Neutron-proton analyzing power at 12 MeV and inconsistencies in parametrizations of nucleon-nucleon data

We present the most accurate and complete data set for the analyzing power Ay(theta) in neutron-proton scattering. The experimental data were corrected for the effects of multiple scattering, both in the center detector and in the neutron detectors. The final data at En = 12.0 MeV deviate considerably from the predictions of nucleon-nucleon phase-shift analyses and potential models. The impact of the new data on the value of the charged pion-nucleon coupling constant is discussed in a model study.


INTRODUCTION
There are reasons why low-energy (E N ≤ 20 MeV) Nucleon-Nucleon (N N ) scattering data might appear to be of limited use in constraining N N phase-shift analyses (PSAs) [1,2] and potential models (PMs) [3,4,5,6,7]. For one thing, the deuteron bound-state properties already provide a fairly stringent constraint for any N N PM, and might seem sufficient. For another, low-energy scattering data can provide constraints only for the lower partial wave N N interactions and, even then, can not determine individual partial waves. For example, the low-energy analyzing power, A y (θ), is governed by the three angular momentum L = 1 interactions, 3 P 0 , 3 P 1 , and 3 P 2 . Although N N data provide constraints on the 3 P phase shifts taken together, it cannot determine each parameter unambiguously [8].
Despite the very small magnitude of N N A y (θ), its importance derives from the fact that it is possible experimentally to measure such data to great precision. As a result, N N A y (θ) can provide a crucial test of our understanding of the N N interaction and of the nuclear force in general.
In principle, this inconsistency can be reduced by assuming a charge-splitting of the pion-nucleon coupling constant, i.e., one could assume that the neutral pion couples to the nucleon with a different strength than the charged pion. In Refs. [9,10] it was shown that the combination of g 2 π 0 /4π = 13.6 and g 2 π ± /4π = 14.4 creates a sufficiently large value for the quadrupole moment of the deuteron, and reproduces the low-energy p-p 3 P 0 phase shifts.
At the same time that the analyses of Refs. [9,10] were performed, there were indications that n-p differential cross-section data at intermediate energies favored a larger value for g 2 π ± /4π. On this, see Ref. [15] for a comprehensive overview of recent determinations of g 2 π /4π and especially Ref. [16], which quotes g 2 π ± /4π = 14.50 ± 0.26 obtained from n-p differential cross section data at E n = 162 MeV. However, the recent n-p differential cross section data obtained at IUCF at 194 MeV [17] do not support this larger value of g 2 π ± /4π. Although it seems likely that there is no significant charge splitting in the pion-nucleon coupling constants at intermediate energies, the question remains unresolved at low energies. On the one hand, the theoretical models used to account for the charge dependence of the singlet N N scattering lengths, 1 S 0 , do not allow for any large charge splitting of g 2 π /4π. On the other hand, many lowenergy data suggest a significant charge splitting. We report here on the results of a new n-p A y (θ) experiment carried out at E n = 12.0 MeV utilizing improved datataking and data-analysis techniques. For references to previous n-p A y (θ) measurements see Refs. [18,19,20]. Our results confirm the inconsistencies between lowenergy analyzing power and available theoretical models of the N N interaction.

EXPERIMENTAL SETUP
The experimental setup is shown in Fig. 1. Polarized neutrons with mean energy of 12.0 MeV and total energy spread of about 400 keV were produced via the polarization-transfer reaction 2 H( d, n) 3 He at 0 • . The polarized deuteron beam was accelerated to E d = 9.40 MeV and entered through a 4.6 µm Havar foil into a small (3.14 cm long, 0.48 cm radius) gas cell filled with 7.8 atm of deuterium gas and capped with a 0.1 cm thick gold beamstop. The gas cell was mounted inside a 1.8 m-thick wall made of concrete, paraffin, iron, copper, and lead, to shield the neutron detectors from the direct flux of the neutron source. Typical deuteron beam intensities on target were 1.5 µA and typical values for the deuteron vector polarization |p z | were 0.65. The polarized neutrons produced at 0 • relative to the incident deuteron beam passed through a collimation system to produce a rectangular shaped neutron beam at the position of the proton-containing active target labelled "Center Detector" in Fig. 1. The center detector (CD) consisted of an upright cylinder made of the plastic scintillator material NE102A with dimensions 1.9 cm diameter and 3.8 cm height. The CD was located at a distance of 172 cm from the neutron source and was mounted via a short light guide onto a 5 cm diameter photomultiplier tube (PMT).
