APPENDICES

I. INDEX TO DEFINITIONS

AN attempt has been made to define specifically, at some point in the text, most of the technical terms that are associated with the theory of ionization. For convenience of reference, the most important of these terms are collected into the brief index which is given below. The references are to the pages on which the term is defined.

Atomic life[21], [110] Photosphere[35], [47]
Azimuthal quantum number[8], [204]Quantum number[8], [204]
Boundary temperature[27]Quantum relation[11]
Displacement Rule[13]Residual intensity[51]
Effective level[135]Reversing layer[47], [49]
Effective temperature[27]Rydberg constant[14], [155]
Excitation potential[15]Saturation[52], [135]
Fractional concentration[105]Series notation[55], [203]
Inner quantum number[204]Spectroscopic valency[10]
Ionization potential[15]Subordinate lines[12], [100]
Ionization temperature[30], [132]Temperature class[24], [112]
Marginal appearance[105], [135], [179]Total quantum number[8], [205]
Optical depth[27], [35]Ultimate lines[11], [111]
Partial electron pressure[10]Valency[10]
Partition function[107]Wings[50], [179]

II. SERIES RELATIONS IN LINE SPECTRA

A SYNOPSIS of the normal series relations in line spectra has been published by Russell and Saunders (Ap. J., 61, 39, 1925). A transcription of the passages containing definitions of spectroscopic quantities that are mentioned in the present volume is given below:

“Every spectral line is now believed to be emitted (or absorbed) in connection with the transition of an atom (or molecule) between two definite (quantized) states, of different energy-content—the frequency of the radiation being exactly proportional to the change of energy. The wave-number of the line may therefore be expressed as the difference of two spectroscopic terms which measure, in suitable units, the energies of the initial and final states. Combinations between these terms occur according to definite laws, which enable us to classify them into systems, each containing a number of series of terms, which are usually multiple—

“Any term

may be expressed in the form

where

is the Rydberg constant and

an integer. For homologous components of successive terms of the same series,

changes by unity, while the “residual”

is sometimes practically constant (Rydberg’s formula), or, more often, is expressible in the form

(Hicks’s formula), or

(Ritz’s formula). In many cases this approximation fails for the smaller values of

; and prediction becomes very uncertain, though a plot of the residuals usually gives a smooth curve....

“The principles of selection, which determine what combinations among these numerous terms give rise to observable lines, are very simply expressed in terms of two sets of quantum numbers.

“The azimuthal quantum number (

) is i for all terms of the s-series, 2 for those of the p-series, 3 for the d’s, 4 for the f’s, 5 for the g’s, 6 for the h’s, and so on.

“Combinations usually occur only between terms of adjacent series for which the values of

differ by a unit. A great many lines are, however, known for which the change of

is 0, and a few for which it is 2. In the simpler spectra, such lines are faint, except when produced under the influence of a strong magnetic field; but in the more complex spectra they are often numerous and strong.

“The inner quantum number (

) differs from one component of a multiple term to another, and also in the various series and systems, according to the following scheme.

SeriesSingletsDoubletsTripletsQuartetsQuintetsSextetsSeptets
1sj = 0112233
2p11,20,1,21,2,31,2,32,3,42,3,4
3d22,31,2,31,2,3,40,1,2,3,41,2,3,4,51,2,3,4,5
4f33,42,3,42,3,4,51,2,3,4,51,2,3,4,5,60,1,2,3,4,5,6
5g44,53,4,53,4,5,62,3,4,5,62,3,4,5,6,71,2,3,4,5,6,7

“Combinations occur only between terms for which

differs by 0 or ± 1. If, however,

in both cases, no radiation occurs. Lines corresponding to a change of

are found in strong magnetic fields, and a very few in their absence.

“The combination of two multiple terms gives rise, therefore, to a group of lines (which may number as many as eighteen). Such groups have been called multiplets by Catalan. Their discovery has afforded the key to the many-lined spectra....

“In such a group, those lines for which the changes in

and

, in passing from one term to the other, are of the same sign, are the strongest, and those in which they are of opposite sign the weakest. These intensity relations are of great assistance in picking out the multiplets.

“Combinations between terms of different systems (consistent with the foregoing rules) often occur. Such lines are usually, though not always, faint....

“The serial number

of the term (which is equivalent to the total-quantum number) plays quite a subordinate rôle, being of importance only when series formulae have to be calculated. An extensive analysis of a spectrum is possible without it, though determination of the limits of the series, and the ionization potential, demands its introduction.”