Measurement of spin observables in the quasifree $np\to {\left\{pp\right\}}_s{\pi }^{-}$ reaction at 353 MeV

The transverse spin correlations $A_{x,x}$ and $A_{y,y}$ have been measured in the $\vec{d}\vec{p}\to p_{\text{spec}}{\left\{pp\right\}}_s{\pi }^{-}$ reaction at COSY-ANKE at 353 MeV per nucleon. Here ${\left\{pp\right\}}_s$ denotes a proton-proton pair with low excitation energy, which is dominantly in the ${}^1{S}_0$ state. By measuring three protons in the final state it was possible to extract events where there was a spectator proton $p_{\text{spec}}$ so that the reaction could be interpreted in terms of quasifree $\vec{n}\vec{p}\to {\left\{pp\right\}}_s{\pi }^{-}$. The proton and neutron analyzing powers in this reaction were also deduced from this data set by averaging over the polarizations of the deuteron beam and hydrogen target, respectively. The values of $A_y$ were shown to be consistent with a refined analysis of our earlier results obtained with a polarized proton incident on a deuterium target. Taking these data in combination with our previous measurements of the differential cross sections and analyzing powers in the $\vec{p}p\to {\left\{pp\right\}}_s{\pi }^0$ reaction, a more robust partial wave decomposition was achieved. Three different acceptable solutions were found, and the only way of resolving this ambiguity without further theoretical input would be through a measurement of the mixed spin-correlation parameter $A_{x,z}$.

Figure 1

Top view of the ANKE spectrometer setup, showing the positions of the Positive (PD), Negative (ND), and Forward (FD) detectors, as well as the Silicon Tracking Telescope (STT). The dipoles D1 and D3 deflect the circulating proton beam in and out of the spectrometer, whereas D2 serves as an analyzing magnet. Typical proton trajectories (labeled $p$) in the FD and PD systems are indicated, as are the axes of the coordinate system at the target.

Figure 2

(a) Experimental (histogram) and simulated (shaded area) distribution in the deuteron rest frame of spectator proton energies from the $dp\to {\left\{pp\right\}}_s{\pi }^{-}{p}_{\text{spec}}$ reaction for the selected $T_{\text{free}}$ range. (b) Experimental distribution of effective beam energies; the region selected for analysis is shown by the shading.

Figure 3

Missing-mass squared for the (a) $dp\to p_{\text{spec}}{\left\{pp\right\}}_{s}X$ and (b) $dp\to dpX$ reactions. The data with error bars were obtained with hydrogen in the cell. The shaded area shows the scaled background and the line the total fitted function.

Figure 4

Experimental asymmetry in the quasifree $\vec{n}p\to d{\pi }^0$ data for (a) the target polarization and (b) the beam polarization. The curves show the SAID predictions for $A_y$ in $\vec{p}p\to d{\pi }^{+}$ at 353 MeV [45], scaled with the value of polarization to fit the data, which are shown with their statistical errors.

Figure 5

The experimental $pd\to p_{\text{spec}}{\left\{pp\right\}}_{s}X$ missing-mass-squared spectrum. (a) Spectrum measured using the first two STT layers without the time criterion (points with error bars) and the constructed and scaled background (filled area) [26]. The data obtained using the time criterion (line) show almost no background. (b) Spectrum for the same angular bin and detector combination obtained from the first STT layer only by using the timing information.

Figure 6

Analyzing power $A_y^p$ for the quasifree $\vec{p}n\to {\left\{pp\right\}}_s{\pi }^{-}$ reaction at 353 MeV with the $E_{pp}<3$ MeV cut. The published ANKE data [26] are shown with the shaded error bands. The black circles show the reanalyzed ANKE data with statistical errors using $E_{pp}$ cuts of (a) 3 MeV and (b) 1.5 MeV. The TRIUMF data [27] are represented by the blue triangles.

Figure 7

Observables measured for the $pn\to {\left\{pp\right\}}_s{\pi }^{-}$ reaction at 353 MeV using the $E_{pp}<3$ MeV cut. (a) The unpolarized differential cross section. The published ANKE data [26] are shown by the shaded error bands and the curve is a direct cubic fit to these data. The black circles show the data with statistical errors obtained in the new ANKE double-polarized experiment. Since no absolute normalization was here achieved, these values were scaled by an arbitrary overall factor. The TRIUMF data [28] are shown by the blue triangles. (b) The proton analyzing power $A_y^p$ (points) and neutron analyzing power $A_y^n$ (shaded bands) obtained simultaneously in the double-polarized experiment.

Figure 8

Spin-correlation coefficients for the $\vec{n}\vec{p}\to {\left\{pp\right\}}_s{\pi }^{-}$ reaction at 353 MeV with statistical errors as a function of the pion emission angle. (a) $A_{y,y}$. The horizontal line represents a fit with a constant value. (b) The values of $A_{x,x}$ were subsequently deduced by demanding that $A_{y,y}=1$ for all pion angles. The systematic uncertainties of the ${90}^{\circ }$ point (blue star, shifted for visibility) deduced from Eq. (7) are much larger than the purely statistical errors shown.

Figure 9

Predictions of the partial wave analysis for the $pn\to {\left\{pp\right\}}_s{\pi }^{-}$ reaction at 353 MeV with the $E_{pp}<3$ MeV cut. Also shown are the ANKE experimental data with statistical errors. The full, long-dashed, and short-dashed lines correspond to solutions 1, 2, and 3, respectively, as noted in Table . (a) Differential cross-section taken from Ref. [26], (b) $A_y^p$ data from this work, (c) $A_{x,x}$ data from this work, and (d) $A_{x,z}$, for which there are yet no experimental data.