Neutrons scattered to the left or right were detected by five pairs of neutron detectors positioned symmetrically relative to the incident neutron beam direction in the horizontal scattering plane. The neutron detectors (NDs) were filled with the liquid scintillator material NE213. These detectors had excellent neutron-gamma pulse-shape discrimination capabilities and had an active volume of 4.3 cm wide, 11.9 cm high and 7.5 cm deep. They were viewed by 5 cm diameter PMTs through 0.5 cm thick Pyrex glass windows and 7.5 cm long light guides. The neutron detectors were mounted onto (lowmass) 30 cm high stands and placed on an aluminum ring surrounding the CD. The center-to-center distance between the CD and the neutron detectors ranged from 45 cm to 70 cm depending on scattering angle. The angular separation between the neutron detectors was 12 • (lab). In order to cover the angular range from θ lab = 16 • to 72 • in 4 • steps, three settings of the five detector pairs were required. The absolute magnitude of the neutron polarization was measured with a neutron polarimeter located downstream of the n-p scattering arrangement. The polarimeter consisted of a 4 He gas scintillator pressurized to 100 atm (95% He, 5% Xe) and a pair of neutron detectors positioned at θ lab = 58 • , which were identical to those used for n-p scattering. In order to reduce instrumental asymmetries for the n-p and n-4 He measurements, the deuteron vector polarization p z , and therefore the neutron polarization, was flipped at a frequency of 10 Hz (between up and down relative to the horizontal scattering plane). The n-p and n-4 He data were accumulated simultaneously in six runs, each lasting about 250 datataking hours.
The data-acquisition electronics recorded the center detector pulse height (CDPH), the neutron time of flight (NTOF) between the CD and the NDs, and spectra for each ND, including pulse-shape information. Since the energy of the scattered neutrons varied from E n ′ = 11.1 MeV at θ lab = 16 • to E n ′ = 1.1 MeV at θ lab = 72 • , different hardware thresholds were used for the NDs. In addition, three different gains were used for the CD signals (using different dynodes).
Software cuts were set on the CDPH and the pulse height in the NDs to eliminate pulses at the extreme ends of the spectra. Gates were also set on the neutrons in the pulse-shape discrimination spectra and wide gates were set on the elastic peak of the NTOF spectrum. All four of these cuts (identical for spin-up and spin-down spectra) were used to generate two-dimensional (2D) spectra of CDPH versus NTOF, for scattering to the left and right NDs and for neutron spin up and spin down. An example of such a spectrum is shown in Fig. 2 where the CDPH scale has been temporarily compressed in order to fit within 64 channels. Tight NTOF gates were set in these 2D spectra eliminating the tails of the peak, as shown in Fig. 2, in order to identify the elastic scattering events of interest (again, identical for spin-up and spindown spectra). These new NTOF gates were used to sort the final CDPH spectra (now in their full 512-channel resolution) corresponding to each neutron detector and spin state. The CDPH spectra were used to determine the np yields and scattering asymmetries, after applying the corrections described in the following section. The above process was also followed to sample the accidental (i.e., time uncorrelated) background by using an NTOF cut located at times shorter than the gamma peak. The accidental background proved to be extremely small.

