Z^{3}_{1} contribution to the energy loss of heavy charged particles
Abstract
The Z^{3}_{1} contribution of distant collisions to the average energy loss of heavy charged particles is obtained by extending Bethe's quantummechanical calculation to the next highest order in Z_{1}. The secondorder Born approximation for the inelasticcollision cross section is simplified by using two major approximations. The infinite summation over terms arising from the coupling to intermediate states of the target atom is approximated with the aid of a parameter and the closure relation. This parameter is proportional to the average excitation energy of the intermediate states as described in the literature. The atomic form factors are simplified through a dipole expansion. Results are obtained in terms of an average excitation energy of the medium. Exemplary results for stopping in Al are presented for estimated values of the average excitation energy of the intermediate states. These results approach the classical and experimental values as the velocity of the penetrating particle increases, agreeing within 20% at β=0.3.
 Publication:

Physical Review A
 Pub Date:
 September 1979
 DOI:
 10.1103/PhysRevA.20.818
 Bibcode:
 1979PhRvA..20..818M
 Keywords:

 Atomic Weights;
 Born Approximation;
 Energy Dissipation;
 Heavy Ions;
 Particle Collisions;
 Stopping Power;
 Charged Particles;
 Inelastic Collisions;
 Quantum Mechanics;
 Scattering Cross Sections;
 Nuclear and HighEnergy Physics