By Savely G. Karshenboim (Editor), Valery B. Smirnov (Editor)

The chapters offer in-depth stories masking precision measurements, exact calculations, basic constants, frequency criteria, and assessments of basic idea. the newest growth in every one of those parts is usually defined for the professional. the themes chosen for this ebook are principally complementary to these of the sooner comparable quantity, LNP 570.

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**Extra resources for Precision Physics of Simple Atomic Systems**

**Example text**

Actually NR correction presents the diﬀerence between the theoretical value for the transition frequency and the frequency that corresponds to the maximum of the distorted Lorentz curve. The deduction of the transition frequency from the asymmetrical Lorentz line proﬁle becomes ambiguous and the improvement of its accuracy beyond the limit given by (30) is impossible. 6 Relativistic Coulomb Green Function In the relativistic theory of the hydrogen atom and especially in the highly charged hydrogen-like ions where relativistic eﬀects are important, the relativistic Coulomb Green function (RCGF) is widely exploited.

X Let us now return to (9). By the substitution r = 2√−2E the left-hand side of this equation can be reduced to the Whittaker equation d2 U (x) 1/4 − µ2 ν 1 + U (x) = 0 , + − 2 dx x x2 4 (16) Z where ν ≡ √−2E , µ = l + 12 . Equation (16) is solved on the interval 0 ≤ x ≤ ∞ and the boundary conditions reduce to the requirements that U (x) should be ﬁnite at x = 0 and should turn to zero at x = ∞. The linearly-independent solutions that satisfy these requirements are the Whittaker functions Mν,µ (x) and Wν,µ (x) correspondingly.

An important feature of the Coulomb mechanism is that the transition energy is shared by the recoiling particles (the x− p and the two hydrogen atoms) having comparable masses, therefore the Coulomb deexcitation can lead to signiﬁcant acceleration of exotic atoms during the cascade. The deceleration of the exotic atoms takes place in the elastic and Stark collisions. In most cases the exotic atoms are epithermal during the cascade, with the characteristic kinetic energy being much higher than the target temperature.