https://doi.org/10.1140/epjd/e2004-00143-x
On the low-velocity limit of the Bohr stopping formula
1
Institute for Theoretical and Experimental Physics,
B. Cheremushkinskaya 25, 117218 Moscow, Russian Federation
2
Max-Planck-Institut für Quantenoptik,
Hans-Kopfermann-Str. 1, 85748 Garching, Germany
Corresponding author: a basko@itep.ru
Received:
2
July
2004
Published online:
26
October
2004
The low-velocity limit of the classical Bohr stopping model
is investigated by applying non-perturbative methods. For the
repulsive Coulomb interaction between a heavy projectile and a
harmonically bound electron, the stopping cross-section 
is
found to scale as 
in the limit of 
, where v is
the projectile velocity. This scaling is obtained by establishing a
corresponding scaling law for the energy transfer 
in a
single collision with an impact parameter b, namely, that
is a function of a scaled variable 
. For the
opposite case of the Coulomb attraction, direct numerical calculations
reveal that the energy transfer 
exhibits sharp resonances
along the b axes when v becomes sufficiently small. The latter
results in a characteristic non-regular behaviour of 
near
maximum. Suitable fitting formulae are proposed for the corresponding
stopping numbers 
.
PACS: 34.50.Bw – Energy loss and stopping power / 52.40.Mj – Particle beam interactions in plasmas
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005
