Measurement of the absolute differential cross section for $\mathit{np}$ elastic scattering at 194 MeV

A tagged medium-energy neutron beam was used in a precise measurement of the absolute differential cross section for $\mathit{np}$ backscattering. The results resolve significant discrepancies within the $\mathit{np}$ database concerning the angular dependence in this regime. The experiment has determined the absolute normalization with $\pm 1.5\%$ uncertainty, suitable to verify constraints of supposedly comparable precision that arise from the rest of the database in partial wave analyses. The analysis procedures, especially those associated with the evaluation of systematic errors in the experiment, are described in detail so that systematic uncertainties may be included in a reasonable way in subsequent partial wave analysis fits incorporating the present results.

Figure 1

Comparison of previous $\mathit{np}$ scattering differential cross section measurements (a) from Uppsala [7] and Los Alamos [10] and (b) from PSI [9] and Los Alamos [10] near 200 MeV. The Los Alamos data in each case are represented by solid squares and the other data by open circles. The experimental results are compared to the Nijmegen PWA93 [5] partial wave analysis solution evaluated at appropriate energies. The Los Alamos data were renormalized by factors of 1.092 in (a) and 1.078 in (b) to bring them into agreement with the PWA. The relative cross sections reported in [9] were similarly normalized here, while the reported absolute cross section scale for the Uppsala data was retained.

Figure 2

Top view of the $\mathit{np}$ scattering experiment setup.

Figure 3

Particle identification plot for one DSSD-BD combination for (a) tagged proton candidates and (b) tagged neutron candidates. The two-dimensional gate used as part of the selection criteria for 1-punch tagged neutron events is shown in panel (b), and again in panel (a), where its location can be gauged with respect to both recoil deuterons and recoil protons that punch through the backing detector.

Figure 4

The reconstructed energy (a) and horizontal transverse coordinate (b) of tagged neutrons at the secondary target for 1-punch events, 2-stop events, and their sum (solid black line).

Figure 5

The ADC outputs of two BDs plotted against one another, revealing regions of 1-punch tagged neutron events, but also a region dominated by correlated noise in both quadrants. Events along the $x$ and $y$ axes, where one BD signal falls in the pedestal region, are also mostly valid 1-punch events.

Figure 6

The correlation for apparent 2-stop $\mathit{np}$ scattering candidates between the higher of the DSSD energy depositions for the two recoil protons in the tagger and the difference in predicted $x$ coordinates at the secondary target from neutron tagging vs forward proton ray-tracing. The long correlated tail contains corrupted punch-through events for which electronic loss of backing detector energy information has led to misidentification of the event and large systematic errors in the tagging.

Figure 7

The subtraction of the simulated corrupted events removes the tail from the 2-stop event sample. The simulated spectrum has been normalized by matching to the 2-stop subsample characterized by backing detector information with valid times but zero energy.

Figure 8

Distribution of $\mathit{np}$ scattering event candidates with respect to $y_{\mathrm{tag}}$ and to $\Delta E$ scintillator pulse height for the CH${}_2$ and C targets separately and for the difference between them.

Figure 9

The distribution of $\mathit{np}$ scattering candidate events after subtraction of C from CH${}_2$ data with respect to $\Delta E$ ADC and proton lab angle. The lines show the boundaries of the gate applied to event stream 2 to select free scattering events.

Figure 10

The distribution of $\mathit{np}$ free scattering events in the scattering angle bin ${\theta }_p^{\mathrm{sc}}=3^{°}\text{−}{6}^{°}$ with respect to forward proton energy deposition in the rear hodoscope. The curve represents a fit with a Gaussian plus exponential tail. The tail represents valid free scattering events where the proton undergoes a nuclear reaction in the stopping scintillator.

