Momentum-space calculation of proton-deuteron scattering including Coulomb and irreducible three-nucleon forces

Three-nucleon scattering equations with irreducible three-nucleon force are solved in momentum-space. The Coulomb interaction between the two protons is included using the method of screening and renormalization. The need for the renormalization of the scattering amplitudes is demonstrated numerically. The Coulomb and Urbana IX three-nucleon force effects on the observables of elastic proton-deuteron scattering and breakup are studied.

Figure 1

Real and imaginary parts of nonrenormalized (left side) and renormalized (right side) $\mathit{pd}$ elastic scattering amplitudes (in arbitrary units) at $E_p=9$ MeV shown as functions of the c.m. scattering angle. The initial and final particle spin projection quantum numbers are $m_p=\frac{1}{2}$, $m_p^{\text{'}}=-\frac{1}{2}$, and $m_d=m_d^{\text{'}}=1$. Results for the $\mathrm{AV}18+\mathrm{UIX}$ force model obtained with the screening radius $R=5$ fm (dashed curves), 10 fm (dash-dotted curves), 15 fm (dotted curves), and 20 fm (solid curves) are compared.

Figure 2

Real and imaginary parts of the renormalized $\mathit{pd}$ elastic scattering amplitude. The initial and final particle spin projection quantum numbers are $m_p=m_p^{\text{'}}=\frac{1}{2}$ and $m_d=m_d^{\text{'}}=1$. Curves are as in Fig. 1.

Figure 3

Differential cross section and analyzing powers for $\mathit{pd}$ elastic scattering at 9-MeV proton laboratory energy as functions of the c.m. scattering angle. Results for AV18 (dashed-dotted curves) and $\mathrm{AV}18+\mathrm{UIX}$ (solid curves) force models, both including Coulomb, and for $\mathrm{AV}18+\mathrm{UIX}$ without Coulomb (dotted curves) are compared with the experimental data from Ref. [23].

Figure 4

Differential cross section and analyzing powers for $\mathit{pd}$ elastic scattering at 135-MeV proton laboratory energy. Results for AV18 (dashed-dotted curves), $\mathrm{AV}18+\mathrm{UIX}$ (solid curves), CD Bonn (dotted curves), and $\mathrm{CD}\mathrm{\hspace{1em}\hspace{1em}}\mathrm{Bonn}+\mathrm{\Delta }$ (dashed curves) force models, all including Coulomb, are compared with the experimental data from Ref. [25] (solid circles) and Ref. [26] (open squares).

Figure 5

Differential cross section for $\mathit{pd}$ breakup at 13-MeV proton laboratory energy in space star (left), quasifree scattering (middle), and collinear (right) configurations as function of the arclength $S$ along the kinematical curve. Curves are as in Fig. 3 and the experimental data are from Ref. [29] (solid circles). For the space-star configuration also the $\mathit{nd}$ data from Refs. [30, 31] (open and solid squares) are shown.

Figure 6

Differential cross section for $\mathit{pd}$ breakup at 130-MeV deuteron laboratory energy in selected kinematical configurations with small relative azimuthal angle. Curves are as in Fig. 3 and the experimental data are from Refs. [32, 33].

Figure 7

Differential cross section for $\mathit{pd}$ breakup at 130-MeV deuteron laboratory energy in selected kinematical configurations with large relative azimuthal angle. Curves are as in Fig. 3 and the experimental data are from Ref. [32].

Figure 8

Deuteron analyzing power $A_{\mathit{xx}}$ for $\mathit{pd}$ breakup at 130-MeV deuteron laboratory energy in selected kinematical configurations. Curves are as in Fig. 3.