In this paper we review the results of a series of high-accuracy measurements on the neutron-deuteron (n-d) scattering system at incident neutron energies below 20 MeV. These measurements were designed to: 1) provide data of sufficient accuracy to be used to refine the parametrization of the nucleon-nucleon force, 2) to test the reaction dynamics in the “rigorous” calculations of three-nucleon (3N) breakup reactions, and 3) identify 3N scattering observables that are specifically sensitive to three-nucleon forces and/or off-shell effects. At TUNL we have measured vector analyzing powers Ay (θ) for n-d elastic scattering and the breakup reaction to an accuracy better than ± 0.005 and ± 0.020, respectively. Recent results on items 1) and 2) will be presented. Also, results of cross-section measurements for n-d and p-d breakup will be compared to a “rigorous” 3N calculation.

Experimental methods to measure the vector analyzing powers over a broad range of kinematic configurations in the n-d breakup reaction have been developed at TUNL. These techniques employ the polarized beam facilities at TUNL and use the 2H(d, n)3He reaction as a source of low-energy polarized neutrons. Our methods permit measurements to a high statistical accuracy over a large fraction of three-nucleon phase space. The techniques are described and experimental spectra along with kinematic calculations are presented.

Measurements of the differential cross sections and analyzing powers have been made for $^{28}$Si(n,${n}_{0}$) and $^{28}$Si(n,${n}_{1}$) for incident neutron energies between 8 and 17 MeV. These data have been combined with previous differential and total cross-section data to obtain the most complete data set for neutron scattering from $^{28}\mathrm{Si}$ over the 8--40 MeV energy range. The data have been described within the framework of a symmetric rotational model using phenomenological coupled-channels calculations. Nuclear moments were deduced and they are in good agreement with those obtained from electron scattering and Coulomb excitation measurements. Various calculations were performed to determine the sensitivity of the data and calculations to the signs of the potential deformation parameters ${\ensuremath{\beta}}_{2}$ and ${\ensuremath{\beta}}_{4}$. The systematic analysis of the analyzing power data enabled the determination of the deformation length for the spin-orbit potential. Comparisons between neutron- and proton-scattering data and calculations were made to test the sensitivity of this type of data to charge symmetry breaking in the nuclear force and to investigate the isospin dependence of the absorptive part of the nucleon-nucleus scattering potential for $^{28}\mathrm{Si}$. The results of these comparisons suggest that the differences between $^{28}$Si+n and $^{28}$Si+p scattering can be attributed solely to Coulomb effects.

The vector analyzing power for the $n+d\ensuremath{\rightarrow}n+n+p$ breakup reaction was measured at 12 MeV. Data for $n\ensuremath{-}p$ final-state interaction and $n\ensuremath{-}p$ quasifree scattering, along with elastic-scattering data, are compared to rigorous three-nucleon calculations using the Paris and Bonn $N\ensuremath{-}N$ potentials. Calculations agree with the quasifree data and with the elastic and $n\ensuremath{-}p$ final-state-interaction data except around ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=120\ifmmode^\circ\else\textdegree\fi{}$.

High-accuracy analyzing-powerAy(θ) data forn-d elastic scattering at 12 MeV have been measured using the polarized-neutron facilities at the Triangle Universities Nuclear Laboratory (TUNL). The present data have been combined with our previousn-d measurements at 10, 12, and 14.1 MeV to form the highest-accuracyAy(θ) data set forn-d elastic scattering below 20 MeV. These data are compared to recent Faddeev-based neutron-deuteron (n-d) calculations which use the Paris and Bonn equivalent separable potentials PEST and BEST, as well as Doleschall's representation of theP- andD-wave nucleon-nucleon interactions. None of these models adequately describe the data in the angular region around the maximum ofAy(θ). Possible reasons for the discrepancies are discussed. The sensitivity of the present Faddeev-based calculations to various angular momentum components of the nucleon-nucleon interaction are examined.

Differential cross sections at 16.44 and 17.57 MeV and analyzing powers at 8.0, 9.1, 11.1, 13.5 and 15.0 MeV have been measured for the 9Be(p, n0)9B reaction and combined with previous measurements for 9Be(p, p0)9Be, 9Be(p, n0)9B and 9Be(n, n0)9Be to form the first model-complete data base for a Lane model analysis. Energy dependences of the model parameters (including Coulomb corrections) have been handled in a consistent manner. The real central part of the isovector Lane model potential exhibits no surface peaking for this nucleus. Strong evidence is found for a complex spin-orbit part of the isovector potential describing nucleon scattering from 9Be.

Time-of-flight techniques were used to measure the analyzing power for the scattering of neutrons from 9Be at energies from 9 to 17 MeV. Because of the high nuclear density of beryllium, particular attention was paid to finite-geometry and multiple-scattering effects. For representing the data, an unusual method of Legendre-coefficient analysis was used to establish the smooth energy dependence of both the cross section σ(θ) and the analyzing power Ay(θ). Spherical optical-model calculations were able to describe the σ(θ) and Ay(θ) data simultaneously, but only after the introduction of an imaginary spin-orbit potential Ws.o.(r). The geometry of the Ws.o.(r) term was found to be the same as that of the surface-peaked imaginary central potential. Coupledchannels calculations using a quadrupole-deformed rotational model built on the 32− ground state were able to describe inelastic scattering to the 52− and 72− excited states, but also required a Ws.o.r potential.

