Polarized proton+${}^{4,6,8}$He elastic scattering with breakup effects in the eikonal approximation

We study the elastic scattering of polarized protons from He isotopes. The central and spin-orbit parts of the optical potential are derived using the Glauber theory that can naturally take account of the breakup effect of the He isotopes. Both the differential cross section and the vector analyzing power for $p+{}^{4,6,8}\text{He}$ scattering at 71 MeV are in reasonable agreement with experiment. Scattering observables at 300 MeV are predicted. The Pauli blocking effect is examined at 71 MeV.

Figure 1

Density distributions of ${}^{4,6,8}$He calculated with the VMC wave functions. Solid and dotted lines denote the neutron and proton distributions, respectively.

Figure 2

Optical potentials for $p+{}^{4,6,8}\text{He}$ elastic scattering at 71 MeV. The central and spin-orbit potentials are shown in Fig. 2a and 2b, respectively. The left and right panels are the real and imaginary potentials, respectively. The spin-orbit imaginary potentials of ${}^6$He and ${}^8$He are set to be zero. Solid and dash-dotted lines are the potentials of the full eikonal model and the folding model, respectively.

Figure 3

Angular distributions for $p+{}^{4,6,8}\mathrm{He}$ elastic scattering at 71 MeV. The upper panels show the differential cross sections and the lower panels the vector analyzing powers. Solid lines are full eikonal calculations (10), dotted lines are the approximation in the leading-order cumulant expansion (12), and dash-dotted lines are the folding model calculations (11). Experimental data are taken from Ref. [7] for ${}^4$He, from Refs. [1, 26] for ${}^6$He, and from Refs. [2, 27] for ${}^8$He.

Figure 4

Angular distributions for $p+{}^{4,6,8}\mathrm{He}$ elastic scattering at 71 MeV compared between calculations and experiment. Solid lines are the results of the present model with the Pauli-blocking effect, while dash-dotted lines are the results taken from Ref. [5]. See the caption of Fig. 3 for the experimental data.

Figure 5

Optical potentials for $p+{}^4\mathrm{He}$ elastic scattering at 71 MeV. The upper two panels show the central and spin-orbit real potentials while the lower two panels show the imaginary potentials. Solid and dotted lines denote the potentials of the full calculation with and without the Pauli-blocking effect, respectively.

Figure 6

Optical potentials for $p+{}^4\mathrm{He}$ elastic scattering at 300 and 550 MeV. The upper two panels show the central and spin-orbit real potentials while the lower two panels show the imaginary potentials. Solid and dash-dotted lines denote the full and folding potentials at 300 MeV, whereas dotted and dash-dot-dotted lines denote the full and folding potentials at 550 MeV.

Figure 7

Angular distributions for $p+{}^4\mathrm{He}$ elastic scattering at 300 and 550 MeV. Displayed are the differential cross section (a), the vector analyzing power (b), and the spin-rotation function (c). The values of $V_{\mathrm{so}}$ are 0.1 and $-$0.05 for the real and imaginary potentials at 300 MeV and 0.9 (0.09 for the folding calculation) and $-$0.025 at 550 MeV. Solid, dotted, and dash-dotted lines indicate the same types of calculations as those of Fig. 3. Experimental data are taken from Ref. [31] for 300 MeV and from Ref. [32] for 500 MeV.

Figure 8

Angular distributions for $p+{}^6\text{He}$ elastic scattering at 300 MeV. The left panels show the results calculated with $V_{\mathrm{so}}=0.1$ for the real potential, the same strength as that of ${}^4$He at 300 MeV, while the right panels show the results with $V_{\mathrm{so}}=0.2$. The spin-orbit imaginary potential is set to be 0.05, which is the same as that of ${}^4$He. Solid, dotted, and dash-dotted lines indicate the same types of calculations as those of Fig. 3.

Figure 9

The same as Fig. 8 but for $p+{}^8\text{He}$ elastic scattering at 300 MeV.