Figure 11

Comparison of the measured (solid line with sizable statistical fluctuations) and simulated (dotted line) distributions of free (CH${}_2$-C) $\mathit{np}$ scattering events in the angle bin ${\theta }_p^{\mathrm{sc}}={42}^{°}\text{−}{45}^{°}$ with respect to proton azimuthal scattering angle ${\varphi }_p^{\mathrm{sc}}$ for the 1-punch (a) and 2-stop (b) data samples. Forward detector geometry parameters, plus a single overall normalization parameter per angle bin and data sample, were adjusted to optimize the fit simultaneously for all angle bins and both data samples.

Figure 12

The simulated acceptance of the 1-punch data sample. The inset shows a greatly magnified vertical scale for the most forward proton scattering angles.

Figure 13

The fractional differences between the absolute differential cross sections extracted for different analyzed data subsamples. The plotted error bars take into account only the independent statistical (including those from background subtractions) uncertainties for the three samples. Slightly different correction factors $c_i$ were applied to the cross sections for different samples, as indicated in Table , before the comparison was made.

Figure 14

Absolute differential cross section from the present experiment compared with data from Ref. [7] and with PWA calculations at two relevant energies. The error bars on the present results are statistical, including background subtraction. The width of the shaded band at the bottom, representing the net absolute systematic uncertainty, including that in the overall normalization, is comparable to or smaller than the statistical error at each angle.

Figure 15

The distribution of DSSD arrival time difference between the two recoil protons for tagged neutron events, shown for all 2-stop events (following subtraction of the corrupted events as per Sec. 3b) and for 2-stop events where the lower of the two DSSD energy depositions ($E_{p2}$) exceeds 2.0 MeV. The vertical lines indicate the prompt coincidence gate (central region between the inner two lines) imposed in the analysis, plus two displaced gates used to assess accidental coincidence background in event stream 1. The long tail seen for events with $E_{p2}⩽2.0$ MeV, arising from detector noise and imperfect software corrections for time walk near the front-end discriminator threshold, leads to an overestimate of the accidental coincidence yield, but the correction and uncertainty still remain quite small.

Figure 16

The difference distributions in $x$ (left) and $y$ (right) coordinates determined from tracking of the forward proton vs reconstruction of the tagged neutron, for the 1-punch data sample after CH${}_2$-C subtraction. The vertical lines indicate the location of software gates used to remove events that may be complicated by sequential reactions or tagging errors.

Figure 17

The reconstructed (a) $y_{\mathrm{tag}}$ spectrum for the CH${}_2$ target before background subtraction and (b) $\Delta E$ pulse height spectrum for CH${}_2$-C for the ${\theta }_p^{\mathrm{sc}}$ bin $3^{°}\text{−}{6}^{°}$. The superimposed curves in both frames represent fits used in estimating background subtraction accuracy.

Figure 18

$\mathit{np}$ scattering opening angle spectra reconstructed for events where a large-angle proton fires at least the first two MWPCs and a forward neutron appears to fire the rear scintillator hodoscope. For such coincidence events, a clear free scattering peak is seen with the CH${}_2$ production target (upper frame), whereas no hint of such a peak is seen for the C target (lower). The solid curves are fits with a Gaussian peak superimposed on a quadratic background. The distribution shape for C reflects the quasifree $\mathit{np}$ scattering opening-angle spectrum convoluted with the coincidence acceptance of the forward detector array.

Figure 19

The estimated fractional cross section error introduced by neutron polarization effects for the 1-punch and 2-stop event samples, plotted as a function of $\mathit{np}$ scattering angle.

Figure 20

The relative differences of the present absolute $\mathit{np}$ scattering differential cross sections and of two SAID PWA solutions [4, 30] from the Nijmegen PWA93 solution [5, 24], all at $E_n=194$ MeV. The SP40 solution is from a 2003 analysis of the database from 0 – 400 MeV, while SP05 is the current SAID solution, fitted over the range 0–3.0 GeV, including the present data in the fit.

Figure 21

The effect on the present analysis of neglecting tagger information about the neutron incidence angle in the reconstruction of the $\mathit{np}$ scattering angle for each event. The solid circles represent the final results (before multiple scattering corrections), while the open squares result when the scattering angle is estimated only with respect to the central neutron beam direction. Note the suppressed zero on the cross section scale.