Berlin 2001 – wissenschaftliches Programm
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A: Atomphysik
A 20: Atoms in Fields
A 20.8: Vortrag
Freitag, 6. April 2001, 17:30–17:45, H1058
Relativistic precession of elliptic wave packets — •Piotr Rozmej1, Robert Arvieu2, Ilya Averbukh3, and Marcin Turek4 — 1Technical University, 65-246 Zielona Góra, Poland — 2Institut des Sciences Nucléaires, 38026 Grenoble-Cedex, France — 3Weizmann Institute of Science, 76100 Rehovot, Israel — 4University MCS, 20-031 Lublin, Poland
We present a theoretical description of the precession of the elliptic wave packet (EWP) built from eigenstates of the Dirac equation for the hydrogenic atom. In 1989 by Gay, Delande and Bommier [1] have constructed coherent elliptic wave packets (EWPs). The probability density for this state, composed from states with the same n but different l,m quantum numbers, is fairly localized on a Kepler orbit (classical ellipse) with given average value of angular momentum lav.
In non-relativistic theory such a state doesn’t move in
time as all partial waves gain a common phase factor related
to non-relativistic energy.
In relativistic theory the situation is different.
Phases of partial waves vary with l and the probability density
moves slowly. For relatively short time the relativistic
precession of the classical ellipse, where the probability
density was initially concentrated, is observed. The precession
period is given by
Tprec= (2πℏ)/(dE/dl)
l=lav =
TKep(2 lav2)/(Zα)2 =
TLS ,
where TKep is the classical period of the electron
in state n. This period is also the period
of spin-orbit motion TLS, discussed by us already for
relativistic circular wave packets [2].
1. J-C. Gay, D. Delande and A. Bommier, Phys. Rev. A 39,
6587 (1989).
2. R. Arvieu, P.Rozmej and M. Turek, Phys. Rev. A 62,
022514
(2000).