Chronicle

Conference on Theoretical Physics

On May 1–22 of this year, an All-Union Conference on Theoretical Physics, convened by the Ukrainian Physico-Technical Institute, was held in Kharkov. The conference was attended by theoreticians from Moscow, Leningrad, Kharkov, and other cities; in addition, there were many foreign scholars, among whom it is first of all necessary to mention Prof. Niels Bohr (Denmark). Besides the special sessions of the conference, at which a dozen and a half papers were read, two open sessions were also arranged. At the first of these the People’s Commissar of Education of the Ukrainian SSR, Comrade Zatonsky, spoke on the subject of science in the USSR and abroad, after which Prof. Bohr gave a brilliant popular lecture entitled “The Problem of Causality in Atomic Physics.”

In this note we shall give a very brief survey of the content of the work of the conference. The brevity of the survey is necessary because the Kharkov conference (in contrast, for example, to the Leningrad nuclear conference in September 1933, at which papers of a review character were read for the most part) was devoted chiefly to the discussion of theoretical work in the process of its preparation; many authors presented unfinished and not fully thought-out work, and the discussion was not always sufficient to clarify together all unclear questions. It is therefore possible that many things discussed at the conference will never be published: the conference had rather the character of a production meeting, not of a congress whose purpose is to display achievements. In our note we shall present only what may be of interest not only to theoreticians.

Williams (England) spoke about his experiments in which he studied the scattering of $\gamma$-rays of ThC″ by thin layers of lead (this was the only experimental paper at the theoretical conference). It is known that the $\gamma$-line of $2.65 \cdot 10^6$ electron-volts, emitted by ThC″, is absorbed in lead about 50% more strongly than in light elements. Of this 50%, about 20% is explained by photoelectric absorption; the remaining 30%, according to the hypothesis proposed by Blackett and Occhialini, is explained by the formation of “pairs.” This is in agreement with the calculations of Oppenheimer and Plesset, who, on the basis of Dirac’s theory, find that the formation of pairs at this frequency must correspond to an absorption in lead equal to 25% of the absorption according to the Klein–Nishina formula.

The theory asserts that the additional absorption must also lead to a corresponding scattering caused by the annihilation of the positrons formed. A quantum with energy $2.65 \cdot 10^6\ \mathrm{V}$ must produce one pair, and the positron formed must have a kinetic energy of about $10^6$ electron-volts. Williams had the clever idea of testing the Blackett–Occhialini hypothesis by studying rays scattered by very thin layers: if the thickness of the layer is less than the mean free path of the positron (i.e., than

then the distance that it travels before its annihilation), there will be no scattered rays at all. If the thickness of the layer increases further, then the scattering at first grows proportionally to the thickness of the layer and only then tends toward saturation. This is what was found, and, consequently, Williams’s experiments directly confirm the hypothesis explaining the additional absorption of γ-rays by the formation of pairs. But, along with the discovery and divergence from the theory: the thickness of the layer at which scattered radiation first appears turned out to be smaller than that predicted by the theory. Williams explains this by saying that positrons are formed not with an energy of \(10^6\) electron-volts, but with much slower ones; more precisely, that a γ-quantum with an energy of \(2.65\) electron-volts produces not one pair with high kinetic energy, but two much slower pairs. This also makes it possible to explain the fact, noted by Gray and Tarrant, that the scattered radiation amounts in intensity not to 40% of the primary radiation (which would be the case if one pair arose), but to almost twice as much.

During the discussion, the hypothesis proposed by Williams was subjected to criticism and was found to be unlikely. The hypothesis proposed by Frenkel (Leningrad), which consists in the fact that a γ-quantum with an energy of \(2.65 \cdot 10^6\) V produces only one slow pair and therefore is not absorbed completely—the remainder of the energy leaving in the form of a scattered quantum—met with the greatest success. Bohr pointed out that, although the probability of this effect decreases rapidly with the length of the wave, it increases still more rapidly with an increase of the atomic number, and that therefore it is quite probable that, for lead, it will turn out to be sufficiently large.

M. S. Plesset (USA) presented a new (unpublished) work by Dirac, in which Dirac manages to give a relativistically invariant character to his theory of the origin of charge density caused by a field, under the action of an external field on electrons in negative states. The charge density is obtained in the form of a sum of two terms, of which one contains all the infinities associated with the action of the electron on itself, while the other is regarded by Dirac as the true charge density, which in turn gives rise to the field. A shortcoming of this work by Dirac remains that the choice of a hypothesis leading to a finite true density is carried out in a not entirely unambiguous manner.

