45 



329 



equal lo zero, independent of the values of the /'s, we nnisl expect llial there will 

 be no possibility for a transition between two stationary states for which 

 n'j — n" = 7,', .... n,' — == r". If the coeflicicnt in question is equal to zero, 

 independent of the values of the /'s, only for the displacement of the particles in 

 a certain given direction, we must expect that a transition for which n\ — /i" = r°, 

 .... n'f — = T° will give rise to a radiation polarised perpendicular to this direc- 

 tion. An important application of this consideration may be made to systems pos- 

 sessing an axis of symmetry, as for instance the systems discussed in ,§ 3 (and in 

 § 4). For these systems the motion of the electron may, as it is directly seen from 

 some simple general considerations given by Bohr*), be resolved in a number of 

 linear harmonic vibrations of frequencies ZyW, -f t.^<o.^ parallel to the axis of 

 symmetry, and of a number of circular harmonic rotations of frequencies riWi-\- 

 72^2 + 0^3 perpendicular to this axis. We must therefore expect that only such 

 transitions will be possible for which /j, remains unaltered, giving rise to an emission 

 of light polarised parallel to the axis, and such for which n., decreases or increases 

 by one unit, giving rise to an emission of light which is circularly polarised 

 perpendicular to the axis. Since for the systems under consideration will 

 represent the angular momentum of the electron round the axis of symmetry, we 

 see that during transitions of the first kind this angular momentum remains 

 unaltered, while for transitions of the second kind it decreases or increases by 2~-'* 

 While these considerations in many cases allow us to draw definite conclusions 

 as regards the polarisation with which the dilTerent lines of the spectrum of an 

 atomic system are emitted, we meet, however, with a very difficult problem if we 

 ask for a closer estimate of the intensity with which a spectral line, correspond- 

 ing to a possible transition between two stationary states characterised by values 

 for the ii's in (99) which are not large, is emitted. In fact, this intensity will in 

 the first place depend on the a-priori probability A'„ for the spontaneous occurrence 

 of the transition in question. Although, of course, we must claim that the proba- 

 bility of spontaneous transition between two given states depends on the mechani- 

 cal properties of the system and on the two sets of numl)ers n\, . . . iil and /i", . . . n" 

 characterising these states, we cannot expect to obtain an exact expression for this 

 probability which depends in a simple way on the amplitudes of the harmonic 

 vibrations of frequency {n[ — n")a)i-\- . . . (/i« — /J7)a>« in the motion in these states: 

 just as it is clearly impossible to express the frequency of the cmillcd radiation 



M loc. cit. Part I, p. 33. 



-' Compare in this connection Bohk (loc. cit. Part I, p. 34), who has pointed out that a considera- 

 tion of conservation of angular momentum, which taltes into account the amount of angular momentum 

 present in the electromagnetic radiation emitted during a transition, gives a convincing support of the 

 assumption that liie angular momentum of tiic system lound the a.\is cannot change liy more than /' 2,t 

 Compare also A. HuniNOWicz (Pliys Zeitschr. XIX. p. 441, p. 4C.t (1918)), who hy a similar consideration 

 of conservation of angular momentum has independently arrived at some of the conclusions drawn by 

 Bohr as regards the spectrum of atomic systems possessing an axis of symmetry. 



