By Anatoli V. Andreev
Atomic Spectroscopy provides a entire dialogue at the normal method of the idea of atomic spectra, according to using the Lagrangian canonical formalism. This procedure is built and utilized to provide 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 basic technique. The unique 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 uncomplicated analytical shape. The e-book is of curiosity to experts, graduate and postgraduate scholars, who're concerned into the experimental and theoretical examine within the box of contemporary atomic spectroscopy.
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Extra resources for Atomic Spectroscopy: Introduction to the Theory of Hyperfine Structure
29) is i R (r) = CIF (1 + 1 - y,21 + 2 , 2 ~ rt) where F (a, b, z ) is the confluent hypergeometric function, y = Z/(nae). Here aB is the Bohr radius 26 Schrodinger equation The asymptotic form of the confluent hypergeometric function F (a, b, z) at z = 0 is F ( a ,b, la1 -t 0) -t 1. 30) does not obey the boundary condition at r = 0. The asymptotic form of confluent hypergeometric function F (a, b, Z) at z -t oo is It is seen that the second term in this equation infinitely increases when r -t co.
E. 52) is the sum of two terms. One of them depends on the relative position coordinate, r, another term depends on the center-of-mass coordinate, R. 52). Hence, both angular momenta are the integrals of motion. e. 51). Hence without any additional analysis, we can easily write the equation for the energy spectrum of the hydrogenlike atom, when q, = - lei and qb = Z [el where me is the electron mass, and m, is the nucleus mass. 53b) are the plain waves $ (R) = CKexp ( i K R ) . To find the wave function $ (R) in the case of trapped atom, we need in the profile of the potential well of atomic trap.
The wave functions of the s states are maxima at r = 0 , the wave functions of states with 1 > 0 turn into zero at this point. We have mentioned above that the product R 2 ( r )r 2 , proportional to the probability for particle to be inside the spherical layer ( r ,r d r ) , is called by the charge density. The charge density distribution for the above states is shown in Fig. 2. It is seen that the maximum of charge density moves away from the center with the increase of the principle quantum number n.
Atomic Spectroscopy: Introduction to the Theory of Hyperfine Structure by Anatoli V. Andreev