Proton-Proton Scattering Near the Interference Minimum and the Shape Parameter

Abstract

At a laboratory proton energy of 382.43 keV, $p-p$ scattering exhibits nearly complete destructive interference, and the $s$-wave phase shift may be determined from the location, $E_{min}$, of the minimum in the cross section for 90${\mathrm{°}}_{\mathrm{c}.\mathrm{m}.\mathrm{}}$ scattering, with comparable precision. A determination of the phase shift at $E_{min}$ to one part in ${10}^3$ may be combined with recent Wisconsin results between 1.4 and 3 MeV to give information about the shape-dependent term in the effective-range expansion. Measurements have been made of the relative cross section at six energies near that of the minimum, using a scattering chamber with annular slits of 90° vertex angle and a group of coincident pairs of silicon particle detectors. The energies of the data points were established by a radio-frequency, time-of-flight absolute velocity gauge, with an uncertainty of less than 50 eV. The scattering chamber was differentially pumped upstream and downstream. The operating pressure was 0.3 Torr, and the upstream energy loss of about 150 eV was measured directly by noting the offset of the ${\mathrm{F}}^{19}(p, \alpha \gamma ){\mathrm{O}}^{16}$ resonance when hydrogen was present in the chamber between the velocity gauge and a differentially pumped C${\mathrm{F}}_4$ gas target. The minimum was relocated at $E_{min}=382.43\mathrm{}\pm 0.20$ keV, and the corresponding $s$-wave phase shift with respect to the "electric" wave functions including vacuum polarization is found to be ${{\delta }_0}^E=0.25501\mathrm{}\pm 0.00020$ rad. The shap-dependent parameter inferred from these results is significantly positive, $P=+0.028\mathrm{}\pm 0.014$. This may be considered strong evidence in favor of one-pion-exchange effects in the $s$-wave interaction.