Abstract
1. In order to explain the fact that the scattering of high velocity α-particles by the lighter elements does not obey the Rutherford scattering law, it is necessary to assume that the inverse square law does not hold for the force between an α-particle and a nucleus when the distance between them becomes exceedingly small. There is evidence to show that the inverse square law does hold down to distances of about 10
-12
cm., but that, as the distance is further reduced, the repulsive force changes to an attractive one, and it has been assumed by Gamow and others that the potential energy of an α-particle in the field of a nucleus varies with the distance, as is shown in fig. 1 by the curve
t q p o
.The divergence from Coulomb’s law, which is represented by the curve
t q v u
, does not become marked until a distance
a
is reached, but, for distances less than
a
, the force changes sign. Sexl has used a simplified form of such a potential field to calculate the decay periods of radioactive substances, and, in the present paper, an account is given of a method by which the anomalous scattering of α-particles by helium can be explained by assuming a potential field of the above type. In order to obtain a form for which the calculation is not unreasonably difficult, the field was simplified to the curve
t q v w x
of fig. 1. This field is defined by the two parameters
a
and
d
, and it is shown how the values of these parameters may be determined from the experimental results; the actual values obtained for the mutual potential energy of two α-particles are shown to scale in fig. 8. It is of interest to note that Sexl assumed the depth
d
of the “hole” to be zero in the case of the heavy elements, whereas it appears in this discussion that the depth is quite large in the case of helium (fig. 8), and that it is essential for the explanation of the experimental results to have the parameter
d
at our disposal.
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