Diffractional Scattering of Fast Deuterons by Nuclei

Abstract

The elastic scattering cross section ${\ensuremath{\sigma}}_{e}$ and the diffractional disintegration cross section ${\ensuremath{\sigma}}_{d}$ for fast deuterons incident on absolutely black nuclei are determined, and the energy spectrum of the disintegration products is found. For $R\ensuremath{\gg}{R}_{d}\ensuremath{\gg}\ensuremath{\lambda}$ [where $R$ and ${R}_{d}$ are the radii of the nucleus and of the deuteron, respectively, and $\ensuremath{\lambda}$ is ${(2\ensuremath{\pi})}^{\ensuremath{-}1}$ times the wavelength of the deuteron], the cross sections are ${\ensuremath{\sigma}}_{e}=\ensuremath{\pi}{R}^{2}+\frac{2}{3}\ensuremath{\pi}(1\ensuremath{-}\mathrm{ln}2)R{R}_{d}$ and ${\ensuremath{\sigma}}_{d}=\frac{1}{3}\ensuremath{\pi}(2\mathrm{ln}2\ensuremath{-}\frac{1}{2})R{R}_{d}$.The total cross section for all processes (including the stripping and the absorption of the deuteron) is ${\ensuremath{\sigma}}_{t}=2\ensuremath{\pi}{R}^{2}+\ensuremath{\pi}R{R}_{d}$.The disintegration cross section for fast deuterons, taking into account the diffraction and the Coulomb interaction, is found. If the nucleus is absolutely black and if $R\ensuremath{\gg}{R}_{d}$, there is no interference between the diffractional disintegration and the disintegration due to the Coulomb interaction. If in this case $n=\frac{Z{e}^{2}}{\ensuremath{\hbar}v}\ensuremath{\ll}1$ (where $v$ is the velocity of the deuteron), the disintegration cross section due to the Coulomb interaction is a small correction to the diffractional disintegration cross section. If $n\ensuremath{\gg}1$ and $E\ensuremath{\gg}B$ (where $E$ is the energy of the deuteron and $B$ is the height of the Coulomb barrier), the disintegration cross section can also be found; in this case it is determined mainly by the Coulomb interaction and is ${\ensuremath{\sigma}}_{f}=(\frac{4\ensuremath{\pi}}{3}){n}^{2}{{R}_{d}}^{2}\mathrm{ln}(\frac{{R}_{d}}{\ensuremath{\lambda}})$.Expressions are found for the elastic scattering cross section for a deuteron, taking into account the semitransparence of the nuclei.