Exchange Character Research Articles

The interaction of neutron and alpha-particle

The phenomenological neutron-alpha interaction is determined from the phase shifts in the scattering of neutrons on alpha particles, over the neutron energy range 0–10 MeV. From the notion of the alpha particle, acting as a single unpolarised unit in the scattering, comes the assumption that the interaction is mainly of the ordinary velocity-independent type, which may be easily subjected to phenomenological analysis. A new general analysis relates useful phase parameters to parameters defining interaction potential. For a consistent solution, on the basis of an ordinary potential with spin orbit coupling, which would give the main phase data, for the S, P and D waves, one requires the interpretation of the S phases in terms of an attractive potential which has one bound state, rather than by a predominantly repulsive interaction. On this interpretation the ‘bound state’ is not observed because the wave function for the corresponding (ls) 5 state will vanish identically by the exclusion principle. Using the group resonance formalism the ordinary potential so obtained can be related to fundamental force parameters in a consistent way, because the neutron-alpha interaction is indeed seen to have only a secondary velocity-dependence for these force parameters. The fundamental force-parameters are close to those required by low energy nucleon-nucleon data; they give the correct alpha binding energy, and have an exchange character which is non-saturating without a repulsive core.

A MODIFICATION OF THE ONE-PARTICLE FORMULA FOR NUCLEAR GAMMA-RADIATION

The one-particle theory of isomeric γ-transitions in nuclei consistently overestimates the probability per unit time of decay. It is shown that, by modifying the one-particle model to take account of the readjustment of the wave functions of all the nuclear particles during the predominantly one-particle transition, satisfactory agreement with experiment can be obtained. The fact that odd-proton transitions are depressed more than odd-neutron ones is attributed to the exchange character of the force giving rise to the readjustment.

The Collisions of Nucleons with Deuterons

A considerable amount of theoretical data (assuming central nuclear forces) is now available concerning the elastic scattering of nucleons with energies up to 16 MeV by deuterons. Buckingham, Hubbard and Massey have taken the force to be of exponential shape with range consistent with the binding energy of the deuteron and triton while Christian and Gammel have used Yukawa and gaussian shape interactions with ranges consistent with all relevant two-body data but which are considerably too short to give the correct binding energy of the triton on the assumption of purely central forces. In the present paper the former calculations have been extended to allow fully for the contributions from high order phases. The dependence of the theoretical predictions on the assumptions made about the range, shape and exchange character of the nuclear forces is discussed in detail. It is shown that the observed data are inconsistent with the assumption of mainly ordinary forces even for the least sensitive case of the short range gaussian interaction. Extension of the theory to include explicitly the tensor force is likely to be worth while as providing useful information about nuclear forces.

The Scattering of Nucleons by Alpha Particles - the s-Phases

The s-phase shifts for scattering of neutrons and of protons by alpha particles have been calculated over the energy range 0-4 Mev. A central interaction between nucleons of gaussian form has been assumed, the constants being consistent with the binding energy of the deuteron and alpha particle. The resonating group structure method has been employed to provide integro-differential equations for the wave functions which describe the scattering. These equations are internally consistent in that the functions used to describe the resonating groups are only assumed to satisfy the usual variational integral condition in terms of the alpha particle binding energy. The s-phases were determined by accurate numerical solutions of the equations. Very good agreement was obtained with the phases derived from analysis of observed data both for neutron and for proton scattering, provided the internucleonic forces were taken to be of symmetrical exchange character. The work is a necessary preliminary to an investigation of the p-phases in terms of an internucleonic spin-orbit interaction.

Neutron-Deuteron Scattering at High Energy

The neutron-deuteron total scattering cross section at high energy has been calculated by expressing it as a sum over two-particle states over a wide range of energy. A sum rule was then applied to give the total cross section, that is, the elastic and inelastic cross sections. The calculations were performed with a Serber type exchange force for the neutron-proton force in agreement with present neutron-proton scattering data and a neutron-neutron force of arbitrary depth and exchange character. The neutron-neutron well depth was then determined for an ordinary, Serber type and pure exchange force between the two neutrons by making use of the experimental neutron-deuteron total cross section. The neutron-deuteron elastic scattering was then calculated for the three different types of neutron-neutron exchange and was found to agree best with the experimental value for the Serber type exchange (no force in odd states). The cross section for production of low energy protons was also calculated and confirmed the Serber type exchange force between the two neutrons when compared with the experimental value. Finally, a qualitative discussion of the angular and energy distribution of the low and high energy protons was given.

