Spin correlation coefficient for proton-${}^3\mathrm{He}$ elastic scattering at 100 MeV

We present the measured spin correlation coefficient $C_{y,y}$ for $p\text{−}{}^3\mathrm{He}$ elastic scattering at 100 MeV at the angles ${\theta }_{\mathrm{c}.\mathrm{m}.}=46.9^{\circ }$–$149.2^{\circ }$ in the center-of-mass system. The $C_{y,y}$ data and the existing cross section data are compared with rigorous four-nucleon scattering calculations based on realistic nucleon-nucleon potentials. Large differences are seen in the regime around the cross section minimum for both observables. The $\mathrm{\Delta }$-isobar effects estimated by the $NN+N\mathrm{\Delta }$ coupled-channels approach are small for the cross section. Meanwhile, in $C_{y,y}$, the $\mathrm{\Delta }$-isobar effects improve the agreement with the data. The analysis of the $p\text{−}{}^3\mathrm{He}$ elastic scattering amplitudes implies the necessity of three-nucleon forces ($3N\text{Fs}$) that enhance the vector components in the amplitudes. The obtained results indicate that the spin correlation coefficient $C_{y,y}$ expands the knowledge of the nuclear interactions with the $\mathrm{\Delta }$ isobar or those including $3N\text{Fs}$ that are masked in nucleon-deuteron elastic scattering.

Figure 1

Schematic layout of the experimental setup for the measurement of the spin correlation coefficient.

Figure 2

Light output spectra of scattered protons obtained by the NaI(Tl) scintillators at ${\theta }_{\mathrm{lab}.}={55}^{\circ }$ and ${95}^{\circ }$. The hatched regions indicate events obtained with the reference cell.

Figure 3

Angular distributions of the spin correlation coefficient $C_{y,y}$ for $p\text{−}{}^3\mathrm{He}$ elastic scattering at 100 MeV. 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 black solid (CD Bonn) and blue dotted (INOY04) lines. The red dot-dashed line is the calculation based on the CD $\text{Bonn}+\mathrm{\Delta }$ potential.

Figure 4

Angular distributions of the cross section $d\sigma /d\mathrm{\Omega }$ for $p\text{−}{}^3\mathrm{He}$ elastic scattering at 100 MeV. Data are from Ref. [16]. For descriptions of the calculations, see Fig. 3.

Figure 5

Effects of the $2N$ dispersion (dot-dashed 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 100 MeV are shown as functions of the c.m. scattering angle for the cross section in the panel (a) and the spin correlation coefficient $C_{y,y}$ in the panel (b). For the cross section, the result of each contribution is shown as a ratio to the prediction based on the CD Bonn potential. For the spin correlation coefficient $C_{y,y}$, the differences from the prediction of the CD Bonn potential, Eq. (5), are presented.

Figure 6

(a) Angular distributions of $C_{y,y}$ and components $C_{y,y}^{\left(i\right)}(i=1,\cdots ,4)$ for CD Bonn compared with the present experimental data. The thick solid (black) line denotes $C_{y,y}$. Dashed (green), dotted (blue), dot-dashed (red), and dot-dot-dashed (magenta) lines denote $C_{y,y}^{\left(1\right)}, C_{y,y}^{\left(2\right)}, C_{y,y}^{\left(3\right)}$, and $C_{y,y}^{\left(4\right)}$, respectively. (b) Effects of the $\mathrm{\Delta }$-isobar on $C_{y,y}$ and components $C_{y,y}^{\left(i\right)}(i=1,\cdots ,4)$ are defined in Eq. (5). The notation of the lines is the same as in panel (a).

Figure 7

Calculations with the modified amplitudes of the CD Bonn for (a) the differential cross section and (b) $C_{y,y}$. Solid curves are the results of CD Bonn. In panel (a), the dashed curve is the result for ${\lambda }_h=2.4$. In the panel (b), the dashed and dot-dashed curves are the results for set A, $({\lambda }_h,{\varphi }_h)=(2.4,{36}^{\circ })$, and for set B, $({\lambda }_h,{\varphi }_h)=(2.4,{251}^{\circ })$, respectively.

Figure 8

(a) Differential cross section for $p{\text{−}}^3\mathrm{He}$ scattering at $E_p=100$ MeV. Solid curves are results with CD Bonn, while dashed curves are results with CD $\text{Bonn}+\mathrm{\Delta }$. Experimental data are taken from Ref. [16]. (b) Differential cross section for $d\text{−}p$ elastic scattering at 135 MeV/nucleon. Solid curves are results with CD Bonn, dashed curves are results with CD $\text{Bonn}+\mathrm{\Delta }$, and long-dashed curves are results with CD $\text{Bonn}+\mathrm{\Delta }+\mathrm{U}2$. Experimental data are taken from Ref. [34].