By Anatoli V. Andreev

** Atomic Spectroscopy **provides a accomplished dialogue at the common method of the idea of atomic spectra, according to using the Lagrangian canonical formalism. This method is constructed and utilized to give an explanation for the hydrogenic hyperfine constitution linked to the nucleus movement, its finite mass, and spin. The non-relativistic or relativistic, spin or spin-free particle approximations can be utilized as a kick off point of common method. The precise consciousness is paid to the idea of Lamb shift formation. The formulae for hydrogenic spectrum together with the account of Lamb shift are written in easy analytical shape. The publication is of curiosity to experts, graduate and postgraduate scholars, who're concerned into the experimental and theoretical study within the box of recent atomic spectroscopy.

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**Additional info for Atomic Spectroscopy: Introduction to the Theory of Hyperfine Structure**

**Sample text**

53b) we get 38 Schrodinger equation where ,B = M a / & , and n R is the non-negative integer. 57) is degenerated with respect to the combination of the quantum numbers n R and I . In this case, the combination is the sum of doubled radial quantum number and orbital quantum number, p = 2 n ~2 . + Interaction of trapped atom with electromagnetic field Let us consider the interaction of the trapped atom with the electromagnetic field. e. 60) is usually omitted, because its mean value over the period of optical oscillations does not depend on the coordinate.

60) is usually omitted, because its mean value over the period of optical oscillations does not depend on the coordinate. Therefore, for the hydrogen atom (when Z = I), we get H h2 2% = --A,. + U ( 7 ) + -A14 ~ T h2 (R)p - %AR C + U ( R ). 61) we can see that in hydrogen atom, in contrast to the hydrogenlike ions, the transitions between the trap levels without change in the intra-atomic electron state are prohibited. However it should be noted that the energy distance between the states of atom in the atomic trap hR is usually much smaller than the energy distance between the different electron states in atom hR << << En - Em.

61) we can see that in hydrogen atom, in contrast to the hydrogenlike ions, the transitions between the trap levels without change in the intra-atomic electron state are prohibited. However it should be noted that the energy distance between the states of atom in the atomic trap hR is usually much smaller than the energy distance between the different electron states in atom hR << << En - Em. Therefore, if the frequency of electromagnetic wave is close to the frequency of the intra-atomic electron transitions w, = = (En - Em) /h = w and at the same time R << w , then the probability of the above mentioned transitions is very low for ions too.