Wolfenstein parameters for $s_{1/2}$ proton knockout ($p,2p$) reactions

A complete set of Wolfenstein parameters ($D_{i^{\text{'}}j}$), induced polarizations ($P$), and analyzing powers ($A_y$) have been measured for ($p,2p$) reactions on ${}^6\mathrm{Li}$, ${}^{12}\mathrm{C}$, and ${}^{40}\mathrm{Ca}$ targets in order to investigate possible nuclear medium effects on the nucleon-nucleon ($\mathit{NN}$) interaction. Most of these observables show significant reductions from the values for proton-proton scattering as monotonic functions of the nuclear density relevant to these reactions. The reductions of these $D_{i^{\text{'}}j}$ are reasonably reproduced by nonrelativistic plane-wave and distorted-wave calculations based on the impulse approximation, demonstrating that these suppressions are attributed to changes of the two body kinematics due to the finite separation energies of these reactions, while the reductions of $A_y$ and $P$ are much more prominent than the calculations. The relativistic calculations, which partly explain the $A_y$ and $P$ reductions, cannot reproduce the $D_{i^{\text{'}}j}$ data, but all the data are consistently reproduced when the parameters of the $\mathit{NN}$ interaction in a meson exchange model are renormalized, suggesting possible modifications of the $\mathit{NN}$ interaction by the surrounding nuclear medium.

Figure 1

The two-arm spectrometer system at RCNP: D, D1, and D2 denote dipole magnets, Q, Q1, and Q2 quadrupole magnets, SX a sextupole magnet, while MP is a multipole magnet for aberration correction. See the text for polarization transfer measurements using the DSR and the FPP.

Figure 2

Separation energy spectra for ($p,2p$) reactions. Each vertical axis is a linear scale in arbitrary units. The shaded areas are used for determining the $D_{i^{\text{'}}j}$ values. In the case of the ${}^6\mathrm{Li}$ target, the contribution from ${}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}$ contaminations, included in the shaded regions, are subtracted by using experimental data for ${}^6\mathrm{Li}$O and ${}^{\text{nat}}$C targets.

Figure 3

Comparison of theoretical predictions to experimental data for polarization transfer coefficients, $D_{\mathit{nn}},D_{s^{\text{'}}s},D_{s^{\text{'}}l},D_{l^{\text{'}}s},D_{l^{\text{'}}l}$, analyzing powers, $A_y$, and induced polarizations, $P$, for exclusive proton knockout from the 1$s_{1/2}$ states in ${}^6\mathrm{Li}$ and ${}^{12}\mathrm{C}$ as well as from the 2$s_{1/2}$ state in ${}^{40}\mathrm{Ca}$ at an incident energy of 392 MeV and for kinematics corresponding to zero recoil momentum as specified in Table . The data, shown by closed circles, are plotted as functions of the effective mean density (in units of the nuclear saturation density, ${\rho }_0$). The closed squares denote the data for $p\text{−}p$ scattering. The thin dashed and solid lines respectively denote the nonrelativistic distorted wave and plane predictions, whereas the thick dashed and solid lines respectively represent the relativistic distorted wave and plane wave results. The thin solid lines are connected to $p\text{−}p$ scattering points, which are given by the SP07 phase shift solution. The dotted lines represent the nonrelativistic DWIA including relativistic $M^{*}$ corrections (see text). For 1$s_{1/2}$ knockout from ${}^{12}\mathrm{C}$, the open circles correspond to Rho-Brown corrections to the relativistic distorted wave model for $\xi =\chi =0.85$, whereas the open squares denote the relativistic distorted wave results with modified meson-nucleon coupling constants. The open triangles show results when only the $g_{\sigma }$ value is reduced by 4% from parameters used in the calculation denoted by the open squares.