Proton-${}^3\mathrm{He}$ elastic scattering at intermediate energies

We present a precise measurement of the cross section, proton and ${}^3\mathrm{He}$ analyzing powers, and spin correlation coefficient $C_{y,y}$ for $p\text{−}{}^3\mathrm{He}$ elastic scattering near 65 MeV, and a comparison with rigorous four-nucleon scattering calculations based on realistic nuclear potentials and a model with $\mathrm{\Delta }$-isobar excitation. Clear discrepancies are seen in some of the measured observables in the regime around the cross section minimum. Theoretical predictions using scaling relations between the calculated cross section and the ${}^3\mathrm{He}$ binding energy are not successful in reproducing the data. Large sensitivity to the $NN$ potentials and rather small $\mathrm{\Delta }$-isobar effects in the calculated cross section are noticed as different features from those in the deuteron-proton elastic scattering. The results obtained above indicate that $p\text{−}{}^3\mathrm{He}$ scattering at intermediate energies is an excellent tool to explore nuclear interactions not accessible by three-nucleon scattering.

Figure 1

Schematic layout of the experimental setup for the measurement of the cross section and the proton analyzing power $A_y$.

Figure 2

Light output spectrum of scattered protons obtained by the NaI(Tl) scintillator at ${\theta }_{\mathrm{lab}.}$ = ${75}^{\circ }$. The hatched region indicates events obtained with the empty target cell.

Figure 3

Schematic layout of the experimental setup for the measurement of the ${}^3\mathrm{He}$ analyzing power $A_{0y}$.

Figure 4

Angular distributions of $d\sigma /d\mathrm{\Omega }$ as well as $A_y$ at 65 MeV, $A_{0y}$ at 70 MeV, and $C_{y,y}$ at 65 MeV for $p\text{−}{}^3\mathrm{He}$ elastic scattering. Experimental data (solid circles) are compared with the calculations from the solutions of exact AGS equations. Only statistical errors are indicated. Calculations based on the $NN$ potentials are shown with magenta dash-dotted (AV18), black solid (CD Bonn), red dot-dot-dashed (INOY04), green solid (SMS400), and green dashed (SMS500) lines. Black dashed lines are calculations based on the CD $\mathrm{Bonn}+\mathrm{\Delta }$ potential.

Figure 5

Relation between the ${}^3\mathrm{He}$ binding energy and the cross section for $p\text{−}{}^3\mathrm{He}$ elastic scattering at around 65 MeV in panels (a), (b), and (c); and that between the ${}^3\mathrm{H}$ binding energy and the cross section for $d\text{−}p$ elastic scattering at 70 MeV/nucleon in panels (d), (e), and (f). The result of the cross section for each nuclear potential is shown as a ratio to the corresponding experimental data. The dashed vertical straight lines denote the experimental binding energy of the ${}^3\mathrm{He}$ in panels (a)–(c) and that of ${}^3\mathrm{H}$ in panels (d)–(f). For the scattering data the statistical (systematic) errors are shown with bars (bands). Correlation lines obtained with the results of the $NN$ potentials are shown with red lines.

Figure 6

Effects of the $2N$ dispersion (dash-dotted lines), those of $3N$- and $4N$-forces (dotted lines), and the total $\mathrm{\Delta }$-isobar effects (solid lines) in the $p\text{−}{}^3\mathrm{He}$ elastic scattering at 65 MeV are shown as a function of the c.m. scattering angle for the cross section in panel (a) and the spin correlation coefficient $C_{y,y}$ in panel (b). For the cross section, the result of each contribution is shown as a ratio to the calculation based on the CD Bonn potential. For the spin correlation coefficient $C_{y,y}$, the differences from the calculation of the CD Bonn potential are presented.