Vector and tensor analyzing powers in deuteron-proton breakup at 130 MeV

High-precision data for vector and tensor analyzing powers for the ${}^1\mathrm{H}$$(\mathrm{d⃗},\mathit{pp})n$ reaction at a 130-MeV deuteron beam energy have been measured over a large part of the phase space. Theoretical predictions based on various approaches to describe the three nucleon ($3N$) system reproduce very well the vector analyzing power data and no three-nucleon force effect is observed for these observables. Tensor analyzing powers are also very well reproduced by calculations in almost the whole studied region, but locally certain discrepancies are observed. For $A_{\mathit{xy}}$ such discrepancies usually appear, or are enhanced, when model $3N$ forces, TM99 or Urbana, are included. Problems of all theoretical approaches with describing $A_{\mathit{xx}}$ and $A_{\mathit{yy}}$ are limited to very small kinematical regions, usually characterized by the lowest energy of the relative motion of the two protons.

Figure 1

Definition of the coordinate systems for the studied breakup reaction with transversally polarized deuterons: The laboratory system ($x^{\prime },y^{\prime },z^{\prime }$), with $z^{\prime }$ along the beam momentum direction ($\mathsf{p}$${}_d$) and $y^{\prime }$ vertically upward, is used to define the angular configuration of the outgoing protons (with momenta $\mathsf{p}$${}_1$ and $\mathsf{p}$${}_2$). The reaction coordinate system is defined according to Ref. [32], with $z$ along the beam momentum direction and $x$ obtained by projection of $\mathsf{p}$${}_1$ onto the plane perpendicular to $z$. The angle $\varphi$ is defined as the angle between the $y$ axis and the spin quantization axis $s$, which in the studied case is vertical (parallel to $y^{\prime }$).

Figure 2

Schematic view of the experimental setup. The beam direction, the position of the target in the scattering chamber, the MultiWire Proportional Chamber (MWPC) and the $\Delta E$ and $E$ detectors are shown.

Figure 3

A schematic diagram of the electronics circuit.

Figure 4

An example of the $E_2$ versus $E_1$ energy spectrum for selected angular configuration of the breakup process (${\theta }_1={20}^{°}$, ${\theta }_2={15}^{°}$, ${\phi }_{12}={90}^{°}$). A sample $\Delta S$ bin is marked as a shaded area.

Figure 5

Examples of asymmetry distributions obtained for pure tensor polarization state $P=(0,-2$), for two (mirror) kinematical configurations with ${\theta }_1={25}^{°}$, ${\theta }_2={20}^{°}$, ${\phi }_{12}=\pm {140}^{°}$, and $S=100$ MeV. In the two top panels asymmetries $f_P^{\xi }(\varphi )$ for these configurations are presented, and in the two bottom panels their linear combinations, $g_P^{\xi }(\varphi )$ and $h_P^{\xi }(\varphi )$ (see text), are shown. The error bars represent statistical uncertainties. The lines result from the fit of the corresponding functions, as described in the text.

Figure 6

An example of the distribution of $A_{\mathit{xy}}$ versus $S$ for one geometry of the outgoing protons, specified in the panel. The results obtained for all beam states with nonzero tensor polarization (characterized with values of $P_Z$ and $P_{\mathit{ZZ}}$ in the legend) are shown together with their weighted average. For clarity, the data points corresponding to individual states have been slightly shifted in $S$.

Figure 7

The global ${\chi }^2/$DOF results presented as histograms and grouped with respect to the type of observable. Results of the free fit method are shown together with consistency check in the upper panel: ${\chi }^2/$DOF calculated for $O_i$ with respect to 0. In the lower panel the results of the parity-constrained fit are presented.

Figure 8

Set of maps of the ${\chi }^2/$DOF for all studied configurations; columns correspond to the five studied analyzing powers and rows to various theoretical calculations; see labels in the figure. Individual maps are shown for angular configurations defined by the relative azimuthal angle given on the abscissa: from $0^{°}$ to ${180}^{°}$ with step of ${20}^{°}$ and by pairs of polar angles (${\theta }_1,{\theta }_2$) on the ordinate, from bottom to top: (${15}^{°}$,${15}^{°}$), (${20}^{°}$,${15}^{°}$), (${25}^{°}$,${15}^{°}$), (${30}^{°}$,${15}^{°}$), (${20}^{°}$,${20}^{°}$), (${25}^{°}$,${20}^{°}$), (${30}^{°}$,${20}^{°}$), (${25}^{°}$,${25}^{°}$) and (${30}^{°}$,${25}^{°}$). White sectors in the map mark the configurations for which the particular observable could not be extracted.

Figure 9

Examples of vector analyzing power distributions obtained for geometries with central values of angles as shown in the panels. Error bars show statistical uncertainties alone. Experimental data are compared to bands representing results of ChPT calculations at N2LO (green, light gray) and N3LO (orange, dark gray).

Figure 10

Examples of tensor analyzing power distributions for the geometries where description of the data by theoretical calculations is not perfect. Meaning of the bands as in Fig. 9.

Figure 11

The same data as in Fig. 9 but compared to calculations with realistic potentials without (cyan, light gray) and with (magenta, dark gray) TM99 $3N$ force. The results of the coupled-channels calculations with the explicit $\Delta$ excitation, with and without Coulomb interaction, are shown as solid and dashed lines, respectively.

Figure 12

The same data as in Fig. 10 but compared to calculations with the realistic potentials. Meaning of lines and bands as in Fig. 11.

Figure 13

Examples of tensor analyzing power results obtained for configurations in which significant effects of the TM99 3NF are predicted. Meaning of lines and bands as in Fig. 11.

Figure 14

Quality of description of vector analyzing powers given by various models, presented as ${\chi }^2$ per degree of freedom in function of the relative energy of the two breakup protons.

Figure 15

The same as in Fig. 14 but for tensor analyzing powers.