The £-ray spectra of N 13 , F 17 , Na 24 , Si 31 , P 32 , CI, A 41 and K 42 have been investigated by measuring the curvatures of the tracks due to the /3-rays in a cloud chamber traversed by a known magnetic field. By allowing the tracks to be formed in hydrogen the scattering of the tracks is so reduced that the distribution curves are felt completely to represent the true distributions for momenta greater than lOOOHp. It is found that the shapes of these curves are in very good accord with the Konopinski-Uhlenbeck modification of the Fermi theory for the first five elements mentioned above (two positron emitters and three electron emitters). The spectra of the last three
904LETTERS TO potentials enter explicitly in the density matrix, and lead to the existence of non-Maxwellian forces. With this definition of the dynamical operators, one has thus to abandon either Dirac's expression for the charge and current density or the validity of the conservation laws for energy and momentum. In particular one would not otherwise obtain consistent results, in computing on the one hand the induced charge density, and on the other the polarization energy, of the epd in an electrostatic field. The simplest way of obviating these difficulties is to modify the density matrix in a way which does not depend on the electromagnetic field strengths present: i.e., to subtract from the operator given by the Dirac theory of the electron the expressions for the state of the electron distribution in the absence of external fields, for which all negative states are full. This procedure leads directly to the theory of the positron as we have developed it. On this theory one finds a polarization of a vacuum by an electromagnetic field which is infinite, and which can only be rendered reasonably unambiguous by special conventions about the way in which the divergent expressions occurring are to be handled. 2 This theory is therefore not only unable in general to predict the reaction of the epd to its own field, but can make no unambiguous statements about the fields induced by the epd under the influence of a given external field.Nevertheless we believe that these difficulties in no way impair the limited validity of the theory of the positron, a validity which is limited to those questions which do not involve essentially the reaction of the electrons and positrons to their own radiation fields and thus does not extend to problems in which there are external fields whose frequency is of the order of the critical value mc z /e 2 . For at least insofar as the fields are themselves produced by electrons and positrons, the polarization of the epd manifests itself 3 in effects which are not unambiguously separable from the unknown effects of the radiation reaction of • the particles. An instructive illustration of this may be found in the question of the fluctuations of the charge density of the epd, which was brought to our attention by Dr. Bloch. If we consider, for instance, the case of an empty epd in no external field, for which the expectation value of the charge density vanishes everywhere, we readily find that the expectation value of the square of the charge within any volume is infinite, corresponding to the fact that there are infinite fluctuations in the charge density. If we now ask in what measure it is possible to observe these fluctuations, we see that, to detect them, we must have an observing system (e.g., galvanometer) which will react in accordance with the electron-theoretic laws to electromagnetic fields of arbitrarily high frequency. If we admit that our instruments will not respond to waves of The capture of a neutron followed by the ejection of an a-particle is now a well-known process in...
where T is the period. The value n n determines the coefficient of refraction n of electromagnetic waves in a ferromagnetic metal, while nk determines their coefficient of absorption 3 k: n=(
two elements did, but would lie on a line directly joining the points for the elements. The thermal conductivity of aluminum is definitely abnormal in its temperature variation, but the conductivities of all its usual alloys except those containing silicon are capable of close representation by a single curve at a given temperature.
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