Spin-correlation coefficients and phase-shift analysis for $p+{}^3\mathrm{He}$ elastic scattering

Angular distributions for the target spin-dependent observables $A_{0y}$, $A_{\mathit{xx}}$, and $A_{\mathit{yy}}$ have been measured using polarized proton beams at several energies between 2 and 6 MeV and a spin-exchange optical pumping polarized ${}^3\mathrm{He}$ target. These measurements have been included in a global phase-shift analysis following that of E. A. George and L. D. Knutson [Phys. Rev. C 67, 027001 (2003)], who reported two best-fit phase-shift solutions to the previous global $p+{}^3\mathrm{He}$ elastic-scattering database below 12 MeV. These new measurements, along with measurements of cross-section and beam-analyzing power made over a similar energy range by B. M. Fisher et al. [Phys. Rev. C 74, 034001 (2006)], allowed a single, unique solution to be obtained. The new measurements and phase shifts are compared with theoretical calculations using realistic nucleon-nucleon potential models.

Figure 1

Diagram of the experimental arrangement. The polarimeter chamber at left was used with the detectors either horizontal, as shown, or vertical. The polarimeter cell was removed from the beam during data taking to allow the beam to reach the target chamber. The coordinate system used to define the scattering observables is also shown.

Figure 2

${}^3\mathrm{He}$($p,p$)${}^3\mathrm{He}$ spectrum taken at 5.54 MeV and ${90}^{°}$.

Figure 3

Steering of the incoming proton beam and scattered particles by the sine-$\theta$ coil’s magnetic field. The target cell and detectors are shown from above. The beam is incident from the left on the gas cell along the dotted line, but deflected as shown by the magnetic field, which is oriented out of the page. Similarly, the scattered particles travel along curved paths to the detectors. The figure is not to scale, and the size of the effect is exaggerated for clarity.

Figure 4

Instrumental target asymmetries measured at 2.25 MeV with the sine-$\theta$ coil’s magnetic field both on and off. A simple calculation of the effect of magnetic steering that ignores the finite size of the beam and target is also shown.

Figure 5

Present measurements of $A_{0y}$ at five proton beam energies, together with the global PSA fit. Measurements of Szaloky and Seiler [30] and Alley and Knutson [13] as well as theoretical calculations of Deltuva and Fonseca [36] using the CD-Bonn potential [37] are also shown.

Figure 6

Present measurements of $A_{\mathit{yy}}$ at five proton beam energies, together with other results as mentioned for Fig. 5.

Figure 7

Present measurements of $A_{\mathit{xx}}$ at three proton beam energies, together with other results as mentioned for Fig. 5.

Figure 8

Phase-shift results, in degrees, as functions of proton laboratory energy in MeV. Both the global and single-energy results of this analysis are shown, as well as the previous results of Alley and Knutson [35] and George and Knutson [6].

Figure 9

Comparison of the present $P$-wave phase shifts, in degrees, with the theoretical results of Deltuva and Fonseca [36] using the CD-Bonn and Doleschall INOY04 potentials and the results of Viviani [42] using a potential derived from chiral potential theory (ChPT). The splitting $\delta$ is defined in the text.

Figure 10

Comparison of the present observables $A_{0y}$ and $A_{\mathit{yy}}$ measured at 4 MeV, along with the $A_{y0}$ measurements of Fisher et al. [4], with the theoretical results of Viviani [42] using a using a potential derived from chiral potential theory (ChPT). The results of Deltuva and Fonseca [36] using the CD-Bonn and INOY04 potentials are also shown.