EGAS41 - Swansea University

41 st EGAS CP 143 Gdańsk 2009
Cross sections of Penning ionization for Rydberg atoms
M. Zaharov 1 , N. Bezuglov 1 , A. Klucharev 1 , A. Ekers 2 , K. Miculis 2 , T. Amthor 3 ,
M. Weidemüller 3 , I. Beterov 4 , F. Fuso 5 , M. Allegrini 5
1 Faculty of Physics, St.Petersburg State University, 198904 St. Petersburg, Russia
2 Laser Centre, University of Latvia, LV-1002 Riga, Latvia
3 Physikalisches Institut, Universität Heidelberg, 69120 Heidelberg, Germany
4 Institute of Semiconductor Physics, 630090 Novosibirsk, Russia
5 Dipartimento di Fisica Enrico Fermi and CNISM, Università di Pisa, Italy
Collisions of two Rydberg atoms can lead to ionization via two mechanisms: associative
and Penning ionization. Associative ionization is a short-range process, which requires
close encounters enabling overlap of Rydberg atom wave functions. In contrast, Penning
ionization is a long-range process, which occurs while atoms are well separated in space
at antinuclear distances r ≫ n ∗2 (where n ∗ is the effective quantum number, atomic units
are used) due to the long-range dipole-dipole interaction.
We study the formation of atomic ions in an Auger-type scheme: one of the Rydberg
atoms undergoes a dipole transition from the initial state n 1 l 1 to a lower state n ′ l ′ , while
the other one is excited from the initial state n 2 l 2 to the ionization continuum. Such
ionization can take place if (n ′∗ ) −2 > (n ∗ 1) −2 + (n ∗ 2) −2 . Perturbation theory [1] allows one
to express the Penning ionization cross section σ PE for alkali atom pairs as
σ PE =
˜Γ
2.5
v 2.5 ; ˜Γ = ∑ n ′ cσ ph
πω n1 n ′ |D n1 n ′|2 , (1)
where σ ph (ω n1 n ′) is the photoionization cross section for the atom in the n 2l 2 state, and
D n1 n ′ is the reduced dipole matrix element for the n 1 → n ′ transition at frequency ω n1 n ′.
n1
50
40
30
20
10
v 2/5 PE
0
10 20 30 40 50
n2
60000
50000
40000
30000
20000
10000
Figure 1: The reduced cross section v 2.5 σ PE for two Na atoms with l 1 = l 2 = 0.
We have evaluated the Penning ionization cross sections using the semiclassical analytical
formulae for photoionization cross sections and dipole matrix elements derived in
[1] for Rb and Na atoms. The resulting σ PE is an oscillating function of the principal
quantum numbers n 1 , n 2 (see Fig. 1). The nature of the oscillation is discussed in [2].
Acknowledgment
Support by the Russian Foundation for Basic Research within the EINSTEIN CONSORTIUM/RFBR
bilateral project ”Nonlinear dynamic resonances at collective interactions of cold atoms” is acknowledged.
References
[1] N.N.Bezuglov, A.N. Klucharev, M. Allegrini, Opt. Spectrosc. 79, 680 (1995).
[2] T. Amthor, J. Denskat, C. Giese at al., Eur. Phys. J. D, (2009) in print.
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