Showing papers on "Scattering length published in 1977"
TL;DR: In this paper, an integral equation is used to derive formal expressions for the scattering of a plane wave from a single homogeneous flaw embedded in an isotropic elastic medium, and an optical theorem is also derived.
Abstract: An integral equation is used to derive formal expressions for the scattering of a plane wave from a single homogeneous flaw embedded in an isotropic elastic medium. Expressions are found for the scattered amplitudes and differential cross sections. An optical theorem is also derived.
233 citations
TL;DR: In this paper, the authors derived the momentum transfer cross section for electron-argon collisions in the range 0-4 eV from an analysis of recent measurements of DT/μ as a function of E/N at 294 K.
Abstract: The momentum transfer cross section for electron-argon collisions in the range 0–4 eV has been derived from an analysis of recent measurements of DT/μ as a function of E/N at 294 K (Milloy and Crompton 1977a) and W as a function of E/N at 90 and 293 K (Robertson 1977). Modified effective range theory was used in the fitting procedure at low energies. An investigation of the range of validity of this theory indicated that the scattering length and effective range were uniquely determined ,and hence the cross section could be accurately extrapolated to zero energy. It is concluded that for e ≤ 0.1 eV the error in !he cross section is less than ± 6 % and in the range 0.4 ≤ e (eV) ≤ 0.4 the error is less than ± 8 %. In the range 0.1 < e (eV) < 0.4 the presence of the minimum makes it difficult to determine the errors in the cross section but it is estimated that they are less than −20 %, +12 %. It is demonstrated that no other reported cross sections are compatible with the experimental results used in the present derivation.
170 citations
TL;DR: In this paper, a multielectron target by a heavy particle is approximated in terms of amplitudes for scattering from individual target electrons by treating the motion of the projectile classically and ignoring correlations, the wave function for the system is expressed as a product of single-electron wave functions.
Abstract: Scattering from a multielectron target by a heavy particle is approximated in terms of amplitudes for scattering from individual target electrons. By treating the motion of the projectile classically and ignoring correlations, the wave function for the system is expressed as a product of single-electron wave functions. The probability amplitude for scattering into specific states is then a product of single-electron scattering amplitudes. In this approximation, cross sections for excitation and ionization involving many electrons are expressed in terms of a binomial distribution of single-electron probabilities. The standard connection of this amplitude for multiple excitation and ionization, ${A}^{\mathrm{if}}(B)$, to the corresponding scattering amplitude, $f(\ensuremath{\theta})$, is given, and the validity of this approximation is discussed.
170 citations
TL;DR: In this paper, the authors considered the problem of scattering in 9C with a time-dependent perturbation V(t), where Ha=-d is the negative Laplacian in Rn.
Abstract: Let 9C be the Hilbert space L2(Rn)(n >_ 3) and let {H(t) = Ho + V(t), t R1} be a family of Schrodinger operators in 9C with a time-dependent perturbation V(t), where Ha=-d is the negative Laplacian in Rn. We suppose that {-iH(t) ;; t R1} generates a unitary evolution group {U(t, s) ; -oo < t, s < oo}, Fundamental problems in scattering theory under these circumstances are as follows. (1) When do the strong limits
142 citations
TL;DR: In this article, the elastic scattering of positrons from noble gases has been formulated using a polarized-orbital approximation, in which all multipole moments of the positron-atom interaction are included and the polarized orbital is calculated by a perturbed Hartree-Fock scheme.
Abstract: The elastic scattering of positrons from noble gases has been formulated using a polarized-orbital approximation. In principle all multipole moments of the positron-atom interaction are included and the polarized orbital is calculated by a perturbed Hartree-Fock scheme. The scattered wave is readily obtained from a potential scattering problem and is used to calculate Zeff and the angular correlation as well as the scattering cross sections of interest. Numerical results are presented for positron-helium scattering in the elastic region.
138 citations
TL;DR: Differential cross sections of elastic and inelastic scattering of 1.37 GeV α-particles from 40, 42, 44, 48Ca have been measured as discussed by the authors, and the angular distributions show that the scattering process is quite diffractive.
108 citations
TL;DR: In this article, a set of total cross-sections for scattering of electrons by He has been evaluated over the energy range of zero to 3000 eV by means of the analysis of experiments and theories on total cross sections for elastic scattering, ionisation and excitation, and on differential cross-section for elastic and inelastic scattering.
