The value of is dependent on the effective level, and hence upon the excitation potential. Without the introduction of unjustified assumptions, more than one critical potential cannot be deduced from observations of intensity maximum. The excitation potential corresponding to a line could be roughly inferred from the observed maximum, by observing the shift of predicted maximum produced by the level effect (discussed in Chapter IX) if the ionization potential were known. There are, however, no data as yet that could be used in drawing inferences of this kind.

DURATION OF ATOMIC STATES

The successful application of theory to the astrophysical determination of the life of an atom requires the fulfilment of special conditions. The requirements of the idea developed by Milne[434] demand that the atom shall exist in appreciable quantities in only two states simultaneously. This condition is fulfilled by the ionized atoms of the alkaline earth elements, and it is with calcium that the estimates here discussed are concerned.

The investigation relates to the calcium present in the high-level chromosphere, where, owing to remoteness from the photosphere, thermal ionization is negligible. Photoelectric ionization may be operative in removing the first electron from the calcium atom, but the sun is too deficient in light of wave-length 1040 for second stage photoelectric ionization to be appreciable. The calcium present in the high-level chromosphere is probably largely in the once ionized condition, since an atom once ionized is likely to remain so for a long time, owing to the scarcity of free electrons in the tenuous outer regions of the sun. The present investigation neglects altogether the neutral and doubly ionized calcium atoms, and furthermore assumes that the transfers corresponding to the and lines of the series are the only ones that occur in appreciable quantities. The latter assumption is apparently not accurately fulfilled, as the lines of Ca+ have recently been detected in the high level chromosphere.[435]

In the simple case of the Ca+ atom (neglecting the small number of atoms that are giving rise to the lines) only two states of the atom are possible: the normal state, called by Milne the state, and the excited, or state. A given atom exists alternately in these two states. If be the average time spent in the state, and the average time spent in the state, the average time spent by an atom in traversing its possible cycle of changes is . Now is connected with the probability of an emission, and with the probability of an absorption. Clearly depends at least partly upon the energy supply, but is an atomic constant measuring the readiness with which the atom recovers its normal state after an absorption. It is, in fact, the “average life” evaluated from Milne’s equations. The ratio , expressing the relative tendencies of Ca+ atoms to emit and to absorb the and lines, is the residual intensity at their centers, with respect to the adjacent continuous background.

Einstein’s theory of radiation[436] is used in evaluating from the relation where is the ratio .

From ordinary quantum principles, and both and may be derived by eliminating between the two equations.

The only measured quantity in the formula is , and from the fact that is the “residual intensity” within an absorption line, we know that it must lie between 0 and 1. Hence a maximum value of may be derived for . On the insertion of the data given by Schwarzschild[437] for the residual intensity of the and lines, 2.6 magnitudes fainter than the continuous background, and corresponding to a value of equal to 0.11, the deduced value of is . The agreement of this value with those obtained in the laboratory for the atoms of hydrogen and mercury has been commented upon in a previous chapter.[438]

FOOTNOTES:

Notes in this chapter

Note 1 · Milne, M. N. R. A. S., 84, 354, 1924.Note 2 · Curtis and Burns, unpub.Note 3 · Phys. Zeit., 18, 121, 1914.Note 4 · Sitz. d. Preuss. Ac., 47, 1198, 1914.Note 5 · Chapter I, p. 21.