The nature of statistical fluctuations with applications to cosmic rays

I. The square of the mean deviation D of the combined effect of several random processes releasing an average of x, y, z ... particles per unit time and producing a, b, c ... ion pairs, respectively, per particle, is D2=a2x+b2y+c2z+..., regardless of whether the separate effects are added or subtracted by the experimental arrangement. For tube-counters, point-counters, scintillation screens and particle counting chambers, a=b=c=1; for ionization chambers a, b, c ... are unequal. II. From the standpoint of statistical fluctuations, the use of two identical instruments in a differential circuit is inferior to the use of a single instrument. III. The natural observational limit for the measurement of x particles against a background of y particles is x=0.67(y)1/2. IV. The statistical fluctuations in the ionization produced by cosmic rays in a spherical ionization chamber are treated rigorously and the fluctuations due to heterogeneity of range and to showers are derived. V. Application to existing data shows that the showers observed in cloud-chamber photographs of the cosmic radiation are also present in the ionization chamber in about the same frequency and multiplicity as indicated by the cloud-chamber results. The tube-counter investigations of the cosmic-ray flux are also in agreement with the deductions from the statistical fluctuations in the ionization chamber. An upper limit of 70±10 ion pairs per cm in air at 1 atmosphere is set for the total ionization along the path of an individual cosmic-ray secondary. The size and the relative frequency of occurrence of showers is appreciably greater at 14,700 feet elevation than at sea level. These showers are quite distinct from the ionization bursts or Stösse observed by Hoffmann, Steinke and others

Reflection of high velocity electrons from solid surfaces

Bothe(1) has derived an expression for the angular distribution of electrons which are transmitted by matter and which have penetrated sufficient thickness to become completely diffused, and finds fair agreement with experimental work done with β-particles. It becomes of interest(2) to know the angular distribution of electrons emitted backwards from solid surfaces, since it is possible that the two distributions are similar. This question, together with the determination of absolute values of reflection, was studied during an investigation on scattering of high velocity electrons by thin foils

Further Studies on the Origin of Cosmic Rays Helium Annihilation Rays and the Cause of Their Variability with Time

We find definite evidence that a new band of rays which we interpret as helium annihilation rays does come in vertically at about the predicted latitude. We present a discussion of the possible composite character of the so-called silicon annihilation band and of the so-called oxygen annihilation band. We then bring forward an explanation of the cause of our large and already reported variability in the cosmic-ray intensities found in high altitude electroscope flights at Bismarck, Omaha, and Oklahoma City. We also make a new and more accurate determination of the value of the field sensitive and the non-field sensitive components of the incoming cosmic rays

A hypothesis as to the origin of cosmic rays and its experimental testing in India and elsewhere

The hypothesis here adopted as to the mode of origin of the cosmic rays makes possible the prediction of five definite cosmic-ray bands, each of which should reach the earth in a particular latitude, and of four plateaus of unchanging cosmic-ray intensity, these plateaus being delimited by the latitudes of entrance of the successive bands. These bands will be designated as (1) a silicon band of energy 13.2 Bev, (2) an oxygen-nitrogen band of mean energy 7.1 Bev, (3) a carbon band of energy 5.6 Bev, and (4) a helium band of energy 1.9 Bev. The experimental evidence that has been so far obtained in India and elsewhere for the existence of these five bands and four plateaus may be thus summarized: The evidence seems to be excellent for the existence of the silicon band and the joint nitrogen-oxygen band, and some indications have appeared for the existence of the carbon band and the helium band. Also all of these bands are found, roughly at least, in the predicted latitudes and of right order of intensities. The evidence also appears to be good for the existence of at least three of the four above-mentioned plateaus of constant cosmic-ray intensity

Further tests of the atom-annihilation hypothesis as to the origin of the cosmic rays

1. Tests in Mexico. The authors had predicted that since the hypothetical silicon-annihilation rays should have enough energy (13.2 Bev) to get vertically through the earth's magnetic field at the equator in Peru, though not in India, there should be found, both at sea level and at all altitudes in the Americas, when vertically incoming rays alone are under test, a very long plateau of uniform cosmic-ray intensities extending north from Mollendo, Peru to about the latitude of Victoria, Mexico (mag. lat. 32.8°). There the strong band due to oxygen annihilation rays (7.5 Bev) should first appear, to be followed in going still further north when the latitude of 40° N magnetic had been reached, by the full entrance of the nitrogen annihilation band (6.5 Bev). The experimental findings were in accord with these predictions. 2. Tests in the United States. In going from Pasadena (mag. lat. 40.7° to St. George, Utah, but 4.1° (280 miles) nearer to the N magnetic pole than Pasadena, the carbon-annihilation band (5.6 Bev) was expected to appear, to be followed by a flat plateau clear up to latitude 54° N magnetic, when helium annihilation rays (1.88 Bev) were expected to appear. A ballon flight at St. George (mag. lat. 44.8°) and another at Pocatello, Idaho (mag. lat. 51°) yielded preliminary results in harmony with these predictions. 3. Evidence that the act of atom-annihilation actually transforms the rest mass energy of an atom into an electron pair. The flat plateau between St. George and Pocatello (mag. lat. 51°) corresponding to the absence of abundant atoms of atomic weight between that of carbon and that of helium, and the definite appearance of a new band between Omaha (mag. lat. 51.3°) and Bismarck (mag. lat. 56°) constitute new and strong evidence for the transformability of the complete rest mass energy of an atom into an electron pair