DATA ANALYSIS
After the sorting procedure described above and the subtraction of the accidental events, the data still contained a number of finite-geometry and multiplescattering effects. To remove these effects, Monte-Carlo calculations were performed to simulate the experiment. Two effects are due exclusively to the finite size of the center detector (CD) and the neutron detectors (NDs) and have a slight effect on single-scattering events. First, because there is a range of angles subtended by each detector set at each nominal angle and because the cross section of n-p elastic scattering varies over this range, we must report an effective angle. These were calculated by our code and are listed in the first column of Table I. This effect is small; the largest shift is no more than a half of a degree. The second finite-geometry effect concerns the value of A y (θ) itself, again due to the range of angles subtended by each ND. Effective A y (θ) values were calculated by our Monte-Carlo code and these were compared to the values from the code's library. The ratio between these two values was then applied to the data. Once again, the correction is small; only the first four angles had corrections that were larger than the uncertainty of the calculation (about 0.00012).
In addition to elastic scattering, multiple scattering events occur in the CD. About 50% (depending on ND angle) of these events were eliminated as a result of the neutron time of flight (NTOF) gate. Nevertheless, the center detector pulse height (CDPH) spectrum contained multiple scattering events amounting to approximately 2% of all single scattering events. Our Monte-Carlo simulation showed that the only significant processes were those due to double scattering, specifically neutron double scattering from hydrogen ( 1 H-1 H), neutron scattering from hydrogen and subsequent scattering from carbon ( 1 H-12 C), and neutron scattering from carbon and subsequent scattering from hydrogen ( 12 C-1 H). In performing these calculations, we used complete libraries of cross-section and polarization data for both n-1 H and n-12 C scattering. We will return to the subject of the n-12 C library in our discussion of the PDE correction.
We also removed edge-effect events from the data, which result when recoil protons leave the CD before depositing their full energy. Along with the double scattering events, these counts elongate the tails of the CDPH peak, especially to the left (low-energy) side.
A sample CDPH spectrum is shown in Fig. 3 (top panel). The solid curve represents our Monte-Carlo simulation for a scattering angle of θ lab = 36 • , while the small open circles show the experimental data. A greatly expanded view is shown in the middle panel, where the open circles again indicate the experimental data. The curves labeled "double" are the calculated double scattering contributions 1 H-1 H, 1 H-12 C, and 12 C-1 H. The dotted curve labled "edge" is the calculated pulse-height distribution due to edge effects. Finally, the curve labeled "single" is the calculated single scattering contribution (plus the edge effects). All of the calculations are normalized to the data.
Another expanded view is displayed in the bottom panel of Fig. 3. Here, "data with subtraction" shows the data after the removal of all counts due to double scattering and edge effects (labeled "ms+edge"). Even after this subtraction, a small background remains, amounting to about 0.3% of the single-scattering events. A number of fits were used to estimate this remaining background, ranging from a linear fit between channel numbers 150 and 350 to a parabolic fit between channel numbers 180 and 280. Due to the smallness of the remaining background, the asymmetry proved to be independent of our background choice, within statistical uncertainties. We also concluded that the background was unpolarized. For all ND angle settings we approximated the remaining background by a linear function connecting the left and right sides of the CDPH peak (for example, in Fig. 3 from channel 180 to 280). The remaining background seen above channel 290 in the bottom panel of Fig. 3 is due to cross-talk effects between two adjacent detectors, specifically neutron scattering from the detector positioned at a larger scattering angle (and shorter distance from the CD) to the detector of interest.
Three sets of gates were used to calculate the yields and asymmetries, at 10% (shown in Fig. 3 by the dashed  lines), 30%, and 50% of the CDPH peak maximum. In Fig. 3, this is done for N ↑ L , for spin up scattering to the left ND at θ lab = 36 • . Similarly, the yields N ↑ R , N ↓ L , and N ↓ R were obtained to calculate the asymmetry ǫ = The nominal gates were the 30% set. The other two gates (the 10% and 50% set) were used to check on the appropriateness of the background subtraction. Within statistical uncertainty, the results for ǫ proved to be independent of the choice of the gate width.
