Neutron interferometric measurement of the scattering length difference between the triplet and singlet states of $n\ensuremath{-}^{3}\mathrm{He}$

Neutron interferometric measurement of the scattering length difference between the triplet and singlet states of $n - {}^{3}{He}$

M. G. Huber, M. Arif, W. C. Chen, T. R. Gentile, D. S. Hussey, T. C. Black, D. A. Pushin, C. B. Shahi, F. E. Wietfeldt, and L. Yang

Phys. Rev. C 90, 064004 – Published 15 December 2014

Abstract

We report a determination of the $n - {}^{3}{He}$ scattering length difference $Δ b^{'} = b_{1}^{'} - b_{0}^{'} = [- 5.411 \pm 0.031 (statistical) \pm 0.039 (systematic)]$ fm between the triplet and singlet states using a neutron interferometer. This revises our previous result $Δ b^{'} = [- 5.610 \pm 0.027 (statistical) \pm 0.032 (systematic)]$ fm obtained using the same technique in 2008 [Huber et al., Phys. Rev. Lett. 102, 200401 (2009); Huber et al., Phys. Rev. Lett. 103, 179903(E) (2009)]. This revision is attributable to a reanalysis of the 2008 experiment that now includes a systematic correction caused by magnetic-field gradients near the ${}^{3}{He}$ cell which had been previously underestimated. Furthermore, we more than doubled our original data set from 2008 by acquiring 6 months of additional data in 2013. Both the new data set and a reanalysis of the older data are in good agreement. Scattering lengths of low- $Z$ isotopes are valued for use in few-body nuclear effective field theories, provide important tests of modern nuclear potential models, and, in the case of ${}^{3}{He}$ , aid in the interpretation of neutron scattering from quantum liquids. The difference $Δ b^{'}$ was determined by measuring the relative phase shift between two incident neutron polarizations caused by the spin-dependent interaction with a polarized ${}^{3}{He}$ target. The target ${}^{3}{He}$ gas was sealed inside a small, flat-windowed glass cell that was placed in one beam path of the interferometer. The relaxation of ${}^{3}{He}$ polarization was monitored continuously with neutron transmission measurements. The neutron polarization and spin-flipper efficiency were determined separately using ${}^{3}{He}$ analyzers and two different polarimetry analysis methods. A summary of the measured scattering lengths for $n - {}^{3}{He}$ with a comparison to nucleon interaction models is given.