SPINNING ELECTRONS
221
XVI. 2]
The result obtained has great physical interest for it shows that
the assumptions of Uhlenbeck and Goudsmit really lead to the
correct doublet separation and at the same time to an explanation
of the anomalous Zeeman effect, when the problem is treated
by the new quantum mechanics. Thus the theory of the spinning
electron connects the anomalous Zeeman effect with the optical
and relativity doublets, and accounts for them as manifestations
of the magnetic properties of the electron. It must be supposed
that the axis of the electron precesses about a magnetic field
with an angular velocity differing from that of the Larmor
rotation. In fact an angular velocity (e/m 0 c) H, twice the Larmor
precession, must be assumed. Starting from this idea, values
of the Land6 factor, g, can be obtained differing from unity.
The procedure may be outlined as follows : Assuming that the
electron has the above-mentioned precession about the magnetic
field in a system of axes in which its centre is instantaneously at
rest, the secular rate of change of direction of its axis when it
revolves in an orbit can be found. “ Assuming that there is
some total angular momentum which is secularly conserved,
that which the electron itself adds to that of the orbit having
magnitude h/Agcc, the secular motion of the system can be found.
An approximate formula for the doublet and Zeeman effect
separations follows. The new quantum mechanics of Heisenberg
transforms this into a formula which fits the observed doublet
separations and Zeeman effect exactly, as far as first order terms
in the relativity correlation are sufficient.”
(4) Paschen-Back Effect.—The gradual transformation of the
multiplet structure as the magnetic field increases, known as
the Paschen-Back effect (p. 211), can be explained by supposing
that the influence of the field on the precession of the spin axis
becomes comparable with the effect due to the orbital motion in
the atom.
(5) Statistical Weight.—Another paradox which has been
resolved by means of this spinning electron is that in connection
with the statistical weight of a term. By this we mean the total
number of states which must be associated with a particular
spectral term. The weight to be assigned to the core is R, where
R denotes the maximum multiplicity. If the electron be a
point charge the total number of states of total quantum number
n must be asymptotically equal to n 2 for large values of n, and
the total number of states of core and orbital electron must be
R n 2 . Actually it is found to be 2R W 2 for all values of n in all
cases. The only way out of this difficulty is to suppose that the
electron has a structure.
(6) Atomic Models.—The capabilites of the spinning electron
in the construction of models of atoms and also of molecules