Interaction of Neutrons and Protons

D. Iwanenko

Editor’s Notes

Russian physicist Dmitri Iwanenko here argues that Fermi’s recent theory of beta radioactivity, while successful in some regards, makes some erroneous predictions. For decays observed in light nuclei, the theory gives a roughly correct link between the rate of decay and the maximum energy of the ejected particles. However, if one uses the theory to consider nuclear binding as an exchange of force-mediating particles similar to the electromagnetic force, one finds the force is only large enough at a distance between nucleons of about 10–17 m, which is far too small. Iwanenko concludes that Fermi’s theory is thus only a very crude approximation.　　中文

AS electrons and positrons are expelled in some reactions from nuclei, we can try to treat these light particles like the photons emitted by atoms. Then the interaction of heavy particles (protons, neutrons) can be considered as taking place via light particles described by the equations of a ψ-field in the same manner as electromagnetic, for example, Coulomb, interaction takes place through an electromagnetic field, or photons.　　中文

The first order effects are the expulsion (or absorption) of an electron, which case was treated recently by Fermi, or of a positron. We may remark that the application of Fermi’s formalism to positron disintegration of light nuclei (which we get by changing the sign of the charge number and taking for the latter the appropriate value) gives results which fit, though not very accurately, the observed relation between the half-period and the maximum energy of the disintegration particle1. Though there seems to be a quantitative disagreement between Fermi’s theory (applied to positrons) and positron disintegration, on the other hand the calculated values for K and Rb support Fermi’s assumption of the existence of quadripole transitions of heavy particles, giving too big values for the half periods in comparison with the usual dipole disintegrations. The exceptional position of K and Rb is in some way rather anschaulich. We may remark that the Sargent–Fermi rule, in contrast to the Geiger–Nuttall law, shows a less pronounced dependence on the charge number, so that for qualitative considerations even the wave functions of free particles can be used.　　中文

The second order effects give specially the probability of production of pairs, which is in the case of the ψ-field less effective than in the electromagnetic case, as the charge, e, is much bigger than Fermi’s coefficient, g (the “charge” for the ψ-field). The most important second order effect is the subsequent production and annihilation of an electron and positron, in the field of proton and neutron, which leads to the appearance of an interaction exchange energy (Heisenberg’s Austausch) between proton and neutron, quite in the same way as Coulomb interaction can be conceived as arising from the birth and absorption of a photon in the case of two electrons. Instead of e2/r one gets here an interaction of the order g2/chr5, which is easily verified dimensionally. The exact calculations were first carried out by Prof. Ig. Tamm, who also insisted on development of this method. With g~10–50 (the computations were carried out by V. Mamasichlisov), which value is required by the empirical data on heavy radioactive bodies, we get an interaction energy of a million volts, no at a distance of 10–13 cm. but only at r~10–15 cm., which is inadmissible. We may ask about the value of r, which would give a self-interaction energy of the order of the proper energy of a heavy particle. This value is of the order 10–16 cm., which is that of the classical radius of a proton.　　中文

The appearance of these small distances is very surprising and can be removed only by some quite new assumptions. Fermi’s characteristic coefficient g appears to be connected also with distances of this order of magnitude.　　中文

(133, 981-982; 1934)

D. Iwanenko: Physical-Technical Institute, Leningrad.

Reference:

1. cf. D. Iwanenko, C.R. Ac. Sci. U.S.S.R., Leningrad, 2, No. 9, 1934.