No abstract
Relative intensities for a large number of multiplets have under each resultant spin, from singlets S=0, to octets been calculated from well-known theoretical formulas. 6*= 7/2 and include all probable values of L and /. It is These intensities have been tabulated for future reference shown how the same tables apply to jj-coupling, to in making analyses of spectra. The tables are grouped hyperfine structure, and to related multiplets.
Previous attempts to represent graphically the Schrodinger electron cloud for hydrogen-like atoms have been so successful that similar graphical representations have been looked for on the Dirac theory. With a single electron specified on Dirac's theory by a set of four wave functions instead of one, the probability density ^r^* = ^I^I*+^2^2*+^3^3*-[-^4^4* is treated by considering, as on the Schrodinger theory, the independent angular and radial factors separately. Tables and graphs are given for SE^* as a function of 0 alone. The graphs are compared with and shown to correspond closely to the space quantization of the classical electron orbits. Graphs representative of &&* as a function of r alone are given and compared with the electronnucleus distances of the corresponding electron orbits. The radial and angular factors are brought together by means of a mechanical device described previously, 1 which when photographed represents closely the electron-cloud ^^*. Photographs are given for the states l 2 5i /2 , 2 2 P 1/2 ,3/2 3 2 Z) 3 / 2 ,5/2 4 2 F 6/2 , 7/2, and 5 2 G 7/2 ,withm=> ±i, ±f, • • • ±j
It is well known that the solutions of the wave-equation for hydrogen-like atoms may be represented graphically by interpreting SM^* as a probability density. The probability density factors $ m $ m * -[® m ,i] 2 -[R n ,i] 2 -^y* are represented graphically and briefly discussed and compared with the electron orbits of four classical models. Graphs for s, p, d, f, g, and & electrons are given. An attempt to combine the probability density factors and form some graphical representation of W* has resulted in the construction of a mechanical device or model, see Fig. 5, which when photographed, gives very closely the desired result. Photographs for the magnetic states m=0, ±1, ±2, ±3, • • • are given for Is, 2p, 3d, 4/, 2s, 3p, U, 5/, 3s, Ap, and 5d electrons, see Fig. 6.
Wave-lengths and frequency separations of the fine-structure components of 173 spectral lines in singly ionized praseodymium are given. It appears, as may be seen from a reproduction of some of the fine-structure, Fig. 1, that each group of six finestructure lines has the same general appearance but varies in total intensity and width. In some lines given below the intensities and frequency separations within each group decrease toward the red, while all of the rest show similar degradation toward the violet.Theoretical interpretation. These fine structures may be accounted for by assigning an angular momentum, i = (5/2) (h/lir) to the nucleus of the praseodymium atom. This angular momentum space quantized with the total angular momentum of the outside electrons, J, yields for each energy level six components (provided /^5/2), the actual separations between which are given by the strength of coupling between i and /. Since a 6p electron in the atom of praseodymium is part of the time very close to the nucleus and part of the time outside of all of the other electrons, the strength of coupling for an electron configuration involving a singled electron should be very much greater than that for a 6s electron and still greater than that for a 5d or a 4f electron. According to the Bohr-Stoner scheme of the building up of the elements one should expect, and the fine-structure intervals confirm this, that practically all of the energy levels in Pr II have very large /values. S PECTRA arising from neutral and ionized praseodymium atoms offer one of the most interesting studies of hyperfine structure. In a preliminary report 1 on the hyperfine structure in Pr II it was indicated that a large number of lines were made up of six components. At present the finestructures of nearly two hundred lines have been measured, of which about one hundred have been completely resolved into six components. Every fine structure group that has been resolved not only shows six Components, but also reveals within each group a decrease in intensity and interval, either toward longer or toward shorter wave-lengths.The original spectrograms were taken in the fourth order of the 75 ft. grating spectrograph on Mt. Wilson. Although in the fourth order this grat-
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