In order to extract the n-p A y (θ) from the measured asymmetry ǫ(θ), the neutron polarization p n y must be known. For this purpose the n-4 He asymmetry data acquired with the neutron polarimeter referred to above were processed and analyzed in the same way as the n-p asymmetry data. In this case the 4 He recoil pulse height in the high-pressure gas scintillator plays the role of the CDPH in the plastic scintillator used for the np asymmetry measurements. The neutron polarization was obtained from ǫ He (58 • ) = (α He − 1)/(α He + 1) = A y (58 • )p n y , where α He is defined as above. Here, the effective analyzing powerĀ y (58 • ) for n-4 He scattering at E n = 12.0 MeV was calculated for the present neutron polarimeter geometry via Monte-Carlo calculations. The n-4 He phase shifts of Stammbach and Walter [21] were used. All of the relevant multiple scattering processes were included. We obtainedĀ y (58 • ) = −0.554 ± 0.008, where the uncertainty is mainly of a systematic nature reflecting the uncertainty associated with the n-4 He phase shifts. The average neutron polarization was p n y = 0.563 ± 0.008. At such a high level of precision, a subtle systematic effect comes into play, which does not cancel by reversal of the neutron polarization. This is the polarization dependent efficiency (PDE) [19] of the neutron detectors. The NDs contain hydrogen and carbon in the ratio of 1.21:1. The double scattering process 12 C-1 H in the NDs, which accounts for about 10% of the total neutron detection efficiency, is sensitive to the n-12 C A y (θ). If the n-12 C A y (θ) is not constant over the range of neutron energies E n ′ seen by a particular ND, an instrumental asymmetry will occur. Typical values for ∆E n ′ are 800 keV. A realis-tic correction for this effect requires a detailed knowledge of the n-12 C A y (θ), especially in the resonance region of the n-12 C total cross section between 2.0 and 8.5 MeV neutron energy. In this energy regime the n-12 C A y (θ) changes rapidly and therefore causes sizeable PDE effects.
All of the post-1985 n-p A y (θ) measurements have been corrected for the PDE. However, due to the lack of a detailed n-12 C A y (θ) database, especially at low energies, the accuracy of the associated corrections was limited. In assembling our data library, we used the thirty-three n-12 C A y (θ) angular distributions measured by Roper et al. [22] in the energy range from 2.2 to 8.5 MeV. From E n = 0 to 6.5 MeV, we used an R-matrix analysis by Hale [23], which included the data from Ref. [22]. In certain regions (especially for forward angles and for neutron energies between 3.5 and 4.5 MeV), the analysis of Ref. [23] missed the A y (θ) data slightly and we therefore substituted Legendre polynomial fits to the data of Ref. [22] in these regions. Between 6.5 MeV and 8.5 MeV, we used fits to the data of Ref. [22] as well as the recent phaseshift analysis (PSA) of Chen and Tornow [24]. Above E n = 8.5 MeV, we used the Chen-Tornow PSA exclusively. The new data by Roper et al. and the analyses of Hale, Chen and Tornow improved the n-12 C A y (θ) database considerably, making corrections for the PDE more reliable.
We ran our Monte-Carlo code for 20 separate legs, each leg of three million events, and each leg starting from a different random number. The PDE correction to the A y (θ) data was taken as the difference between the A y (θ) result with polarization effects turned on in the NDs and the result with the polarization turned off. The second column of Table I lists our final PDE corrections. Note that they vary greatly from one data point to the other due to the pronounced resonance features in n-12 C scattering at low energy. It is important also to note that our present results agree well with the overall trend of the PDE corrections of Ref. [20], which used a different Monte-Carlo code and a different database. Our reason for having much greater confidence in the present PDE results is due to our extensive and detailed work in revising the data libraries, as outlined above.