Abstract: A set of total cross sections for scattering of electrons by He has been evaluated over the energy range of zero to 3000 eV by means of the analysis of experiments and theories on total cross sections for elastic scattering, ionisation and excitation, and on differential cross sections for elastic and inelastic scattering. Between 0 and 19.8 eV, where no inelastic processes occur, the total cross sections for scattering are equal to those for elastic scattering. Above 19.8 eV the authors have evaluated total cross sections for scattering of electrons by adding those for ionisation, excitation and elastic scattering. The total cross sections thus obtained are probably accurate to about 5% over a large part of the energy range. They appear to be in good agreement with the experimental results of Blaauw et al. (1977).
103 citations
TL;DR: In this article, the authors investigated the general problem of scattering and absorption of waves from a Schwarzschild black hole and derived the unitarity theorem for this problem from the wave equation and its boundary conditions.
Abstract: The general problem of scattering and absorption of waves from a Schwarzschild black hole is investigated. A scattering absorption amplitude is introduced. The unitarity theorem for this problem is derived from the wave equation and its boundary conditions. The formulation of the problem, within the formal scattering theory approach, is also given. The existence of a singularity in space-time is related explicitly to the presence of a nonzero absorption cross section. Another derivation of the unitarity theorem for our problem is given by operator methods. The reciprocity relation is also proved; that is, for the scattering of waves the black hole is a reciprocal system. Finally, the elastic scattering problem is considered, and the elastic scattering amplitude is calculated for high frequencies and small scattering angles.
94 citations
TL;DR: In this paper, relative differential electron-impact cross sections have been measured for elastic scattering for excitation of the 3d104p 2 P 1/2,3/2 and 3d94s2 2D5/2 states of Cu at 6, 10, 20, 60 and 100 eV in the 0 degrees to 140 degrees angular range.
Abstract: Relative differential electron-impact cross sections have been measured for elastic scattering for excitation of the 3d104p 2 P1/2,3/2, 3d94s2 2D5/2 and 3d94s2 2D3/2 states of Cu at 6, 10, 20, 60 and 100 eV in the 0 degrees to 140 degrees angular range. The relative values were normalised to the absolute scale by utilising He as a secondary standard for determining the correct energy dependence and by accepting the value of the calculated elastic differential cross section at 100 eV, 40 degrees as 1.28*10-16 cm2 sr-1. Integral and momentum-transfer cross sections have been obtained by extrapolation to 180 degress. The cross section for the excitation of the 2P state is large compared to that for elastic scattering, and population inversion in this state with respect to the 2D state is readily achieved by electron impact. None of the theoretical predictions utilising classical, Born or static-exchange approximations agree with the experimental results at low impact energies.
90 citations
Book•
30 Jun 1977
TL;DR: In this paper, the Coupling of Angular Momenta and Coulomb Potential were used to scatter one-electron atoms. But they did not consider the effect of one-energy effective range theory.
Abstract: 1. Introduction.- 2. Scattering by a Short-Range Potential.- 3. Scattering by a Coulomb Potential.- 4. Scattering by a Spin-Orbit Potential.- 5. Scattering by One-Electron Atoms.- 6. Low-Energy Effective-Range Theory.- 7. Bound States and Resonances.- 8. Variational Methods and Bound Principles.- 9. Integral Equation Methods and the Born Approximation.- 10. Semiclassical and Eikonal Methods.- Appendix. The Coupling of Angular Momenta.- References.
87 citations
TL;DR: In this article, a coupled channel theory was developed explicitly for the problem of pion scattering and absorption by a deuteron, and the equations were presented in terms of the integral equations of three-body scattering theory.
TL;DR: In this paper, the identification of the partial wave parameter of the JzCCS approximation in molecular scattering theory is considered, and it is shown that if one chooses?=l′ (the final orbital angular momentum) rather than?=J (the total angular momentum), the full body-fixed expression for the scattering amplitude reduces directly to the simple formula used by McGuire and Kouri.
