EGAS41 - Swansea University

41 st EGAS CP 43 Gdańsk 2009
Above threshold two photon transition in H-like ions
S. Zapryagaev 1,∗ , A. Karpushin 1
1 Voronezh State University , Universty pl. 1, Voronezh, Russia 394006
∗ Corresponding author: zsa@main.vsu.ru
Exact calculation of laser-induced processes with H-like ions have attracted considerable
attention over the last decades. These research has additional interest due to highly
precision spectroscopic measurements of fundamental constants with the bound system
experiments. Such investigations are sensitive enough to relativistic, radiative, retardation
and QED – effects. On this reason exact fully relativistic calculations of the two photon
transition amplitudes in hydrogen-like ions have some interest last years [1,2]. Among
the different kinds of the two photon transitions like Raman and Rayleigh scattering
particular interest play the two photon transitions when the energy of photon ¯hω is above
threshold of the one photon ionization I for Dirac state |njm>.
At present report the polarizability of 1s, 2s, 2p j Dirac states of H-like ions with
nuclear charch Z = 1..130 and photon energy from I to 10I were calculated using the
Coulomb Green function G(E) method [3] to sum intermediate states. The total matrix
element to calculate polarizability may be presented in the form”
= α s(ω)+α v (ω)mµ+α t (ω)(3µ 2 −2)[3m 2 −j(j +1)], (1)
where α s , α v and α t are scalar, vector and tensor parts of polarizability accordingly. All
this coefficients α n are complex for energy photon above the one photon ionization.
The exact numerical results of calculation are presented both in the exact table data
and in the following convenient analytical form:
α n = α ner
n
[
1 + cn (αZ) 2] . (2)
Here n ∈ s, v, t, and αs
ner and αt
ner are well known nonrelativistic expressions ≈ Z 4 , but
is the main part of α V ≈ (αZ) 2 , α – is a fine structure constant. For example, in
α ner
v
α s case c s = −0.84626 and αs
ner has known real and imagine part dependent from photon
energy. In general the accuracy of approximated results (2) are ≈ 10 −4 for Z = 1..100,
and ¯hω from I to 10I.
On the base of optical theorem the photoionization and photorecombination crosssection
are calculated in numerical and approximated form like this one
σ phot = 4π c ω Im α [
s = σphot
ner 1 − bnj (αZ) 2] . (3)
Here σ ner
phot is a nonrelativistic photoionization cross-section, and b nj depends from the
Dirac state |njm>. Retardation effects are discussed and calculated too.
References
[1] V. Yakhontov, Phys. Rev. Lett. 91, 093001 (2003)
[2] H.M. Techou Nguano, Kwato Njock, J. Phys. B: At. Mol. Opt. Phys. 40, 807 (2007)
[3] S. Zapryagaev, N. Manakov, V. Palchikov Theory of Multiply Charged Ions with One
and Two Electrons (Energoatomizdat, Moscow 1985)
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