattering cross sections for H(IS) at collision energies below 1 eV

Exact computations of the elastic scattering cross sections for atomic hydrogen, based on the best local 1σ + g 3σ + u potentials, provide an accurate, essentially ab initio prediction of the glory and resonance behavior to be expected in H(IS) beam scatterring experiments.

Messungen und Berechnungen zum elektronenmikroskopischen Streukontrast für 17 bis 1200 keV-Elektronen

Electron transmission experiments under electron microscope conditions were done with C-, Ge- and Pt-films to get information about the influence of electron energy and objective aperture. One gets an exponential law of transmission for small mass thicknesses x of the objects and can calculate the “contrast thickness” xk (in T = exp(— x/xk)). Using the Lenz theory, two constants Xa and ϑ0 are determined, for each element and electron energy, from the measurements of xk at four different objective apertures. xa is related to the total elastic scattering cross section and ϑ0 is the half width of the atomic scattering amplitude ƒ(ϑ). The variation of xa and ϑ0 with electron energy is not in agreement with the theory using the first Born approximation and a simple screened atomic potential. But using these two experimentally determined constants in a plural scattering theory of LENZ, good agreement between calculated and experimental deviations from the exponential law of transmission up to mass thicknesses of 300 µg · cm-2 is obtained. To get better theoretical values of xk, the complex atomic scattering amplitudes were calculated quantum theoretically with the WKB-method and Hartree potentials. The values agree with the experimental results for Ge- and Pt-films. For carbon there is a large contribution by inelastic scattering making a direct comparison with experimental results difficult. The energy dependence of xa shows saturation for high voltages, as expected by theory. At high voltages the difference in the xk-values for films with different atomic numbers is larger, resulting in lower xk-values for platinum. But at very low voltages the xk-values of carbon are lower than those of platinum. Some measurements of xk at 60 keV on targets of noble gases confirm the absence of a large difference in contrast between atoms in the gaseous and condensed amorphous state.

Tests of Born Approximations: Differential and Total Cross Sections for Elastic Scattering of 100- to 400-eV Electrons by Helium

The angular dependence of elastic scattering of 100- to 400-eV electrons by helium atoms has been measured for scattering angles of 5\ifmmode^\circ\else\textdegree\fi{} to 30\ifmmode^\circ\else\textdegree\fi{} with a high-resolution electron spectrometer. The observed relative differential cross sections were converted to an absolute basis by measuring their ratio to known cross sections for excitation to the $2^{1}P$ state. Integration over angles yielded total elastic scattering cross sections. Large deviations from the Born approximation are found, especially for small electron energies and small scattering angles. Experimental and theoretical results are analyzed and compared in some detail. Exchange and polarization are chiefly responsible for deviations from the Born approximation. The Ochkur (Bonham) approximation is shown to be almost equivalent to the first-order exchange approximation for electron energies of 350 and 500 eV. Analytical series expansions for differential and total Born cross sections are given. Our experimental results are in qualitative agreement with results of earlier experiments, but are quantitatively different and extend to smaller scattering angles.

Potential-Well Characteristics from the Energy Dependence of the Glory Extrema in Total Elastic Scattering Cross Sections

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The Momentum Transfer Cross Section for Electrons in Helium

Measurements of the drift velocity, the ratio of diffusion coefficient to mobility, and the "magnetic drift velocity" for electrons in helium have been made at 293�K in the range 1.8 X 10−19 E/N −17 V cm2. From an analysis of the drift velocity data, an energy-dependent momentum transfer cross section has been derived for which an error of less than � 2 % is claimed over the central portion of the energy range. The cross section agrees with the theoretical cross section of La Bahn and Callaway to within 2% over the whole energy range. The agreement with the cross section derived by a number of procedures from the total elastic scattering cross section measured by Golden and Bandel is less satisfactory. The drift data are sufficiently accurate to enable a search to be made for the effects of fine structure in the cross section at low energy. The results do not support the existence of such structure.

Streuung von Helium-Atomstrahlen in Edelgasen

The scattering of Helium atomic beams in rare gases is investigated by measurements of total elastic scattering cross sections. With the device described the dependence of total scattering cross sections of the relative velocity of the scattering atoms was measured. For variation of the beam velocity in the range of 1:8 a He beam source was used which could be cooled down with liquid helium from room temperature to 4.8 °K. The detector is of the universal-detector-type. A Wien filter is used as mass filter. The lowest detectable particle density is 6.3 · 103 He-atoms/cm3. The measured scattering cross sections are in qualitative agreement with the theory ofBernstein.

Observation of undulations of the total elastic scattering cross section for the scattering of helium atomic beams in Xe, Kr and Ar

Observation of undulations of the total elastic scattering cross section for the scattering of helium atomic beams in Xe, Kr and Ar

The elastic scattering of 662 kev gamma rays

Employing a 2.5 curie 137Cs source, total elastic scattering cross sections in Pb, Pt, Ta, Sn and Zr were determined using a collimator geometry similar to that of Wilson at angles 20°, 30°, 45°, 60°, 75° and 90°. The experimental results were compared with theoretical values obtained from the form-factor formula of Bethe and exact calculations of Brown et al. The experimental values in Pb, Pt and Ta are in conformity with the theoretical values calculated from Brown et al. data. The experimental values in Sn and Zr show good agreement with form-factor values.

