Theoretical Angular Distributions Research Articles

Interaction of 0.5- and 1.0-Mev Neutrons with Some Heavy Elements

The angular distributions of 0.5-Mev neutrons elastically scattered by Au, Bi, ${\mathrm{U}}^{238}$, ${\mathrm{U}}^{235}$, and ${\mathrm{Pu}}^{239}$ and of 1.0-Mev neutrons elastically scattered by the latter three materials have been measured. The differential and total elastic scattering cross sections, the elastic transport cross sections, and the inelastic collision cross sections are presented. Some theoretical angular distributions and cross sections based on a complex squarewell model for ${\mathrm{U}}^{238}$ are also included. The angular distributions of fission neutrons produced by 0.5- and 1.0-Mev incident neutrons are found to be isotropic, and the ratio of $\overline{\ensuremath{\nu}}({\mathrm{Pu}}^{239})$ to $\overline{\ensuremath{\nu}}({\mathrm{U}}^{235})$ is 1.3\ifmmode\pm\else\textpm\fi{}0.2 at both energies.

Stripping Reactions and Nuclear Shell Model

It has been pointed out by many authorsll2l that the angular distributions from certain (d, p) and (d, n) reactions should give a sensitive measure of the accuracy of the nuclear structure in ascribing definite orbital angular momentum states to nucleons in a nucleus. This possibility is due to the facts that these reactions proceed mainly by means of a stripping process and that their angular distributions are characterized by the orbital angular momentum l with which the captured particle can be accepted into the appropriate final state. The theoretical expression of the differential cross section for the deuteron stripping reactionll includes the summation over all values of l, allowed by the selection rules. Therefore, each allowed value of l produces a peak in the angular distribution without interfering one another, the peaks corresponding to different l being quite separated. The theoretical angular distribution shows a pronounced peak at small angles, and the maximum resulting from the smallest allowed l is of much larger magnitude than the others. The heights of the the peaks decrease rapidly and the peaks move progressively toward the large angles as l increases. The investigations on the validity of the shell model by the deuteron stripping reaction are necessarily restricted to the lower l values. If the experimental angular distribution is characterized by two l values, it shows evidently the deviation from the pure shell model, i.e., the admixture of orbital angular momentum states. Recently, the necessity3> of the mixing of the configurations in nuclei was pointed out in the studies on the first excited states in the even-even nuclei and on {3-decay with anomalous ft-values. The mixing of the configurations was applied with much success to explain the deviations of the magnetic moments4)5) from the Schmidt limit in odd-A nuclei, and quadrupole moments,6> and the {3-decay and r·transition of the forbidden types. The purposes of this note are to show that the mixing of the configurations can be applied to the deuteron stripping reactions also with success when the angular distributions are characterized by two l values, and that we can determine the percentage of the mixing of the configurations from the observed relative heights of the peaks reversely. We have derived the (d, p) differential cross section in the modified Born approximation. As the result, we have

Proton-Deuteron Scattering at 5.1 Mev and Deuteron-Proton Scattering at 10.2 Mev

A photographic scattering chamber has been used to study the elastic scattering of 5.1-Mev protons by deuterium and 10.2-Mev deuterons by hydrogen, these being the same process in the center-of-mass system. Differential cross sections were obtained from 16.4\ifmmode^\circ\else\textdegree\fi{} to 172.9\ifmmode^\circ\else\textdegree\fi{}. These are in good agreement with other experimental data at about the same energy. Comparison is made with the theoretical angular distribution due to Buckingham, Hubbard, and Massey, based on a symmetrical exchange force. Agreement is close at this energy, favoring exchange rather than ordinary force theories. However, at higher energies (\ensuremath{\sim}10-Mev $p\ensuremath{-}d$) the BHM calculations do not represent the interaction satisfactorily.

The Angular Distributions of the Alpha-Particles and of the Gamma-Rays from the Disintegration of Fluorine by Protons

The theoretical angular distributions of the alpha-particles and of the gamma-rays from the fluorine +proton reactions are given. They are compared with the experimental data, and the following results are obtained: (1) Both angular distributions of the ${\ensuremath{\alpha}}_{\ensuremath{\pi}}$-group and of the ${\ensuremath{\alpha}}_{0}$-group favor the assumption of even parity of ${\mathrm{F}}^{19}$. (2) If the parity of ${\mathrm{F}}^{19}$ is taken as even, then (a) the isotropic angular distribution of the gamma-rays at the resonances of 340 and 669 kev can be interpreted as due to the formation of ${\mathrm{Ne}}^{20}$ compound states of $J={1}^{+}$ by the capture of $s$-protons, (b) the slightly anisotropic angular distribution of the gamma-rays at the resonances of 598, 874, and 1381 kev can be interpreted as due to the formation of ${\mathrm{Ne}}^{20}$ states of $J={1}^{+}$ by a mixture of $s$- and $d$-protons, or of $J={2}^{\ensuremath{-}}$ by $p$-protons, (c) the highly anisotropic distribution of the gamma-rays observed at 1290 and 1355 kev can be interpreted as due to the formation of ${\mathrm{Ne}}^{20}$ states of $J={3}^{+}$, and (d) the experimental data of the gamma-ray angular distribution and of the ratio $\frac{{I(\ensuremath{\alpha})}_{140\ifmmode^\circ\else\textdegree\fi{}}}{{I(\ensuremath{\gamma})}_{90\ifmmode^\circ\else\textdegree\fi{}}}$ are compatible with the assignment ${j}^{\ensuremath{'}}={3}^{\ensuremath{-}}$ for the ${\ensuremath{\gamma}}_{1}$-level of ${\mathrm{O}}^{16}$. In general it is possible to make spectroscopic assignments consistent with the experimental data but unique assignments will await further experimental results.

Note onp-Wave Anomalies in Proton-Proton Scattering

The $p$-wave effects on Bethe's neutral form of meson theory are calculated for proton energies of 2.0 Mev, 2.4 Mev and 3.0 Mev. The range of nuclear force corresponding to a meson mass of 180 electron masses gives effects of the order of a few percent of the total scattering. These effects do not vanish at the scattering angle of 45\ifmmode^\circ\else\textdegree\fi{}. If present, they call for a slight increase in the range of force derived from $s$ scattering. The comparison of the theoretical and experimental angular distributions indicates, however, that $p$-wave effects predicted by the above meson theory with a mass of 180 m are too large since they give too much small angle scattering.