V. A. Fock (Leningrad) spoke about his work, in which he formulated Dirac’s hole theory in configuration space of electrons with positive energy and positrons. In doing this he arrives in a very simple way at the conclusion that there are infinite terms in the expression for the energy, and also points out the difficulties that arise when one attempts to give the theory of holes a relativistic formulation.

L. D. Landau (Kharkov) set forth a witty (unfortunately, not yet fully formulated) idea belonging to R. Peierls and consisting in the following: owing to the possibility of the creation of pairs, any two charged particles turn out to interact with one another not only through the electromagnetic field, but also through pairs. From Peierls’s point of view, the description of this additional interaction based on pairs is excessively cumbersome, and it is necessary to introduce a special new concept of a “pair field,” which would make it possible to describe such interaction in a more direct way. We have an analogous situation in quantum electrodynamics, in which the description by means of the quantized components of the electromagnetic quantities of the field is mathematically quite equivalent to the description by means of photons. But how cumbersome the theoretical formulations would be if, by means of photons, we described the case, for example, of a statistical field.

The concept of a “pair field,” proposed by Peierls, thus relates to the concept of pairs in the same way as, in quantum electrodynamics, the electromagnetic field relates to photons. Landau pointed out the mathematical properties of the pair field connected with the fact that each pair is described by a point in the space of 8 dimensions.

E. Lifshitz (Kharkov) spoke about his work, carried out jointly with L. D. Landau, in which he calculates the probability of the production of pairs in the collision of two charged particles. The calculations are of a very complicated nature, and some of their details still give rise to doubts. (The very same problem was solved by Carlson and Furry; the result obtained by them, as the speaker pointed out, must be incorrect, since it does not satisfy the condition of invariance with respect to a Lorentz transformation; however, Lifshitz’s calculations, perhaps, are not entirely correct either—at least as regards the numerical coefficients—since they give, for the total number of pairs, a result smaller than Williams’s calculations, which evidently take into account only a part of the pairs produced.)

Williams presented his calculations concerning the collision of two charged particles. He calculated 1) the radiation arising in such a collision and 2) the production of pairs. The method used by Williams consisted in decomposing the electromagnetic field of a receding particle into plane harmonic components, and then calculating the sum of the actions produced by each harmonic component separately. Williams’s calculations are also very cumbersome, as are Lifshitz’s calculations; the results of the calculations, as we have already noted, contradict one another.

Lifshitz reported on how the Klein–Nishina formula is derived in Dirac’s new theory, in which it is assumed that all levels with negative kinetic energy are occupied.

I. Waller (Sweden) presented his calculation of the radiation reaction on a radiating electron in nonrelativistic quantum mechanics.

M. N. Bronstein (Leningrad) discussed the question of the limits of applicability of the Klein–Nishina formula. This question was once (at the Rome congress of 1932) discussed by Bohr, who found that the Klein–Nishina formula is applicable even to wavelengths noticeably smaller than the radius of the electron. Bronstein finds, applying the correspondence principle to the initial and final states of the electron in the Compton effect, that for wavelengths comparable with the radius of the electron the Klein–Nishina formula is no longer valid; applying analogous reasoning also to those intermediate states through which, on the basis of quantum electrodynamics, the electron must pass in order to get from the initial state to the final one, the speaker finds that the Klein–Nishina formula ceases to be valid even when the wavelength is only a few times greater than the radius of the electron. In the discussion, Bohr agreed with the speaker’s first assertion (that the Klein–Nishina formula ceases to be valid for \(\lambda \simeq \dfrac{e^{2}}{me^{2}}\)), but did not agree with the second, pointing out that physical meaning need not necessarily be ascribed to the “intermediate states” in the Compton effect.

A lively discussion was provoked by the question of the magnetic moment of the neutron. The calculation of this magnetic moment, which J. Solomon (Paris) spoke about, was recognized during the discussion as erroneous, and therefore we do not set it forth here. I. E. Tamm (Moscow) proposed a method for calculating the magnetic moment of the neutron, based on the magnetic moments of nuclei. It is known that Dandé developed a theory of the magnetic moments of nuclei consisting of an even number of neutrons and an odd number of protons; Tamm developed an analogous

theory for an odd number of neutrons and an even number of protons, and at the same time improved Landé’s theory, explaining those cases which were not explained by Landé. From the Taam calculations it follows that the magnetic moment of the neutron is equal to half a nuclear magneton and is directed opposite to its mechanical moment. In the discussion Bohr stated that the determination of the magnetic moment of the neutron is at present a central problem of nuclear physics, since, if indeed, as Dirac assumes, all the laws of nature are absolutely symmetrical with respect to both signs of electric charge, then a neutron, having a charge equal to zero, should not have a magnetic moment (unless one assumes that there exist two sorts of neutrons with magnetic moments of opposite sign, which is improbable for many reasons). Bohr, apparently, also inclines to the hypothesis of complete symmetry of the laws of nature with respect to both signs of charge, and therefore he is inclined to admit that neutrons do not possess a magnetic moment.

