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Manuscript Title: An implementation of atomic form factors.
Authors: C. Santamarina Rios, J.J. Saborido Silva
Program title: DIFOFA
Catalogue identifier: ADQY_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 151(2003)79
Programming language: Fortran.
Computer: SUN workstation.
Operating system: Solaris 2.6, Linux(RedHat/Debian).
RAM: 120K words
Keywords: Atomic form factors, Atomic physics, Scattering, Cross sections, Photon, Wave function.
Classification: 2.5, 2.7.

Nature of problem:
The scattering of an electron or a proton by a hydrogen-like atom or the collision of a hydrogen-like atom with a more complex atom are three body systems which can be solved perturbatively. The first order solution corresponds to a one photon exchange interaction and is known as the first Born approximation [1-3]. The sensibility of the hydrogen-like atom to a definite momentum of the exchanged photon is given by the Fourier transform of its charge density, known as the atomic form factory. The hydrogen-like form factors have been studied in the framework of Hydrogen-electron collisions and the recent experiments on exotic atoms [4,5] have updated the interest on this topic requiring the knowledge of the form factors of highly excited states.

Solution method:
We have considered an analytical expression of the hydrogen-like atomic form factors [6] and we have implemented it in a FORTRAN code optimizing the addition method and testing the final result.

Restrictions:
For a non-relativistic collision the Born approximation is safely valid if the kinetic energy of the projectile in the laboratory frame obeys [3]:
                                                                   
                      P**2                                               
                      -- >> -E,                                          
                      2M                                                 
 
where E is the bound energy of the hydrogen-like atom initial state. For the case of relativistic collisions it has been shown that multi-photon exchange can lead to significant corrections in the hydrogen-like atom collision [7]. However, the relativistic calculation also involves the atomic form factors - the useful expressions for the multi-photon exchange cross sections as a function of the atomic form factors can be found in [7] - and for many small and medium Z atoms in n <= 10 bound states the discrepancies are less than 10 per cent.

References:
[1] K. Omidvar, Ionization of Excited Atomic Hydrogen by Electron Collision, K. Omidvar, Phys. Rev., 140 (1965) A26.
[2] K. Omidvar, Excitation by Electron Collision of Excited Atomic Hydrogen, K. Omidvar, Phys. Rev., 140 (1965) A36.
[3] S. Mrowczynski, Interaction of Elementary Atoms with Matter, Phys. Rev., A33 (1986) 1549.
[4] B. Adeva et al., CERN/SPSLC 95-1 SPSLC/P 284 (1994).
[5] B. Adeva et al., CERN/SPSC 2000-032 SPSC/P284 Add.2 (2000)
[6] L.G. Afanasyev and A.V. Tarasov, Breakup of Relativistic pi+pi- Atoms in Matter, Yad. Fiz., 59 (1996) 2212; Phys. At. Nuc., 59 (1996) 2130.
[7] L.G. Afanasyev, A.V. Tarasov and O.O. Voskresenskaya, Total interaction cross sections of relativistic pi+pi- -atoms with ordinary atoms in the eikonal approach, J. Phys. G 25 (1999) B7.