Abstract
My topic is a precision calculation of the spin and orbital motion of leptons in weak magnetic mirror traps of the sort used in precision g-2 experiments, done in collaboration with my student, Sara Granger.1,2 The calculation itself is rather complicated and technical but the methods used, the averaging methods of non-linear mechanics, are of general interest with a broad range of applications. Since these methods are not familiar to most physicists, and since one of the topics of this year’s Orbis Scientiae is “Nonlinearities in Natural Sciences”, a discussion of these methods should be appropriate.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sara Granger and G. W. Ford, Phys. Rev. Lett. 28, 1479 (l972).
Sara Granger and G. W. Ford, Phys. Rev. 13D, 1897 (1976).
N.N. Bogoliubov and Y. A. Mitropolsky, “Asymptotic Methods the Theory of Non-linear Oscillations” ( Gordon and Breach, New York, 1951 ).
K. M. Case, Prog. Theor. Phys. Suppl. 37, 1 (1966).
N. N. Bogoliubov and D. N. Zabarev, Ukrain. Mat. Zh. VII, 5, (1955).
N. Minorsky, “Nonlinear Oscillations” (D. van Nostrand Co., Princeton, N. J., 1962 ).
T. P. Coffey and G. W. Ford, J. Math. Phys. 10, 998 (1969).
For a description of the experiments see the accompanying talk by A. Rich.
There are two general ways to obtain this formula. The first is to treat the spin as a classical dynamical variable, and then to write down the most general equation of motion consistent with relativistic invariance. This was the method of L. H. Thomas, Phil. Mag. 3, 1 (1927), and J. Frenkel, Zeit. F. Physik 2h3 (1926). The second method is to use the Foldy-Wouthuysen transformation of the Dirac equation. This was first done by H. Mendlowitz and K. M. Case, Phys. Rev, 97, 33 (1955). The formula is sometimes called the Bargmann-Michel-Telegdi formula, since the publication (Phys. Rev. Lett. 2, 435 (1959))of an equivalent result obtained by those authors using the first method above. It would be better to call it the Thomas formula since it appears explicitly and in full generality in the paper of Thomas.
G. R. Henry and J. E. Silver, Phys. Rev. 180, 1262 (1969); M. Fierz and V. L. Telegdi in Quanta, ed. P. G. 0. Fruend (Chicago Univ. Press, Chicago 1970 ).
D. T. Wilkinson and H. R. Crane, Phys. Rev., 130, 852 (1962).
J. O. Wesley and A. Rich, Phys. Rev., A4, 1341 (l97l)
D. Newman, Private communication.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1978 Plenum Press, New York
About this chapter
Cite this chapter
Ford, G.W. (1978). Lepton Spin Motion in Weak Magnetic Mirror Traps. In: Perlmutter, A., Scott, L.F. (eds) New Frontiers in High-Energy Physics. Studies in the Natural Sciences, vol 14. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2865-0_5
Download citation
DOI: https://doi.org/10.1007/978-1-4613-2865-0_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-2867-4
Online ISBN: 978-1-4613-2865-0
eBook Packages: Springer Book Archive