Testing nuclear forces by polarization transfer coefficients in $d(\overrightarrow{p},\overrightarrow{p})d$ and $d(\overrightarrow{p},\overrightarrow{d})p$ reactions at $E_p^{\mathrm{lab}}=22.7$ MeV

The proton to proton polarization transfer coefficients $K_x^{x^{\text{'}}},K_y^{y^{\text{'}}}$, and $K_z^{x^{\text{'}}}$, and the proton to deuteron polarization transfer coefficients $K_x^{x^{\text{'}}},K_y^{y^{\text{'}}},K_z^{x^{\text{'}}}$, $K_x^{y^{\text{'}}{z}^{\text{'}}},K_y^{z^{\text{'}}{z}^{\text{'}}},K_z^{y^{\text{'}}{z}^{\text{'}}},K_y^{x^{\text{'}}{z}^{\text{'}}}$, and $K_y^{x^{\text{'}}{x}^{\text{'}}-y^{\text{'}}{y}^{\text{'}}}$ were measured in $d(\overrightarrow{p},\overrightarrow{p})d$ and $d(\overrightarrow{p},\overrightarrow{d})p$ reactions, respectively, at $E_p^{\mathrm{lab}}=22.7$ MeV. The data were compared to predictions of modern nuclear forces obtained by solving the three-nucleon Faddeev equations in momentum space. Realistic (semi)phenomenological nucleon-nucleon potentials combined with model three-nucleon forces and modern chiral nuclear forces were used. The AV18, CD Bonn, and Nijm I and II nucleon-nucleon interactions were applied alone or combined with the Tucson-Melbourne 99 three-nucleon force, adjusted separately for each potential to reproduce the triton binding energy. For the AV18 potential, the Urbana IX three-nucleon force was also used. In addition, chiral NN potentials in the next-to-leading order and chiral two- and three-nucleon forces in the next-to-next-to-leading order were applied. Only when three-nucleon forces are included does a satisfactory description of all data result. For the chiral approach, the restriction to the forces in the next-to-leading order is insufficient. Only when going over to the next-to-next-to-leading order does one get a satisfactory description of the data, similar to the one obtained with the (semi)phenomenological forces.

Figure 1

Nucleon to nucleon spin transfer coefficients in Nd elastic scattering at $E_N^{\mathrm{lab}}=22.7$ MeV. Crosses are pd data from [31, 32, 33]. Dashed line is the result of the hyperspherical harmonic expansion method with AV18 potential. Solid line is the corresponding result when the pp Coulomb force is included.

Figure 2

Same as Fig. 1, but for nucleon to vector-deuteron spin transfer coefficients.

Figure 3

Same as Fig. 1, but for nucleon to tensor-deuteron spin transfer coefficients.

Figure 4

Nucleon to nucleon spin transfer coefficients in Nd elastic scattering at $E_N^{\mathrm{lab}}=22.7$ MeV. Crosses are pd data from [31, 32, 33]; ${x}$, s are the corresponding nd data obtained by subtracting the pp Coulomb force effects (see text for explanation). Light (blue) band results from theoretical predictions obtained with the AV18, CD Bonn, Nijm I, and Nijm II NN potentials. Dark (magenta) band is obtained when these interactions are combined with the TM99 3NF. Solid line is the prediction of the AV18 + Urbana IX 3NF.

Figure 5

Same as Fig. 4, but for nucleon to vector-deuteron spin transfer coefficients.

Figure 6

Same as Fig. 4, but for nucleon to tensor-deuteron spin transfer coefficients.

Figure 7

Nucleon to nucleon spin transfer coefficients in Nd elastic scattering at $E_N^{\mathrm{lab}}=22.7$ MeV. Symbols are the same as in Fig. 4. Light (blue) band results from theoretical predictions obtained with the NLO chiral potential with different cutoff parameters. Dark (red) band results when in NNLO the NN and 3N forces are included.

Figure 8

Same as Fig. 7, but for nucleon to vector-deuteron spin transfer coefficients.

Figure 9

Same as Fig. 7, but for nucleon to tensor-deuteron spin transfer coefficients.