Abstract
Energy loss of fast charged particles colliding with an oscillator is considered in the dipole approximation. In this approximation, the problem is solved exactly and the energy loss of the oscillator from the initial state |m〉 = |0〉 is found in the form of the sum of single integrals. It is shown that passing to the limit, the Bethe theory for an atom with small perturbations can be obtained, and in the case of strong fields, the correction to the Bethe theory, analogous to the Bloch correction, can be calculated; in addition, a classical limit coinciding with the Bohr formula is possible.
Similar content being viewed by others
References
J. F. J. Ziegler, J. Appl. Phys/Rev. Appl. Phys. 85, 1249 (1999).
F. Bloch, Ann. Phys. 16, 285 (1933).
J. Lindhard and A. Sorensen, Phys. Rev. A 53, 2443 (1996).
V. Khodyrev, J. Phys. B 33, 5045 (2000).
V. I. Matveev, D. N. Makarov, and E. S. Gusarevich, JETP Lett. 92, 281 (2010).
V. I. Matveev, D. N. Makarov, and E. S. Gusarevich, JETP 112, 756 (2011).
V. I. Matveev and D. N. Makarov, JETP Lett. 94, 1 (2011).
A. Schinner and P. Sigmund, Nucl. Instrum. Methods Phys. Res. B 164–165, 220 (2000).
P. Sigmund and U. Haagerup, Phys. Rev. A 34, 892 (1986).
W. H. Barkas, W. Birnbaum, and F. M. Smith, Phys. Rev. 101, 778 (1956).
H. M. Hennig and P. Sigmund, Phys. Rev. A 40, 101 (1989).
V. A. Khodyrev, Nucl. Instrum. Methods Phys. Res. B 115, 332 (1996).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Pergamon, New York, 1977).
A. I. Baz’, Ya. B. Zel’dovich, and A. M. Perelomov, Scattering, Reactions and Decay in Nonrelativistic Quantum Mechanics (Nauka, Moscow, 1971).
A. M. Dykhne and G. L. Yudin, Sov. Phys. Usp. 21, 549 (1978).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2: Special Functions (Gordon & Breach, New York, 1986).
Niels Bohr, Collected Works (North Holland, Amsterdam, 2008), Vol. 1.
P. Sigmund, Phys. Rev. A 54, 3113 (1996).
H. A. Bethe, Ann. Phys. (Leipzig) 5, 324 (1930).
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1: Elementary Functions (Gordon & Breach, New York, 1986).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Makarov, D.N. Energy loss of charged particles colliding with an oscillator. Tech. Phys. 60, 483–488 (2015). https://doi.org/10.1134/S1063784215040192
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063784215040192