(Received April 3, 1949)
Behaviour of elementary particles in the cosmic-ray in moderate high energy region can be infered by the analysis of cosmic-ray phenomena underground, but few such attempts have ever been made and all of them have failed in giving a satisfactory understanding of the problem. Several years ago one of us (S.T.) tried without success to explain the remarkable bend of the intensity-depth curve on the basis of our knowledge at that time: on the assumption that this bend is caused by the energy loss of the cosmic-ray particles due to radiation and pair creation. Now later developments of cosmic-ray physics, i.e. the discovery of two kinds of mesons, made it possible to remove this unsolved difficulty be explaining this bend as due to the pi-mu decay. Thus the existence of the bend is no longer a puzzling fact, but it provides an important clue to determine the life of pi-mesons. In this situation it seems to be of importance to get forth more comprehensive analysis of the underground phenomena in order to certify the hypothesis about the model of mesons as well as about their interactions with matter.
We shall henceforth discuss how far one can account for the phenomena on the basis of our current picture without introducing extra hypothetical processes. According to our picture primary protons or heavy nuclei produce pi-mesons on colliding with air nuclei; the produced pi-mesons disintegrate into mu-mesons on falling down through the atmosphere entirely or partly according as the agent pi-meson has lower or higher energy. Thus at the ground surface there are pi- and mu-mesons mixed, but pi-mesons as well as nucleons can not penetrate deep into underground because of their strong interaction with matter nuclei. Electronic components falling on the ground surface are so highly absorbable that they are, of course, negligible constituents of the deep rays. Only component surviving down to the great depth is mu-mesons including their secondary products, which are in equilibrium with the mu-mesons. The main constituents of these secondary particles are electrons and photons produced by electromagnetic interactions of the mu-mesons. Besides these particles weakly interacting particles such as neutrini amount more and more with increasing depth, but their effects may be too small to be detectable in the depth under consideration. Therefore we may assume that only mu-mesons and their electromagnetic interactions play a róle in the phenomena underground.
Electromagnetic interactions of charged particles in high energy region are classified into the following three: collision with atomic electrons or ionization, radiation by accerelation in nuclear Coulomb field and creation of electron-positron pair in nuclear Coulomb field. The first and the second processes depend strongly on the spin and the magnetic moment of the particle in the relativistic region, but the third process, the pair creation is almost independent on the spin and the magnetic moment. The frequency of pursts at sea level as well as the fact that the decay electron of mu-meson has a continuous energy spectrum seems to show that this will have spin 1/2 and no intrinsic magnetic moment, though spin 0 may not be definitively ruled out. The possibility of soin 1 should be excluded because this would result in a much larger burst frequency; but this does affect the result considerably as far as the energy loss is concerned. The energy loss is mainly due to ionization as has been hitherto considered by many authors, but it is found that in deepest region one must take into accout the energy loss caused by the emission of bremsstrahlung and the creation of pair. We shall first estimate the magnitude of these three effects (§2), and then go over to the calculation of the range of the mu-meson as function of its energy (§3). We calculate, on the other hand, the energy spectrum of mu-mesons at sea level according to our picture: the mu-mesons are decay products of pi-mesons which are produced in the atmosphere by the primary particles, presumably by protons or eventually by some heavier nuclei (§4). If we thus find the range-energy relation of mu-mesons and their spectrum at sea level, we obtain the intensity- depth curve which can be compared with experiments (§5). In deriving the spectrum of mu-mesons we first neglect the absorption of pi-mesons in the atmosphere because we know at present only very little about how pi-mesons traverse the atmosphere. It is certain that this absorption is not negligible so that we next discuss to what extent this absorption affects the result (§6).
URL : http://ptp.ipap.jp/link?PTP/4/287/
DOI : 10.1143/PTP.4.287