The third column in Table I summarizes our final results for A y (θ) in n-p scattering at E n = 12.0 MeV. Note the small overall uncertainty. The final results include uncertainties in A y (θ) due to statistics, the measurement of beam polarization, the multiple-scattering calculation, the PDE calculation, and the remaining background (typically zero) all added in quadrature. The final uncertainties are about half of those of the previous TUNL n-p A y (θ) measurement at E n = 12.0 MeV [20]. This is partly due to the fact that the Atomic Beam Polarized Ion Source used in the present study produced about four times the deuteron current as the Lamb-Shift source used in the previous study. Figure 4 shows the present n-p A y (θ) in comparison to the N N phase-shift analysis prediction (solid curve) of the Nijmegen group, NI93. Clearly, NI93 provides a larger A y (θ) throughout the entire angular distribution. The accuracy of the neutron polarization determined in the present work does not allow for a renormalization of the A y (θ) data beyond the error bars given in Fig.  4. Furthermore, the present n-p A y (θ) data are in good agreement with the trend established by previous TUNL data where a different method was used for determining p n y [20].

DISCUSSION
As we have pointed out in the introduction, the underlying N N dynamics that characterize A y (θ) precludes us from extracting unambiguous information about the 3 P j N N interactions. However, we can conclude that the NI93 N N PSA overestimates the n-p A y (θ) at E n = 12.0 MeV. This statement is of considerable importance considering the fact that most N N potential model builders use the NI93 PSA results or the associated database for determining the free parameters of their models. One has to conclude that all the recent so-called high-precision N N potential models overestimate the n-p A y (θ) at low energies. This observation has far-reaching consequences for nuclear scattering systems with A > 2, which are much more sensitive to the 3 P j N N interactions than the N N system [25].
Valuable information can be obtained from the present data if they are compared to variations of the theoretical predictions. Here we focus on the charged pion coupling constant [9,10]. Figure 4 shows our data in comparison to three theoretical predictions based on the CD-Bonn N N potential, which use three different values of the charged pion-nucleon coupling constant, g 2 π ± /4π. In these three models, only the S-wave NN interactions of CD-Bonn were refitted. All three predictions use the same neutral pion coupling constant, g 2 π 0 /4π = 13.6. The curve using g 2 π ± /4π = 13.6 is indistinguishable on this scale from the prediction of NI93 (solid curve). The dashed curve in Fig. 4 uses g 2 π ± /4π = 14.0 and the dotted curve uses g 2 π ± /4π = 14.4. The values of χ 2 per degree of freedom associated with the solid, dashed and dotted curves are 6.0, 1.7, and 2.5, respectively. Therefore, this model study confirms and puts on more solid ground the findings of Refs. [9,10] regarding low-energy n-p A y (θ) data and their demand for a charge splitting of g 2 π /4π. In summary, the present data represent the most accurate and complete n-p A y (θ) angular distribution ever reported. Our model study based on the CD-Bonn N N potential model supports a substantial charge dependence of the pion-nucleon coupling constant. Our results are inconsistent with the existing global N N PSAs of the Nijmegen [11] and VPI [12,13] groups and with high-precision N N potential models. However, our re-sults agree with inconsistencies previously noticed between data and predictions for the 3 S 1 -3 D 1 mixing parameter ǫ 1 in n-p scattering at low energies [26] and also with requirements placed on the charged coupling constant by the quadrupole moment of the deuteron [9]. Of course, it is possible that neither of these scenarios is the "correct" one. Perhaps the impasse comes because we are at the point where the precision of our data and the development of our "low energy" theoretical models has pushed the paradigm of meson-exchange based N N potential models beyond its limits.  IG. 2: 2D spectrum of compressed CDPH versus NTOF for scattering to θ lab = 64 • . A tight NTOF gate was set around the elastic neutron peak in order to remove as many background events as possible. Here, for g 2 π 0 /4π, all three curves use 13.6. For g 2 π ± /4π, the calculation using 13.6 coincides on this scale with the Nijmegen NI93 PSA result (solid curve); the dashed curve uses 14.0 and the dotted curve 14.4.