# A method of computation for potential scattering at low and intermediate energies

TL;DR: In this article, a method for computing scattering amplitudes and total cross sections is proposed, which is no more difficult than a second Born computation yet it gives results surprisingly good at low and intermediate energies.

Abstract: A method for computing scattering amplitudes and total cross sections is suggested. This is no more difficult than a second Born computation yet it gives results surprisingly good at low and intermediate energies.

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TL;DR: In this paper, the authors present analytical and numerical results for the T matrix and cross sections (differential and total) for scattering in a strong low-frequency laser field, which explicitly shows departure from the sum rule and it is analyzed as function of the laser field intensity and polarization angle.

Abstract: We present analytical and numerical results for the T matrix and cross sections (differential and total) for scattering in a strong low-frequency laser field. Presented results, based on recently derived expressions for the off- and on-shell low-frequency T matrices are beyond the first Born approximation results of Daniele et al. (1986) for scattering on the Yukawa potential in a laser field. An analytical expression for the total cross section is obtained using the (1,1) Pade approximant to the off-shell low-frequency T matrix. This result explicitly shows departure from the sum rule and it is analysed as function of the laser field intensity and polarization angle. If the laser field is so strong that the laser field induced scattering particle impulse eA0 is comparable with the initial impulse pi this departure has a maximum. For an ultra-strong laser field (eA0>>pi) the total cross section is small in comparison with the field-free section, i.e. the influence of the scattering potential is weak. The results for different values of the screening radius are also presented and it is observed that the departure from the sum rule is larger for long-range potentials (when the interplay between the potential and the intense radiation field is important). The departure is strong for small values of the polarization angle ( Theta i<20 degrees ) and weak for 45 degrees < Theta i<135.

19 citations

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TL;DR: Positron-hydrogen collision cross sections have been calculated for intermediate and high energies as mentioned in this paper, and an expected broad peak is observed in the results for the total cross section in the intermediate energy range.

Abstract: Positron-hydrogen collision cross sections have been calculated for intermediate and high energies. Comparison with earlier theoretical papers has been made wherever possible. An expected broad peak is observed in the results for the total cross section in the intermediate energy range.

8 citations

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TL;DR: In this paper, the impulsive collinear collision of an atom and diatomic molecule, modelled as a harmonic oscillator, is expressed in the momentum space representation of quantum mechanics.

Abstract: The impulsive collinear collision of an atom and diatomic molecule, modelled as a harmonic oscillator, is expressed in the momentum space representation of quantum mechanics. We find an interesting connection between the quantum and the classical picture (assuming the oscillator to be quantized) and a faster convergence in the quantum mechanical numerical solution. In addition, it provides an analytic approximation that is valid for systems initially in the vibrational ground state, which is analogous to the Franck-Condon overlap integrals.

7 citations

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TL;DR: In this paper, the authors applied hyperspherical partial wave theory to the calculation of the triple differential cross sections for the ionization of hydrogen atoms by electron impact at low energies for various equal-energy-sharing kinematic conditions.

Abstract: Hyperspherical partial-wave theory has been applied here in a new way in the calculation of the triple differential cross sections for the ionization of hydrogen atoms by electron impact at low energies for various equal-energy-sharing kinematic conditions. The agreement of the cross section results with the recent absolute measurements of [J. Roeder, M. Baertschy, and I. Bray, Phys. Rev. A 45, 2951 (2002)] and with the latest theoretical results of the ECS and CCC calculations [J. Roeder, M. Baertschy, and I. Bray, Phys. Rev. A (to be published)] for different kinematic conditions at 17.6 eV is very encouraging. The other calculated results, for relatively higher energies, are also generally satisfactory, particularly for large {theta}{sub ab} geometries. In view of the present results, together with the fact that it is capable of describing unequal-energy-sharing kinematics [J. N. Das, J. Phys. B 35, 1165 (2002)], it may be said that the hyperspherical partial-wave theory is quite appropriate for the description of ionization events of electron-hydrogen-type systems. It is also clear that the present approach in the implementation of the hyperspherical partial-wave theory is very appropriate.

6 citations

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TL;DR: In this paper, an approximate solution of the Fredholm integral equation for the scattering amplitude, asymptotically correct up to the first inverse power of the incident particle energy, is obtained in terms of one parameter.

Abstract: An approximate solution of the Fredholm integral equation for the scattering amplitude, asymptotically correct up to the first inverse power of the incident particle energy, is obtained in terms of one parameter. The value of the parameter is determined in two different ways and the approximate solutions of the Fredholm integral equation are utilised to obtain total collisional cross sections, the real part of the forward scattering amplitudes and the differential cross sections for the elastic scattering of electrons and positrons by the helium atom and the hydrogen molecule in the intermediate energy range from 50-1000 eV. It is found that of the two procedures that one which uses self-consistent solution of the Fredholm integral equation gives better values of the cross sections when a comparison is made with the experimental data.

5 citations

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TL;DR: In this paper, a method which has previously been successful in calculating the phase shifts for the scattering of particles by a central potential is applied to the problem of calculating the scattering amplitude directly.

Abstract: For pt. I see abstr. A23284 of 1972. A method which has previously been successful in calculating the phase shifts for the scattering of particles by a central potential is applied to the problem of calculating the scattering amplitude directly. Unlike the work of Walters, there is no singularity to be avoided in the integral equation which is approximated by quadrature. The method has been applied to a variety of central potentials and excellent agreement has been obtained with the results obtained by standard phase shift methods. The limitation of the method is that knowledge of the off-shell second Born matrix elements of the potential is required.

19 citations

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TL;DR: In this paper, the Fredholm expansion of the determinant whose phase gives the elastic-scattering phase shift is "summed" by use of numerical quadrature, reducing the calculation of the phase shift to evaluation of a single finite-dimensional determinant.

Abstract: The Fredholm expansion of the determinant whose phase gives the elastic-scattering phase shift is "summed" by use of numerical quadrature, reducing the calculation of the phase shift to evaluation of a single finite-dimensional determinant The method is essentially exact and is applicable, without modification, to nonlocal potentials Results for the low-energy static and static-exchange scattering of electrons from hydrogen atoms are presented as a simple illustration of the method

15 citations

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TL;DR: In this paper, a method for obtaining exact scattering phase shifts using an integral equation formulation is presented, which is similar to recent work by Reinhardt and Szabo but differs in that in the integral equation used, no inherent singularities have to be avoided.

Abstract: A method is presented for obtaining exact scattering phase shifts using an integral equation formulation. It is similar to recent work by Reinhardt and Szabo but differs in that in the integral equation used, no inherent singularities have to be avoided. The method has been applied to both the exponential and screened coulomb potentials, and has proved to be complementary to the method of numerically integrating the radial equation-this Fredholm integral method converges more quickly for non-zero angular momentum and/or high impact energies. It is, however, applicable to all angular momenta and at all energies, including the zero-energy limit. The main drawback is that knowledge of the second born off-shell matrix elements for the potential is required.

13 citations