THE OUTSIDE OF A STAR 
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by m — — 1, — 2, .... The lines are not equally spaced; the separation 
in the positive branch (in CN) diminishes continually, becomes zero, and 
finally negative so that a head of the band is formed where the series 
doubles back on itself. In other compounds it may be the negative branch 
that inverts. 
The state of the molecule is characterised by two or more quantum 
numbers, of which one, m, corresponds to angular momentum (equivalent 
to n' in §§ 42, 51). We shall call the remaining quantum number or 
numbers n. The band as a whole is due to a transition between two states 
an( i Tig, and the individual lines correspond to different values of m. 
In accordance with Bohr’s selection principle the only possible transitions 
are those in which m changes by + 1 or — 1; a change + 1 on emission 
gives the positive branch and — 1 gives the negative branch. The number 
ing of the lines will be best understood by reference to the converse 
absorption; absorption with change from m to m - 1 units of angular 
momentum gives the line numbered + m and with change from m to m + 1 
units gives the line — m. It should be understood that the main change 
of energy is determined by the transition from n x to n 2 which has nothing 
to do with angular momentum, and can be visualised as a difference in 
closeness of binding of the two atoms; but since by the selection principle 
this transition cannot occur without a consequential jump of m, there is 
a small additional gain or loss of energy which varies with the starting 
value of m and gives rise to the line structure of the band. It is found that 
the two branches have similar intensity curves; this shows that the two 
possible transitions Am — ± 1 are equally probable. 
It can probably be assumed that the molecular absorption coefficient 
is independent of m ; that is to say, the rotation of the molecule will not 
appreciably affect its chance of absorbing a quantum from the radiation 
around it. The whole band occupies only a small length of spectrum; and 
were it not that frequency is observable with extremely high accuracy we 
should scarcely have thought of distinguishing molecules with different 
velocities of rotation. In that case the absorption in the lines ± m will 
be simply proportional to the number of molecules in the state (m, n x ). 
In equilibrium this number depends on the temperature, since by 
Boltzmann’s formula it is proportional to exp (— x m ,nJRT). It would 
seem that measures of relative intensity in a band spectrum—especially 
the value of m for which the intensity is a maximum—are remarkably 
favourable for determining the temperature. Isolated atomic lines can 
only be compared from one star to another and their intensity depends 
on density as well as temperature. But in band spectra the evidence is 
obtained by differential comparisons of the successive lines in the band; 
density affects the absolute intensity (by dissociation of molecules) but 
not the relative intensity.