Angular correlations between protons from the ${\mathrm{Mg}}^{24}(d, p){\mathrm{Mg}}^{25}$ reaction leading to the 3.40-Mev excited state of ${\mathrm{Mg}}^{25}$ and the resulting de-excitation gamma rays were investigated to test the validity of the distorted-wave stripping theory. A natural magnesium target was bombarded by 15-Mev deuterons and proton-gamma coincidences were counted using scintillation detectors in conjunction with conventional fast-slow coincidence circuitry. The correlations were studied at laboratory proton scattering angles of 15° and 45°, each in two mutually perpendicular planes: the reaction plane and the plane perpendicular to it containing the deuteron axis. The angular distribution of protons from this level was also measured and fitted by a Butler stripping curve with $l_n=1\mathrm{}$ and $r_0=5.0\mathrm{}$ fermis.

The coordinate system used to describe the correlations is defined with the $z$ axis in the ${\mathrm{k}}_d\times {\mathrm{k}}_p$ direction and the $x$ axis in the recoil nucleus direction. Correlation functions found by least-squares fits to the experimental data are, for the 15° proton angle, $W({\mathrm{k}}_d, {\mathrm{k}}_p, \frac{1}{2}\pi , \phi )=1-(0.385\mathrm{}\pm 0.023){cos}^2(\phi -{\phi }_0)$, with ${\phi }_0=-27.7\mathrm{}°\pm 2.9°$, and $W({\mathrm{k}}_d, {\mathrm{k}}_p, \theta , {\phi }_r)=1+(0.145\mathrm{}\pm 0.029){cos}^2\theta$, where ${\phi }_r$ is the beam direction. The functions found for the 45° proton angle are $W({\mathrm{k}}_d, {\mathrm{k}}_p, \frac{1}{2}\pi , \phi )=1-(0.366\mathrm{}\pm 0.033){cos}^2(\phi -{\phi }_0)$, with ${\phi }_0=-6.8\mathrm{}°\pm 3.5°$, and $W({\mathrm{k}}_d, {\mathrm{k}}_p, \theta , {\phi }_r)=1+(0.279\mathrm{}\pm 0.038){cos}^2\theta$. These observed correlations are in good agreement with the predictions of the distorted wave theory and not with those of the plane wave theory. It is to be noted in particular that the agreement is excellent at 45° indicating that protons scattered at this angle probably arise from the stripping process in spite of the fact that the disagreement between Butler stripping theory and the measured angular distribution is greatest here. This then suggests that protons observed in the entire region beyond the first maximum of a typical angular distribution are due to stripping and might be adequately described by stripping theory if suitably distorted waves are used in the analysis.

• Received 14 June 1960

DOI:https://doi.org/10.1103/PhysRev.120.492