Abstract: The identification of the partial wave parameter ? of the JzCCS approximation in molecular scattering theory is considered, and it is shown that if one chooses ?=l′ (the final orbital angular momentum) rather than ?=J (the total angular momentum) the full body‐fixed expression for the scattering amplitude reduces directly to the simple formula used by McGuire and Kouri. Results are cited that show that ?=l′ is not only simple, but physically reasonable, and gives much better results than ?=J.
TL;DR: In this article, a covariant procedure has been developed for separation of the infrared-divergent part of the lowest-order bremsstrahlung cross section, and the contribution of this part to the electromagnetic correction to the point particle elastic scattering is calculated exactly for the experiments which measure the energy or the energy and angle of one of the final particle and which do not distinguish between the elastic reaction and bremslung.
TL;DR: In this paper, the interaction V between an incident electron and an atom may be usefully split into two parts, V1 and V2, in such a way that couplings which are readily amenable to perturbation theory are contained in V2 while V1 corresponds to the remaining couplings that cannot be so effectively handled perturbatively.
Abstract: It is proposed that the interaction V between an incident electron and an atom may be usefully split into two parts, V1 and V2, in such a way that couplings which are readily amenable to perturbation theory are contained in V2, while V1 corresponds to the remaining couplings which cannot be so effectively handled perturbatively. By making a distorted-wave Born series expansion in powers of V2 it is possible to calculate the scattering amplitude correct to any order in V2 while treating V1 non-perturbatively. Cross sections for the elastic scattering of electrons on helium and neon are calculated in the energy range 100 eV to 2 keV and compared with experiment.
TL;DR: The sharp step structure in the v=1 excitation function at the v = 2 threshold in e-HF scattering has been employed as a calibration mark in low-energy electron scattering experiments.
Abstract: The pronounced oscillations in the e-N2 cross section at 2 eV provide a convenient energy standard in low-energy electron scattering experiments. The positions of the first five peaks have been recalibrated with an accuracy of 12 meV. The sharp step structure in the v=1 excitation function at the v=2 threshold in e-HF scattering has been employed as a calibration mark. Results are given for 20 degrees , 60 degrees and 120 degrees scattering angles.
Journal Article•
TL;DR: In this paper, the authors compare two recently proposed ab initio optical model methods and obtain an improved absorption potential for the case of scattering of fast charged particles by heavy atoms by argon in the energy region 100 eV-1 keV.
Abstract: The authors compare two recently proposed ab initio optical model methods and obtain an improved absorption potential for the case of scattering of fast charged particles by heavy atoms. Detailed calculations are performed for elastic scattering of electrons and positrons by argon in the energy region 100 eV-1 keV. The differential cross sections for electron scattering are in excellent agreement with recent absolute measurements. Total cross sections for both electron and positron collisions are also discussed.
TL;DR: In this paper, the vibrational excitation of SF6 by electron impact has been studied in a crossed-beam experiment from threshold up to about 3 eV and the energy loss spectra are characterized by very strong vibrational energy-loss spectra compared to elastic scattering.
Abstract: Vibrational excitation of SF6 by electron impact has been studied in a crossed-beam experiment from threshold up to about 3 eV. The energy-loss spectra are characterized by very strong vibrational excitation compared to elastic scattering. At 1 eV the integrated total vibrational excitation cross section gives an absolute value of about 10-15 cm2 which is 1.5 times the elastic cross section. The inelastic processes are dominated by excitation of the nu 1 and nu 3 modes. The differential cross section of the IR active nu 3 mode shows a very steep angular dependence, exceeding the elastic scattering at 10 degrees in the 1 eV region by a factor of more than three.
TL;DR: In this article, the eikonal Born series (EBS) method is used to analyse the elastic scattering of fast electrons and positrons by atomic hydrogen and helium, and the dependence of these terms as a function of the (large) incident wavenumber k and the magnitude Delta of the momentum transfer is discussed.
Abstract: The eikonal Born series (EBS) method is used to analyse the elastic scattering of fast electrons and positrons by atomic hydrogen and helium The properties of the terms of the Born and Glauber series are discussed, and in particular the dependence of these terms as a function of the (large) incident wavenumber k and the magnitude Delta of the momentum transfer A more precise EBS treatment of small-angle scattering is presented by improving the calculation of the second Born term in this angular region The EBS results agree very well with the recent absolute measurements of elastic differential cross sections, both for electron-atomic-hydrogen and electron-helium collisions
TL;DR: In this paper, the elastic energy propagation in a three dimensional elastic medium, in which scatterers are distributed homogeneously and randomly, is studied from the point of view of the scattering theory.
