New measurements of the coherent and incoherent neutron scattering lengths of¹³C

Abstract

The techniques of neutron interferometry and neutron diffraction were used to determine the coherent and incoherent neutron scattering lengths of 13 C. From a neutron interferometry measurement of the optical path difference in liquid samples, 13 CS 2 versus nat CS 2 , we obtain a bound coherent scattering length of b coh,13C = 6.542 ± 0.003 fm, which differs appreciably from the standard tabulated value of 6.19 ± 0.09 fm. The resulting contrast of only 0.106(3) fm with respect to b coh,natC = 6.6484 ± 0.0013 fm has consequences for neutron diffraction experiments involving 13 C isotopic substitution. Combining our result for b coh,13C with precise neutron diffraction measurements of the self-scattering intensities of liquid samples, 13 CS 2 versus nat CS 2 , and 13 CO 2 versus 12 CO 2 , we deduce a bound incoherent scattering length of b incoh,13C = −0.42 ± 0.24 fm that is consistent with the standard tabulated value of −0.52 ± 0.09 fm. The results presented here have required accurate measurements of small effects, for which particular attention has been given to the data analysis.

The structure of liquid carbon dioxide and carbon disulfide

“…Extensive discussion of this point has been presented in Ref. 28. Since the coherent cross section of hydrogen is smaller by a factor of about 40 than the incoherent cross section the impact of the H impurity on the coherent signal is negligible.…”

“…Unfortunately, in the course of this study it was found that the scattering contrast between the carbon isotopes is very small, substantially smaller yet than standard table values would suggest. 28 That makes the direct matrix inversion of the equation system used to determine the partial structure factors ill defined ͑see below͒. We rely on molecular dynamics simulations of molecules interacting through Lennard-Jones and electrostatic total potential models, seeking the optimal parameters leading to the best representation of the three independent scattering data sets.…”

Oxygen as a Site Specific Probe of the Structure of Water and Oxide Materials

“…The experimental procedure is described in Ref. [14] and the full details will be reported elsewhere [15]. The measured values of b17 O ¼ 5:867ð4Þ and b18 O ¼ 6:009ð5Þ fm were reproduced, within the experimental uncertainties, during two interferometry experiments performed a year apart.…”

The bound coherent neutron scattering lengths of the oxygen isotopes

“…Rauch and Werner 2000). Our first interferometry experiment measured b coh for the 13 C isotope to high accuracy (Fischer et al 2008), giving a value that differed significantly from a previous standard value measured by Koester et al (1979). Our result not only explained a long-standing problem in NDIS experiments employing carbon isotope substitution, but provided an accurate scattering length value for 13 C that was used for a PSF analysis of the structures of liquid CS 2 and liquid CO 2 (Neuefeind et al 2009).…”