By Dr. Viatcheslav P. Shevelko (auth.)
Atoms and Their Spectroscopic homes has been designed as a reference on atomic constants and simple techniques regarding atoms. the themes contain strength degrees, Lamb shifts, electrical multipole polarizabilities, oscillator strengths, transition probabilites, and cost move pass sections. additionally the themes of ionization, photoionization, and excitation are mentioned. The publication additionally includes a great number of figures and tables, with abundant references. basic analytical formulation permit one to estimate the atomic features with no resorting to a computer.
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Additional resources for Atoms and Their Spectroscopic Properties
1(r)P,.. ,.. 1(r) ~ (2rr1 ( (n + 1)! )112 2 n 1+1(21 + 1)! (n - 1 - 1)! ] 112 ' r--+oo. 4-7). 10) (r -1 1 z ) =--, n2 ao (r- 2 ) 1 Z2 = n3 (1 + 1/2) a~ ' 1 (r- 3) = n3 1(1 + 1)(1 + 1/2) Z3 a~ ' where a0 is the Bohr radius. The radial wave function P11ir) of the continuous spectra (E > 0) has the form: Pk1(r) = (21C~r1 )! (2kr)1e-ikr F(i/k + 1+ 1, 21 + 2; 2ikr), k2 = (E/Ry) 2 . The functions Pk 1(r) are real. The constant Ck1 depends on the way of normalization. lf one normalizes on the momentum k, then JPkz(r)Pk· 1(r) dr = 00 0 no(k' - k) , 36 1 Atomic Structure and Spectra When k -t 0, one has Ck1 ~ 2k-l+ 112 , J2r 1 Pk1(r) ~ 2 1+ 1 (Sr), where Jn(x) is the Bessel function.
N _ 1 _ 1)! e F( -n • + 1 + 1,21 + 2, 2r/n) _ ( (n + 1)! ,l+112(2r/n) - (n - 1- 1)! n(21 + 1)! 4) where F(m, n; x) is the conftuent hypergeometric function, L::'(x) is the generalized Laguerre polynomial and Mm,ix) is the Whittaker function. 1(r)P,.. ,.. 1(r) ~ (2rr1 ( (n + 1)! )112 2 n 1+1(21 + 1)! (n - 1 - 1)! ] 112 ' r--+oo. 4-7). 10) (r -1 1 z ) =--, n2 ao (r- 2 ) 1 Z2 = n3 (1 + 1/2) a~ ' 1 (r- 3) = n3 1(1 + 1)(1 + 1/2) Z3 a~ ' where a0 is the Bohr radius. The radial wave function P11ir) of the continuous spectra (E > 0) has the form: Pk1(r) = (21C~r1 )!
8) odd term +-+ even term . 10) where j is the total angular momentum. There are no limitations on the principal quantum numbers n and n'. 6) are not fulfilled, the dipole transition is forbidden. However, radiation may be possible but with a probability of about 10 5 times smaller than the dipole one. Such transitions are called forbidden transitions. 8), transitions are possible only between terms of different parity. 12) and S-S transitions are ruled out. , transitions with change of spin AS = 1 (so-called intercombination transitions) are forbidden.
Atoms and Their Spectroscopic Properties by Dr. Viatcheslav P. Shevelko (auth.)