Abstract: The elastic energy propagation in a three dimensional elastic medium, in which scatterers are distributed homogeneously and randomly, is studied from the point of view of the scattering theory. The isotropic scattering is assumed and the scattering process is considered up to the first order. It is assumed that not only the P-wave to P-wave scattering and the S-wave to S-wave scattering but also the S-wave to P-wave conversion scattering and the P-wave to S-wave conversion scattering take place. Green functions corresponding to these single isotropic scatterings are obtained and their properties are exhibited when the elastic energy is radiated spherically from a source. A space-time distribution of the energy density of the single scattered elastic waves is obtained. This model is applied to the short period body wave propagation of a small local earthquake near a hypocenter in the earth, when heterogeneities are interpreted as the scatterers. The temporal development of the seismic energy density, which is closely related to the seismogram, may be explained qualitatively.
TL;DR: In this article, the authors developed a theory of low energy electron loss spectroscopy of vibrational modes of molecules adsorbed on metal surfaces, assuming strong elastic scattering on the metal surface, and direct electron-molecule interaction via the electric dipole field associated with the molecular vibration.
Abstract: We develop a theory of low energy electron loss spectroscopy of vibrational modes of molecules adsorbed on metal surfaces. Differential and total cross sections are calculated in the Distorted Wave Born Approximation, assuming i) strong elastic scattering on the metal surface, ii) direct electron-molecule interaction via the electric dipole field associated with the molecular vibration. The angular distributions are calculated and discussed for molecules adsorbed at various distances above the metal surface and for several electron energies and impact angles. The influence of electronic screening of dipolar oscillations is discussed and the consequences of the classical induced “image” dipoles are explored. It is shown that the “metal surface selection rule” known in IR spectroscopy is only approximately valid in electron scattering. Finally, we give numerical estimates of the inelastic scattering cross sections for the stretching vibrations of CO molecule adsorbed on transition metal surfaces, in reasonable agreement with experiments.
TL;DR: Theoretical differential cross sections for 7 Li+ 24 Mg inelastic scattering have been calculated in the DWA using a double folding model as discussed by the authors, where the trajectories of the target and the projectile are matched to electron scattering data and the nucleon-nucleon interaction is chosen to reproduce the real part of the optical potential at the distance D 1 2 where there is 50 % transmission in the elastic channel.
TL;DR: In this paper, the dispersion relation for forward scattering of electrons by atomic hydrogen has been studied and the discrepancy function Delta (E) has been evaluated in terms of the nonanalyticity of the exchange part of the scattering amplitude for negative energies.
Abstract: Numerical studies of the dispersion relation for forward scattering are reported for electrons scattered by atomic hydrogen. As has previously been shown for electron-helium scattering, the relation of Gerjuoy et al. (1960, 1972) has to be modified. The extra term to be included, the so-called discrepancy function Delta (E), is related to the non-analyticity of the exchange part of the scattering amplitude for negative energies. This function, which corresponds to an integral over the left-hand cut discontinuity, is evaluated.
TL;DR: In this article, three parameter Fermi distributions were used for both protons and neutrons in the Saclay 1 GeV proton scattering data for the Ca and Ni isotopes.
TL;DR: In this article, the contributions of couplings with the available inelastic (p, p′) and pick-up channels to the elastic scattering of 30 MeV protons from 40 Ca, 48 Ca and 208 Pb were studied.
TL;DR: In this paper, the authors considered the low-frequency limit of cross sections for massless scalar, electromagnetic, and gravitational waves scattering on a Schwarzschild black hole and found explicit results for the scattering amplitudes.
Abstract: We consider the low-frequency limit of cross sections for massless scalar, electromagnetic, and gravitational waves scattering on a Schwarzschild black hole. Explicit results are found for the scattering amplitudes, which differ from the Born approximation results.
TL;DR: In this paper, the elastic scattering of high-energy protons from zero-spin nuclei is considered within the framework of Glauber theory, and the sensitivity of the cross sections to the nuclear structure and to the proton-nucleon amplitude is studied.