Measurement of the total neutron-scattering cross-section ratios of noble gases of natural isotopic composition using a pulsed neutron beam

Precision measurements of slow neutron cross sections with atoms have several scientific applications. In particular, the $n\text{−}{}^4\mathrm{He}$ $s$-wave scattering length is important to know both for helping to constrain the nuclear three-body interaction and for the proper interpretation of several ongoing slow neutron experiments searching for other types of neutron-atom interactions. We present new measurements of the ratios of the neutron differential scattering cross sections of the noble gases He, Ar, Kr, and Xe to Ne. All gases used were of natural isotopic abundance. These measurements were performed using a recently developed neutron-scattering apparatus for gas samples located on a pulsed slow neutron beamline which was designed to search for possible exotic neutron-atom interactions and employs both neutron time of flight information and a position-sensitive neutron detector for scattering event reconstruction. We found agreement with the literature values of scattering cross sections inferred from Ar/Ne, Kr/Ne, and Xe/Ne differential cross-section ratios over the $q$ range of 1–7 ${\mathrm{nm}}^{-1}$. However, for the case of He/Ne we find that the cross section inferred differs by 11.3% ($7.6\sigma$) from previously reported values inferred from neutron phase-shift measurements, but is in reasonable agreement with values from other measurements. The very large discrepancy in the He/Ne ratio calls for a new precision measurement of the $n\text{−}{}^4\mathrm{He}$ scattering length using neutron interferometry.

Figure 1

Layout of our experiment as mounted on BL05 at the MLF facility at J-PARC. In this image, the incident neutron beam is parallel to the $z$ axis, which forms a right-handed coordinate system with the $x$ axis, pointing horizontally beam-left, and the $y$ axis, pointing upward. Image taken from Ref. [29].

Figure 2

Ratios of experimental and simulated $q$-intensity spectra, $I\left(q\right)$, with respect to that of neon, $I^{\text{Ne}}(q$).

Figure 3

The percentage difference between our measured values and those in the literature for the free-atom scattering cross sections, with and without propagation of uncertainties from the literature to show the relative sensitivity of our method. Our values were compared with ${\sigma }_f^{\text{He}}=0.857\left(10\right),{\sigma }_f^{\text{Ar}}=0.683\left(4\right),$ using values from Ref. [51], and ${\sigma }_f^{\text{Kr}}=7.61\left(4\right),{\sigma }_f^{\text{Xe}}=4.30\left(2\right),$ using values from Ref. [35]. We chose to compare Kr and Xe to Ref. [35] rather than the values in Ref. [51] due to the lower level of uncertainty for Kr and the availability of the incoherent scattering contribution for Xe in Ref. [51].