Accounting for the factor of seven in the 1975 cold-neutron Stern–Gerlach experiment

The cold-neutron Stern-Gerlach measurement of Hamelin, Xiromeritis and Liaud (1975) has recently been modelled with a constant field gradient of 300 T/m and found to over-predict the published 6 mm beam splitting by a factor of about seven. We account for that factor in full, from the primary sources, and it divides into three. A factor 2.09 is a misattribution: the 1975 article gives the maximum gradient as a range, 1 to 3 x 10^4 G/cm, over several pole geometries, and in the same sentence assigns its Fig. 6 to a tapered dihedral of 5 mm entrance and 8 mm exit gap, whereas 3 x 10^4 G/cm belongs to a 4 mm parallel gap whose own splitting is 12.6 mm - a figure we obtain twice over, from the profile itself and from the author's own summary chart. The remaining factor 3.38, which the modelling paper attributed to its own idealised field, divides once more: integrating the thesis's own field instead of a uniform one removes a factor 1.41, and a factor 2.40 remains between our own best forward calculation of that configuration and the observation. We do not subdivide that 2.40 further. It contains the beam's wavelength distribution - the measured guide spectrum is printed in the thesis's own FORTRAN, runs 1-45 A and peaks at 9 A, against the single lambda=10.000 A implicit in the velocity used - together with whatever else the reconstruction is missing, and the configuration in which the split would have to be made is the one where our modelled profile is least well defined; the two available estimates put the spectrum's share anywhere from 0.84 to 1.96. The boundary between the first two factors, but neither the product nor the misattribution, depends on where the thesis's equivalent current filaments sit; they are not at the pole tips, and the two papers put them at sqrt(3) times the half-gap in four places - one a derivation in the thesis, the others statements of where the gradient maximum lies, the article's two of them both tracing to the field measurements of its Sec. 4. We add a derivation of the D^-2 gradient scaling from a magnetomotive force we find constant to 4.2 % across a factor 3.75 in gap; the observation that the sources state the absolute field of the one configuration that matters four times over, spanning a factor 1.8 in B00*D, the two highest - one of them the value the modelling paper inherited - being the only ones that require a pole induction above the saturation of the pole material; a deterministic forward calculation that returns 0.92, 1.23 and 0.77 of the observed splitting for the three configurations that pass its stability tests, with nothing fitted at all; and the observation that the 1974 thesis had already identified the non-uniformity of the gradient, derived 1/v^1.9 from its own field, and measured lambda^1.83 over six velocity-selector settings. We show that this last measurement does not in fact discriminate between a uniform and a non-uniform gradient, because the peak-to-peak quantity it reports is insensitive to the difference; the measured exponent lies 4.7sigma below what either model predicts, and we report that as unresolved. Classical mechanics with the unreduced neutron moment describes the magnitudes of both datasets to about 25 %, which is the accuracy the field scale, the geometry and the detector-plane acceptance jointly allow; neither dataset requires a modification of the deflection law, and neither is precise enough to exclude one at that level.