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Extra info for Computation of atomic processes : a handbook for the ATOM programs
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.