The analyzing power Ay(θ) and polarization Py(θ) for the 15N(p, n0)15O reaction have been measured for Ep = 4.5–11.3 MeV. The values of the two observables are nearly the same above 11 MeV, where a “quasi-elastic” view of the (p, n) reaction to the analog state should be applicable. Below 10 MeV, however, large spin-flip amplitudes and isospin-mixing ratios provide the two major conditions needed to obtain Py(θ) ≠ Ay(θ), and dramatic differences between the two observables are observed. The size of the differences and their dependence on energy are similar to the results predicted by shell-model calculations. The Py(θ) and Ay(θ) measurements have been combined with existing cross-section data to provide information about spin-flip processes. We also comment on the connection between comparisons of Py (θ) and Ay (θ) in charge-symmetric (p, n) reactions and the recent controversial measurements of a difference between the values of Py(θ) for a reaction and Ay(θ) for the inverse reaction.

Neutron time-of-flight techniques were used to measure the 9Be(p, n0)9B cross section from 0° to 160°(lab) at 10 energies between 8.15 and 15.68 MeV. The data are combined with previous results below 30 MeV in a Legendre coefficient analysis to evaluate the differential and integral behavior of the 9Be(p,n) and 9Be(p, n0)9B cross sections. A coupled-channels Lane analysis of cross sections and analyzing powers for (p,n) quasi-elastic scattering and (p, p) and (n, n) elastic scattering is presented and compared to previous single-channel models.

The analyzing power Ay(θ) for 12C(n,n)12C elastic scattering and for inelastic scattering to the first excited state (Jπ = 2+, Q = −4.44 MeV) of 12C was measured in the energy range from 8.9 to 14.9 MeV in 1 MeV steps. A pulsed polarized neutron beam was produced via the su2rmH(d,n)3He polarization transfer reaction. Monte Carlo simulations were used to correct the data for finite geometry and multiple scattering effects. The Ay data, together with published crosssection data, were analyzed in the framework of the spherical optical model and in the coupled-channels formalism. A good description of the data has been achieved.

Angular distributions of the analyzing power ${A}_{y}(\ensuremath{\bigominus})$ have been measured for elastic scattering of neutrons from $^{54}\mathrm{Fe}$ and $^{65}\mathrm{Cu}$ at 10 and 14 MeV and for inelastic scattering to the first ${2}^{+}$ state of $^{54}\mathrm{Fe}$ at 10 MeV. We have combined the results with previous measurements and analyses of the differential cross sections in the same energy range and have carried out new deformed optical model calculations where the major concern was to study the spin-orbit interaction. The need for an imaginary spin-orbit term ${W}_{\mathrm{SO}}(r)$ is discussed. The (n, n\ensuremath{'}) data are important in reducing an ambiguity found between the deformation ${\ensuremath{\beta}}_{\mathrm{SO}}$ of the real spin-orbit potential and the strength ${W}_{\mathrm{SO}}$ of the imaginary spin-orbit potential.NUCLEAR REACTIONS $^{54}\mathrm{Fe}$, $^{65}\mathrm{Cu}$(n,n), $E=10, 14$ MeV; $^{54}\mathrm{Fe}$(n,n\ensuremath{'}), $E=10$ MeV. Measured ${A}_{y}(E, \ensuremath{\theta})$. Deduced deformed complex spin-orbit potentials. Coupled channels calculations.

The analyzing power Ay(θ) for the 2H(d, n)3Heg.s., reaction was measured from 0° to about 150° (c.m.) at 5.5, 7.0, 8.5, 10.0 and 11.5 MeV. The experiment was conducted with a newly developed pulsing and bunching system for the polarized deuteron beam and used standard time-of-flight neutron detection. The present results disagree in some angular regions with measurements of the same observable reported recently by a Zürich group who detected the 3He particles, but agree with the limited angular distribution measured at 10 MeV by Hilscher and Liers, who also detected 3He particles. The present results are reported in terms of associated Legendre polynomial expansions of the product σ(θ)Ay (θ).

The analyzing power ${A}_{y}(\ensuremath{\theta})$ and differential cross section $\ensuremath{\sigma}(\ensuremath{\theta})$ have been measured for elastic scattering of 10-MeV neutrons from $^{208}\mathrm{Pb}$. These data were analyzed with a spherical optical model which has a real spin-orbit potential with either a three-parameter conventional form or a one-parameter semimicroscopic form. The predictions with both spin-orbit potentials reproduce the data equally well, suggesting that fewer free parameters can be used in spherical optical model calculations. Including an imaginary spin-orbit term ${W}_{\mathrm{SO}}(r)$ in the optical potential greatly improves the fits to the ${A}_{y}(\ensuremath{\theta})$ measurements and establishes the need for ${W}_{\mathrm{SO}}(r)\ensuremath{\ne}0$ in the n + $^{208}\mathrm{Pb}$ potential.NUCLEAR REACTIONS $^{208}\mathrm{Pb}$(n, n); $E=10$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$, ${A}_{y}(\ensuremath{\theta})$; deduced complex spin-orbit potential; spherical optical model calculations.