Partial-wave analysis of nucleon-nucleon elastic scattering data

Energy-dependent and single-energy fits to the existing nucleon-nucleon database have been updated to incorporate recent measurements. The fits cover a region from threshold to 3 GeV, in the laboratory kinetic energy, for proton-proton scattering, with an upper limit of 1.3 GeV for neutron-proton scattering. Experiments carried out at the COSY-WASA and COSY-ANKE facilities have had a significant impact on the partial-wave solutions. Results are discussed in terms of both partial-wave and direct reconstruction amplitudes.

Figure 1

Cross sections for $pp$ elastic scattering. Data from the SAID database [22]. Recent COSY data plotted as solid black circles: (a) 2000, (b) 2200, (c) 2400, and (d) 2800 MeV; older COSY data within $\pm 4$ MeV shown as open black circles. Red solid (green long dot-dashed) lines correspond to the recent SM16 (WF16) solutions. The previous SP07 [8] solution is plotted with blue dashed lines.

Figure 2

Polarized observable $A_y$ for $pp$ elastic scattering. Recent COSY data plotted as solid black circles: (a) 796, (b) 1600, (c) 1800, and (d) 1965 MeV. Data within $\pm 8$ MeV from the SAID database [22] (COSY, SATURN, LAMPF, and ANL) shown as open black circles, open magenta triangles, solid blue triangles, and solid green squares. Notation for energy-dependent fits as in Fig. 1.

Figure 3

Total unpolarized (a) and (b) and polarized (c) and (d) cross sections for $pp$ scattering. Quasidata for total reaction cross sections from Refs. [25] and [5] are given by black crosses and open diamonds, respectively. Pion production threshold shown as a vertical red arrow. Notation for energy-dependent fits as in Fig. 1. Additionally, the older SM97 solution [15] is plotted as magenta short dot-dashed lines.

Figure 4

Histograms (a) for $pp$ scattering data (open blue bars) and observable types (filled green bars) and (b) for $np$ data in the same notation.

Figure 5

Comparison of the SES and energy-dependent (ED) fits in terms of $\delta {\chi }^2=[{\chi }^2\left(\mathrm{ED}\right)-{\chi }^2\left(\mathrm{SES}\right)]/\mathrm{data}$ for (a) $pp$ and (b) $np$ data. The SM16 and SP07 ED fits are displayed as blue solid and black open symbols, respectively.

Figure 6

DAR of $a$ to $e$ for $pp$ elastic scattering at $T_{\mathrm{lab}}=1.8$ GeV as a function of c.m. scattering angle. Real and imaginary parts of the Saclay amplitudes [6] are shown as black open circles. Notation for SAID energy-dependent amplitudes as in Fig. 1.

Figure 7

DAR of $a$ to $e$ for $pp$ elastic scattering at $T_{\mathrm{lab}}=2.1$ GeV as a function of c.m. scattering angle. Notation as in Fig. 6.

Figure 8

DAR of $a$ to $e$ for $pp$ elastic scattering at $T_{\mathrm{lab}}=2.4$ GeV as a function of c.m. scattering angle. Notation as in Fig. 6.

Figure 9

DAR of $a$ to $e$ for $pp$ elastic scattering at $T_{\mathrm{lab}}=2.7$ GeV as a function of c.m. scattering angle. Notation as in Fig. 6.

Figure 10

DAR of $a$ to $e$ for $np$ elastic scattering at $T_{\mathrm{lab}}=0.80$ GeV as a function of c.m. scattering angle. Real and imaginary parts of the Saclay amplitudes [7] are shown as black open circles. Notation for SAID amplitudes as in Fig. 1.

Figure 11

DAR of $a$ to $e$ for $np$ elastic scattering at $T_{\mathrm{lab}}$ = 0.84 GeV as a function of c.m. scattering angle. Notation as in Fig. 10.

Figure 12

DAR of $a$ to $e$ for $np$ elastic scattering at $T_{\mathrm{lab}}$ = 0.88 GeV as a function of c.m. scattering angle. Notation as in Fig. 10.

Figure 13

DAR of $a$ to $e$ for $np$ elastic scattering at $T_{\mathrm{lab}}$ = 0.94 GeV as a function of c.m. scattering angle. Notation as in Fig. 10.

Figure 14

DAR of $a$ to $e$ for $np$ elastic scattering at $T_{\mathrm{lab}}$ = 1.00 GeV as a function of c.m. scattering angle. Notation as in Fig. 10.

Figure 15

DAR of $a$ to $e$ for $np$ elastic scattering at $T_{\mathrm{lab}}=1.10$ GeV as a function of c.m. scattering angle. Notation as in Fig. 10.

Figure 16

Dominant isovector partial-wave amplitudes from threshold to $T_{\mathrm{lab}}=3$ GeV. (a) ${}^{1}S_0$, (b) ${}^{3}P_0$, (c) ${}^{3}P_1$, (d) ${}^{1}D_2$, (e) ${}^{3}F_3$, (f) ${}^{1}G_4$, and (g) ${}^{3}H_5$. Real (imaginary) parts of energy-dependent solutions SM16, WF16, and SP07 are plotted as red solid (dotted), green long dot-dashed (short dot-dashed), and blue short-dashed (long-dashed) lines, respectively. Real (imaginary) parts of SES, corresponding to the energy-dependent fit SM16, are plotted with blue open circles (triangles). All amplitudes are dimensionless.

Figure 17

Phase-shift parameters for dominant isovector partial-wave amplitudes from threshold to $T_{\mathrm{lab}}=3$ GeV. (a) ${}^{3}P_2$, (b) ${}^{3}F_2$, (c) ${}^{3}F_4$, and (a) ${}^{3}H_4$. Saclay SES phase-shifts [6] are shown as black filled circles; SAID SES are plotted as open blue circles. Notation for SAID energy-dependent amplitudes as in Fig. 1.

Figure 18

Dominant isoscalar partial-wave amplitudes from threshold to $T_{\mathrm{lab}}=1.3$ GeV. (a) ${}^{3}S_1$, (b) ${}^{3}D_1$, (c) ${}^{3}D_3$, (d) ${}^{3}G_3$, (e) ${}^{3}G_5$, (f) ${\epsilon }_1$, (g) ${\epsilon }_3$, and (h) ${\epsilon }_5$. Notation as in Fig. 16. Revised SAID solution for ${}^{3}D_3, {}^{3}G_3$, and ${\epsilon }_3$, with a pole, is plotted as magenta short dot-dashed (short dashed) lines for the real (imaginary) parts. Red vertical arrows indicate the WASA resonance mass $W_R$ value and the red horizontal bar gives the full width $\mathrm{\Gamma }$ [12].

Figure 19

Phase-shift parameters for dominant isoscalar partial-wave amplitudes from threshold to $T_{\mathrm{lab}}=1.3$ GeV. (a) ${}^{1}P_1$, (b) ${}^{3}D_2$, (c) ${}^{1}F_3$, and (d) ${}^{3}G_4$. The Saclay SES [7] are given by black filled circles; SAID SES are plotted as open blue circles. Notation for SAID energy-dependent amplitudes as in Fig. 1.