Bound-free heavy-lepton pair production for photon and ion impact on atomic nuclei

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 57, Issue 5, 1998, Pages 3646-3651

  Belkacem, Ali ^a   Sørensen, Allan H ^b  

^a LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^b AARHUS UNIVERSITY   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17344366630     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.57.3646     Document Type: Article

References (22)

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10. We have used the same numerical method and computer code to obtain (Formula presented) as in K. Momberger and A. Belkacem, Lawrence Berkeley Laboratory Report No. LBL-38116, UC-401, 1996 (unpublished), which report therefore may be consulted for details.
11. For later reference note that the expression on the right-hand-side of Eq. (8) holds exactly for the Sauter cross section. By application of the analytical result for the Coulomb (Formula presented) wave in the limit of high energies and low (Formula presented), that is, by writing (Formula presented) in place of (Formula presented), the constant is seen to assume the value (Formula presented) in this limit.
12. We have not been able to track down the reason for this difference. Our numerical cross sections have been checked against the simple estimate (8), which in itself, as explained above, conforms to the Sauter cross section in the high-energy perturbative Coulomb case. Furthermore the relativistic momentum density which enters Eq. (8) has been checked against the corresponding nonrelativistic density, which was obtained independently from the relativistic result in any respect. For the case of (Formula presented), Mikhailov and Fomichev checked their numerical results for electron impact at an energy of 10 units against results based on their analytical formula (11), which they claim to be valid for photon impact on low-(Formula presented) targets. This formula contains the square of the nuclear form factor. However, at the same time it is based on an analytical approximation for the bound-state wave function. Both cannot appear, and in particular the square of the form factor should only be present if both initial and final states are plane waves, as this factor derives from the Fourier transform of the scattering potential.
13. There are some differences between the relative contributions from the various states. For instance, Mikhailov and Fomichev find a much smaller difference between the contributions from the two (Formula presented) states than we do.
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21. For the μ the situation is somewhat different. Here the nuclear capture rate from the (Formula presented) muonic ground state exceeds the natural decay rate for (Formula presented) above, roughly, 10 and reaches values one-and-a-half orders of magnitude higher than the latter at high (Formula presented);
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