Analysis ofp−pData Near the Interference Minimum

Abstract

In the first part of this paper $p\ensuremath{-}p$ elastic scattering data at 90\ifmmode^\circ\else\textdegree\fi{}c.m. near the Coulomb-nuclear interference minimum are analyzed. The energy of the minimum of the 90\ifmmode^\circ\else\textdegree\fi{} cross section is found to be at 0.38243 \ifmmode\pm\else\textpm\fi{}0.00020 MeV. The nuclear $s$-wave phase shift, defined with respect to wave functions which solve the Coulomb plus vacuum polarization potential problem, is found to be ${{\ensuremath{\delta}}_{0}}^{E}=0.25501\ifmmode\pm\else\textpm\fi{}0.00020$, at the precise energy 0.38243 MeV. In the second part of the paper the phase shift just obtained is used, in conjunction with four very accurate phase shifts from 1.4 to 3.0 MeV, to determine the parameters of the $s$-wave effective-range expansion. If this expansion is cut off after three terms (quadratic fit) then the scattering length is found to be $a=\ensuremath{-}7.815\ifmmode\pm\else\textpm\fi{}0.008$ F; the effective range ${r}_{0}=2.795\ifmmode\pm\else\textpm\fi{}0.025$ F; and the shape-dependent parameter $P=0.028\ifmmode\pm\else\textpm\fi{}0.014$. However, it is argued that the first three coefficients in the actual power-series expansion of the effective-range function are not known this well, and in particular, $P$ may be very different from the actual coefficient occurring in the ${k}^{4}$ term.