In two recent papers by Fröhlich, Heitler and Kemmer (1938) and by Kemmer (1938) it has been shown that the properties of the nuclear particles proton and neutron can qualitatively be understood on the assumption that a proton (neutron) is capable of emitting a
heavy positive
(
negative
)
electron
(denoted by Y
+
, Y
-
), transforming itself at the same time into a neutron (proton). The theory of the heavy electron—its wave equation and its interaction with the nuclear particles—was built up in close analogy to the theory of light and its interaction with an electron. We now apply this theory to the passage of a heavy electron through matter, and we shall find that it leads to a qualitative explanation of a number of cosmic-ray facts connected with the penetrating radiation. In applying the theory to collisions of
fast
heavy electrons with nuclei, there is, however, a serious difficulty from the start: From the discussion of the nuclear properties it has become evident that the theory in its present form can only claim validity for relative energies between the heavy electron and the nuclear particles not very much greater than the rest energy
μc
2
of the heavy electron, i. e. up to at most a few times 10
8
e-volts. For higher energies the theory leads to serious mathematical difficulties (diverging self-energy, diverging nuclear forces of higher order, etc.). For cosmic rays the interesting region is just the one for energies greater than 10
8
e-volts. It may be justifiable, in spite of these facts, to apply the theory to cosmic-ray heavy electrons, for two reasons: In the first place it is to be expected that the processes derived from the theory for energies of the order
μc
2
will exist also at higher energies and will preserve a number of their qualitative features. In the second place the theoretical cross-section obtained for these processes at energies of the order 10
8
e-volts will at least be right in the order of magnitude. On the other hand, we must not attach any significance to the way in which the cross-sections are found to depend on energy.
Schwinger–Dyson approach and its application to generate a light composite scalar