Scattering of 0· 5 and 0· 8 mev neutrons on medium weight and heavy nuclei

Differential elastic scattering cross sections have been measured for 0·5 and 0·8 MeV neutrons on nuclei of iron, zinc, zirconium, cadmium, tin, barium, mercury, lead, bismuth and uranium over the range of angles 30–140°. Total elastic scattering cross sections and inelastic collision cross sections were also obtained and the average cosine of the scattering angle, transport cross sections for elastically scattered neutrons and the transport cross section which includes inelastic processes were computed.

Dipole—Quadrupole and Retardation Effects in Low-Energy Atom—Atom Scattering

Simple approximation formulas are derived for the dipole—quadrupole and retardation effects upon the total elastic scattering cross section for atomic collisions in the thermal energy range. For a long-range potential containing both the dipole—dipole and dipole—quadrupole terms, i.e., V(r) = —(C(6)/r6)[1+(β/r2)], one finds ΔQ/QMM≈⅔π(β/QMM) where QMM is the Massey—Mohr cross section for an inverse sixth-power attraction. For a long-range potential including dipole—dipole and retardation effects, approximated by V(r) = —(C(6)/r6)[a/(a+r)], one obtains ΔQ/QMM≈−(π−32QMM12)/a. Since these deviations are small and opposite in sign, it is concluded that the contributions of the dipole—quadrupole and retardation effects to the total cross sections are not sufficient to account for any significant discrepancy between theoretical and experimental Q values.

Angular and energy distributions of neutrons from the interaction of 14 MeV neutrons with Li 6 and Li 7

The angular and energy distributions of the neutrons from the interaction of 14 MeV neutrons with Li 6 and Li 7 were determined from analysis of nuclear plate detectors placed at 10° intervals from 10° to 160°. The angular distributions of the elastically scattered neutrons are similar not only to those expected on the basis of diffraction scattering, but also to those obtained from an optical model analysis with parameters identical to those used for fitting medium-weight and heavy nuclei. The total elastic scattering cross section for Li 6 is 883±95 mb; for Li 7, 969±110 mb. The neutrons from inelastic collisions are much less peaked in the forward direction and exhibit a considerable isotropic component. The measured value for the total cross section for the emission of neutrons for Li 6 is 1.44±0.16 b; for Li 7, 1.61±0.2 b.

Semiclassical Analysis of the Extrema in the Velocity Dependence of Total Elastic-Scattering Cross Sections: Relation to the Bound States

The phenomenon of extrema in the velocity dependence of the total elastic cross section Q(v) for atom—atom scattering in the thermal-energy region is shown to be a quite general one, whenever the interaction potential consists of both attractive and repulsive parts and the resulting well has a ``capacity'' for one or more discrete levels. The phase shift vs angular-momentum dependence exhibits a maximum; since this maximum is a function of the de Broglie wavelength, the cross section exhibits an undulatory velocity dependence. A semiclassical analysis of the extrema velocities (and undulation amplitudes) is presented. Suitable plots are suggested from which one may deduce certain information on the interatomic potential and the diatom bound states. The following rule is proposed: the observation of m maxima in the elastic atom—atom impact spectrum implies the existence of at least m discrete vibrational levels of zero angular momentum for the diatom.

Comparison and Appraisal of Approximation Formulas for Total Elastic Molecular Scattering Cross Sections

The Massey—Mohr (MM), Schiff (S), and Landau—Lifshitz (LL) approximations for the total elastic cross section (Q) are intercompared. All can be shown to follow from the same assumption, (i.e., the classical small-angle deflection function, thence the Jeffreys—Born phases via the semiclassical equivalence relationship), sufficing to determine the velocity dependence of Q. Thus, for V=±C(s)/rs, Q(s)=p(s)[C(s)/hv ]2/(s—1) The coefficient p(s) is the same for the S and LL approximations; the ratio pSLL(s)/pMM(s)≥1, (<1.075); it is 1.0709 and 1.0458 for s=6 and 12, respectively. A numerical calculation for a repulsive (s=12) interaction shows that the SLL formula reproduces the partial-wave calculated Q to within ½%. A graphical presentation suggests the generality of this result; it also indicates the source of bias in the MM approximation. For a ``realistic'' intermolecular potential, (restricting consideration to collisions in the ``thermal'' energy range), the influence of the repulsion is only to produce undulations in Q(v); the correct value of C(6) may be obtained by velocity averaging the ``apparent'' CSLL(6).

High-Velocity Molecular Beam Scattering: Total Elastic Cross Sections for L-J(n, 6) and Exp-6(α) Potentials

Explicit expressions are derived for the total elastic scattering cross sections in the high-velocity region for molecules interacting according to L-J (n, 6) and exp-6(α) potentials. Cross sections are presented in tabular and graphical form.