Reinvestigation of the bound coherent neutron scattering lengths of lithium and its isotopes using neutron Bragg powder diffraction and neutron interferometry

The quality of neutron scattering studies relies upon accurately determined bound coherent neutron scattering lengths b c , whose standard tabulated values can be in need of review. We have measured integrated Bragg peak intensities via neutron diffraction from LiF powders, as well as scattering-length densities via neutron interferometry on LiF aqueous solutions, to accurately redetermine the b c values for the lithium isotopes 6 Li and 7 Li, as well as that for naturally occurring elemental Li as a mix of these two isotopes. As compared to earlier studies going back to 1986, our measurements make use of considerably improved instrumentation, and careful attention was given to the experimental procedure as well as to data analysis, in particular to aspects of systematic error. From the neutron diffraction measurements we obtain b c ( 6 Li) NPD = 2.27(2) fm, b c ( 7 Li) NPD = −2.28(2) fm and b c ( nat Li) NPD = −1.94(2) fm, in excellent agreement with our interferometry results of b c ( 6 Li) INT = 2.28(4) fm, b c ( 7 Li) INT = −2.28(3) fm and b c ( nat Li) INT = −1.93(3) fm, allowing to average them together and to propose recommended values of b c ( 6 Li) Rec . = 2.27(2) fm, b c ( 7 Li) Rec . = −2.28(2) fm and b c ( nat Li) Rec = −1.93(2) fm, where all values correspond to pure isotopes or the standard terrestrial isotopic composition of nat Li. Compared to standard literature values of b c ( 6 Li) Lit. = 2.0(1) fm, b c ( 7 Li) Lit. = −2.22(2) fm, and b c ( nat Li) Lit. = −1.90(3) fm, we note in particular that our recommended value for b c ( 6 Li) is 14% greater in magnitude, which is well outside of experimental uncertainties. Having obtained nearly identical results using two independent experimental techniques with qualitatively different possible sources of systematic error, we have confidence in our recommended b c values. We discuss reasons for the observed discrepancies with respect to previously tabulated values, as well as the relative merits of the various methods to measure bound coherent neutron scattering lengths.