Tamm described how, on the basis of the theory of $\beta$-decay proposed by Fermi, one can calculate the interaction between a proton and a neutron. This interaction is an exchange interaction of the “exchange” type (a proton and a neutron exchange roles by exchanging an electron and a neutrino, or a positron and a neutrino). In his calculation Tamm starts from the assumption that the proton and neutron are stable. As a result of the calculation he obtains an interaction far too weak to explain the bond between a proton and a neutron in the nucleus. Tamm’s report provoked a lively discussion. The computational methods he used were criticized by Landau; opinions on this question were divided.

L. Rosenfeld (Belgium) set forth his theory of the dissociative equilibrium of molecules in stellar atmospheres. This theory is analogous to Saha’s theory, which calculates the number of ionized atoms in stellar atmospheres in statistical equilibrium. Rosenfeld calculates the number of molecules TiO, ZrO and carbon compounds CN, CH, CO, C$_2$ in two cases: 1) the number of oxygen atoms exceeds the number of carbon atoms and 2) conversely. It turns out that the first case corresponds to the main sequence of stars, while the second—to the so-called carbon stars (carbon starts) (spectral classes R—N). In good agreement with experiment one obtains the intensity of molecular bands for different spectral classes and different values of the force of gravity at the surface of the star.

Ya. I. Frenkel (Leningrad) communicated his remarks on the electrodynamical works of Bohr and Infeld.

Bronstein presented his view on the origin of cosmic radiation. Dirac’s hole theory leads to the conclusion that electrons and positrons are always present in equilibrium radiation; the ratio of the energy of such pairs to the energy of the radiation is at first very small, but as the temperature rises it increases, and when

\[ \frac{T}{12} \gg \frac{mc^2}{13} \]

it assumes the value $7/4$. At temperatures of the order of $10^{12}$—$10^{13}$ degrees, effects of the relativistic quantum theory connected with the structure of electrons begin to play an essential role. Bronstein’s report makes the hypothesis that in this temperature region (when, in essence, the very concept of temperature ceases to have meaning) special kinds of forces appear, making possible more or less stable configurations. These configurations (in which the density of matter reaches $10^{15}\ \mathrm{g/cm^3}$) are metastable, as a result of which a spontaneous transition into a state in which the energy is dispersed throughout all space is possible. Processes of this kind, accompanied by the liberation of enormous quantities

the amount of radiant energy and fast charged particles, the speaker explains the flaring-up of “supernova stars.” In the phenomenon of “supernovae” he sees (together with Baade and Zwicky) the source of the origin of cosmic radiation.

L. Ya. Shtrum (Kiev) communicated his considerations concerning the possibility of the artificial transformation of a neutron into a proton and an electron, and of a proton into a neutron and a positron. In his opinion such transformations can be carried out by means of the absorption of radiant energy; moreover, for the first process the smallest energy of the $\gamma$-quantum must be $3mc^2$, and for the second $2mc^2$. The second process is accompanied by the scattering of a $\gamma$-quantum (according to the scheme: $p + 2mc^2 \to n + \varepsilon + 3mc^2$), and by this Shtrum explains the anomalous scattering of $\gamma$-rays (he considers it, contrary to Terfen’s measurements, normally scattered radiation contains quanta of energy $\sim 1.5 \cdot 10^6$ electron-volts).

Williams reviewed the new experimental work on cosmic radiation and subjected it to a detailed analysis.

Landau reported on his calculation (carried out by him jointly with V. S. Sopolinsky) of the probability of the transition of a neutron from one nucleus to another. It is assumed that in both nuclei the neutron can be tightly bound, whence it follows that, in passing from one nucleus to the other, it passes through a region of negative kinetic energies (in the same sense in which $\alpha$-particles pass through such a region in Gamow’s calculation). Since the radius of interaction of the neutron and the nucleus is very small, one may consider that the entire region outside the nucleus corresponds to such a negative kinetic energy. Since the mass of all the particles is sufficiently large, it proves possible to solve the problem by applying a peculiar “quasi-classical” mechanics with the canonical equations of Hamilton, etc., but with imaginary velocities. The work, unfortunately, is still “far from numerical values,” and therefore it is not yet possible to compare it with Lawrence’s experimental data (bombardment of the nuclei of various elements by deuterons).

M. P. Bronstein (Leningrad)