Binding energy of the triton

The variation method is employed to calculate the binding energy of the triton assuming charge-independent, two-body, Yukawa shape interactions between nucleons in which tensor forces are included. More complete trial wave functions are used than employed hitherto in such calculations, and it is found that an interaction of Yukawa shape with constants adjusted to fit the observed data on the binding energy, quadrupole moment and magnetic moment of the deuteron, the low-energy and high-energy scattering of neutrons by protons, the photodisintegration of the deuteron and the coherent scattering of slow neutrons gives an approximately correct binding energy for the triton. Calculations are also carried out with interactions of the same type but with different constants. The exchange character of the forces remains unimportant. It is confirmed that the difference in the binding energies of 3 H and 3 He can be ascribed to the effect of Coulomb repulsion between the protons in the latter nucleus. The wave functions found are used to compute the magnetic moments of the two nuclei but do not contain sufficient admixture of P component to explain the observed values.

Binding Energy of the Triton

The variation method is employed to calculate the binding energy of the triton assuming charge-independent, two-body, Yukawa shape interactions between nucleons in which tensor forces are included. More complete trial wave functions are used than employed hitherto in such calculations, and it is found that an interaction of Yukawa shape with constants adjusted to fit the observed data on the binding energy, quadrupole moment and magnetic moment of the deuteron, the low-energy and high-energy scattering of neutrons by protons, the photodisintegration of the deuteron and the coherent scattering of slow neutrons gives an approximately correct binding energy for the triton. Calculations are also carried out with interactions of the same type but with different constants. The exchange character of the forces remains unimportant. It is confirmed that the difference in the binding energies of $^{3}$H and $^{3}$He can be ascribed to the effect of Coulomb repulsion between the protons in the latter nucleus. The wave functions found are used to compute the magnetic moments of the two nuclei but do not contain sufficient admixture of P component to explain the observed values.

The capture of neutrons by deuterons

The cross-sections for capture of neutrons by deuterons, involving emission of both electric and magnetic dipole radiation, are calculated using the wave functions obtained by Buckingham & Massey (1941) in the course of an application of the resonating-group structure method to the elastic scattering of neutrons by deuterons. The value found for capture of neutrons with emission of magnetic dipole radiation is found to be very sensitive to the particular form taken for the various wave functions, owing to a very high degree of cancellation that occurs in the integrations. As a result it is out of the question at present to provide accurate theoretical values for this process. All that can be said is that the cross-section for capture of thermal neutrons by deuterons is likely to be abnormally small. It may well be 10 -28 cm. 2 or less. This is in general agreement with observation. For capture of fast neutrons with emission of electric dipole radiation there is much less uncertainty in the calculated values although the cross-sections are very small, of the order of a few times 10 -29 cm. 2. The actual value of the cross-section in this case depends on the assumed type of nucleonic interaction, i.e. whether it is of exchange character or not. Results are also given for the inverse process—the photodisintegration of the triton.

On the Neutron-Proton Scattering Cross Section

The sensitivity of the theoretical neutron-proton scattering cross section to possible variations in the quantities defining the potential has been investigated in the energy range from 0 to 6 Mev. It is found that in this energy range the variations in exchange or tensor character and range of the potential which are consistent with what is known about the interaction do not result in so large a modification of the predicted cross section as do variations in shape.A well resembling a Yukawa potential ($A \mathrm{exp}\frac{(\ensuremath{-}\ensuremath{\alpha}r)}{r}$) is found to yield a cross section at 6 Mev which is 10 percent lower than that given by a square well fitted to the epithermal neutron cross section and the binding energy of the deuteron. The Yukawa well is in better agreement with experiment than is the square well. One of the constants entering into the determination of the potential is the epithermal neutron scattering cross section in hydrogen. We have determined this by extrapolating the data of Frisch with the aid of the theory, and obtained a value of 20.8\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{2}$.

Note on the Interaction Between Nuclei and Electromagnetic Radiation

The exchange character of nuclear forces makes it impossible to formulate in a consistent way the coupling between the electromagnetic field and a nucleus described by a model which involves only heavy particles. This difficulty does not occur in a theory which introduces light particles as carriers of the charge in the exchange processes. The actual contribution of these light particles to the transition probabilities is proved to be negligible in the limit of wave-lengths of the radiation large compared with nuclear dimensions and nonrelativistic motion of the heavy particles. In this limit one is justified in taking as coupling term --- (ED), where D is the dipole moment calculated from the heavy particle model, and E is the electric field. A marked influence of the exchange processes on the radiation properties of the nucleus exists even in the limit considered.