PROGRAM SUMMARY
Title of program:
DIFOFA
Catalogue identifier:
ADQY
Ref. in CPC:
151(2003)79
Distribution format: tar gzip file
Operating system: Solaris 2.6, Linux (RedHat, Debian)
High speed store required:
120K words
Number of lines in distributed program, including test data, etc:
631
Keywords:
Atomic form factors, Atomic physics, Scattering, Cross sections,
Photon, Wave function.
Programming language used: Fortran
Computer:
SUN workstation .
Nature of physical 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.
Method of solution:
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.