Differential cross section and analyzing power measurements for $\overrightarrow{n}d$ elastic scattering at 248 MeV

The differential cross sections and vector analyzing powers for $\mathit{nd}$ elastic scattering at $E_n=248$ MeV were measured for $10°–180°$ in the center-of-mass (c.m.) system. To cover the wide angular range, the experiments were performed separately by using two different setups for forward and backward angles. The data are compared with theoretical results based on Faddeev calculations with realistic nucleon-nucleon ($\mathit{NN}$) forces such as AV18, CD Bonn, and Nijmegen I and II, and their combinations with the three-nucleon forces (3NFs), such as Tucson-Melbourne 99 (TM99), Urbana IX, and the coupled-channel potential with Δ-isobar excitation. Large discrepancies are found between the experimental cross sections and theory with only $2N$ forces for ${\theta }_{\mathrm{c}.\mathrm{m}.}>90°$. The inclusion of 3NFs brings the theoretical cross sections closer to the data but only partially explains this discrepancy. For the analyzing power, no significant improvement is found when 3NFs are included. Relativistic corrections are shown to be small for both the cross sections and the analyzing powers at this energy. For the cross sections, these effects are mostly seen in the very backward angles. Compared with the $\mathit{pd}$ cross section data, quite significant differences are observed at all scattering angles that cannot be explained only by the Coulomb interaction, which is usually significant at small angles.

Figure 1

Schematic view of ($n,p$) facility at RCNP. This facility mainly consists of a vacuum chamber for the neutron beam production, a clearing magnet for sweeping the primary beam, and a segmented target system with two MWDC boxes. The recoiled charged particles are momentum analyzed by the LAS and detected at the focal plane.

Figure 2

Solid lines in left and right panels show the spectra of CD${}_2$($n,d$) and CH${}_2$($n,p$), respectively. Shaded spectra were obtained from measurements with graphite targets. By subtracting the spectra of graphite targets from those of CD${}_2$ and CH${}_2$, we obtained the spectra of $\mathit{nd}$ and $\mathit{np}$ elastic scattering.

Figure 3

Schematic layout of neutron time-of-flight (NTOF) facility at RCNP. This facility mainly consists of a swinger magnet, thick collimator wall, 100 m TOF tunnel, and neutron detector NPOL II. Scattered neutrons and the recoiled deuterons are detected by the NPOL II and the active deuteron target, respectively.

Figure 4

Left panel shows the discrimination of neutron beam events from γ beam events; cluster of $\mathit{nd}$ elastic events can be seen. Middle and right panels show the spectra at ${\theta }_{\mathrm{lab}}=13°$ obtained with the BC537 and NE213 scintillators. White and gray histograms represent the energy excitation spectra corresponding to true coincidences and accidental coincidences, respectively.

Figure 5

Differential cross section for $\mathit{Nd}$ elastic scattering at 250 MeV. Solid circles and solid squares represent $\mathit{nd}$ elastic scattering cross sections at 248 MeV obtained with the ($n,p$) and the NTOF facility, respectively. Error bars represent only statistical errors. Open circles are data for $\mathit{pd}$ elastic scattering [27]. Light shaded (blue) band contains predictions of realistic $\mathit{NN}$ potentials: AV18, CD Bonn, Nijmegen I and II. Dark shaded (red) band shows results of combining these potentials with the TM99 3NF. Solid line is a prediction obtained with the AV18 + Urbana IX combination. Dot-dashed and dashed lines are predictions based on CD Bonn $+\Delta$ and CD Bonn potentials as described in Sec. 4b, respectively.

Figure 6

(Color online ) Nucleon vector analyzing powers in $\mathit{Nd}$ elastic scattering at 250 MeV. For the description of data and theoretical curves, see Fig. 5. Error bars represent statistical errors only.

Figure 7

Differential cross sections for $\mathit{Nd}$ elastic scattering at 250 MeV. Solid line is the result of nonrelativistic Faddeev calculation with CD Bonn potential. Relativistic predictions which include the approximations of Eqs. (6, 8), and (7) are shown by the dashed, dotted, and dash-dotted lines, respectively. For explanation of data points, see Fig.5.

Figure 8

Nucleon vector analyzing powers $A_y$ for $\mathit{Nd}$ elastic scattering at 250 MeV. For the description of data and curves, see Fig. 7.

Figure 9

Angular dependence of ratio between the $\mathit{pd}$ and $\mathit{nd}$ elastic scattering cross sections. Circles show the results deduced from the $\mathit{nd}$ and $\mathit{pd}$ data of Ref. [27] with statistical errors only. Hatched area in the lower panel shows systematic errors. Curves show theoretical predictions obtained by including the Coulomb effects in $\mathit{pd}$ calculations. Predictions in the upper panel include the Coulomb effect by the Doleschall approximation. Those in the middle panel include the Coulomb effect by the screening and renormalization approach. Solid and dotted lines represent the predictions based on the CD Bonn $+\Delta$ and CD Bonn potentials, respectively [35]. Dot-dashed line represents the prediction based on the CD Bonn potential [71]. Dot-dot-dashed line represents the prediction taking into account the 2 MeV energy difference between $\mathit{pd}$ and $\mathit{nd}$.