A very high altitude survey of the effect of latitude upon cosmic-ray intensities - and an attempt at a general interpretation of cosmic-ray phenomena

The results of a very high altitude geographical survey extending in airplanes from Northern Canada to Peru, to altitudes of 22,000 feet, and, in three stratosphere flights made within the United States, to altitudes of 60,000 feet, are interpreted in the light of (1) the Epstein and the Lemaitre-Vallarta analysis of the effect of the earth's magnetic field, and (2) the Bowen-Millikan proof that the immediate agents responsible for the ionization of the atmosphere are electrons (+ and -), rather than protons or heavier nuclei. The main conclusions reached are: (1) that the resistance of the atmosphere to incoming electrons is 1 billion volts because of extranuclear encounters, 5 billion volts because of nuclear encounters; (2) that nuclear electron encounters produce only very soft secondaries, both photons and electrons; (3) that incoming photons produce most of the ionization found at sea-level or at sub-sea-level depths; (4) that nearly all of the non-field sensitive part of the ionization of the atmosphere above sea-level is due to photons of energy 200±170 million electron volts; (5) that in the equatorial belt a small part of the ionization is due to incoming secondary electrons of energies as high as 10 billion volts; (6) that these are responsible for the east-west effect and the longitude effect found in the equatorial belt; (7) that the field sensitive part of the ionization increases rapidly with increasing latitude in going from Panama to Spokane because incoming secondaries of energies decreasing from 8 billion to 2 billion volts get through the blocking effect of the field in rapidly increasing numbers with increasing latitude and add greatly in northern latitudes to the underlying ionization of the upper-air produced by the incoming photons; (8) that the only source now in sight of the observed cosmic-ray energies is matter-annihilation; (9) that the softest components of the cosmic rays have the energies corresponding to the partial annihilation or atom building hypothesis, while the hardest components have energies corresponding to the complete atom-annihilation hypothesis; (10) that these processes may conceivably be taking place (1) because of the very low temperatures that facilitate the clustering of hydrogen in interstellar space, or (2) because of such extreme temperature conditions of the opposite sort as are found in novae, as suggested by Zwicky

New evidence as to the nature of the incoming cosmic rays, their absorbability in the atmosphere, and the secondary character of the penetrating rays found in such abundance at sea level and below

The intensity of latitude-sensitive cosmic rays as would be measured by an electroscope placed just outside the atmosphere has been calculated. The ionization due to incoming electrons of 10 billion electron volts energy in this same electroscope placed 1/20th of an atmosphere beneath the top is found to be 13 times that outside. Electrons do not become penetrating by virtue of high energies even up to 17 billion electron volts. Neither protons nor other penetrating particles of any sort enter the atmosphere in significant numbers from outside the atmosphere. The observed penetrating particles and all other cosmic-ray effects, latitude-sensitive and non-latitude-sensitive, found in the lower atmosphere are practically all secondary effects—splashes from the absorption of electrons, or photons, or both taking place in the outer layers of the atmosphere

New light on the nature and origin of the incoming cosmic rays

Cosmic-ray electrons enter the atmosphere only in a definitely limited and relatively narrow energy range. The maximum of this energy distribution curve lies at about 6 billion e-volts. At 1 billion e-volts the curve has fallen to about a third of its maximum value, and on the other side of the maximum at some 17 billion e-volts the incoming energy also has about a third of its maximum value. The observed banded structure may possibly be partly due to the blocking effect of the sun's magnetic field on electrons trying to pass through it to the earth. The total cosmic-ray energy brought in by electrons of energy above 17 billion e-volts plus all that brought in by photons of all energies is about the same as the energy brought in by electrons alone of energies between 6 and 17 billion e-volts, and this energy is fully twice that brought in by all entering electrons of energies less than 6 billion e-volts. The smallness of the fraction of the total incoming energy that can be assigned to photons shows that the cosmic rays cannot ever have come through an appreciable amount of matter in comparison with an atmosphere before entering the solar system. The energies of the incoming rays correspond roughly to the annihilation energies of the atoms of the most abundant elements