Prospects for comparison of matter and antimatter gravitation with ALPHA-g

The ALPHA experiment has recently entered an expansion phase of its experimental programme, driven in part by the expected benefits of conducting experiments in the framework of the new AD + ELENA antiproton facility at CERN. With antihydrogen trapping now a routine operation in the ALPHA experiment, the collaboration is leading progress towards precision atomic measurements on trapped antihydrogen atoms, with the first excitation of the 1S–2S transition and the first measurement of the antihydrogen hyperfine spectrum (Ahmadi et al. 2017 Nature 541 , 506–510 ( doi:10.1038/nature21040 ); Nature 548 , 66–69 ( doi:10.1038/nature23446 )). We are building on these successes to extend our physics programme to include a measurement of antimatter gravitation. We plan to expand a proof-of-principle method (Amole et al. 2013 Nat. Commun. 4 , 1785 ( doi:10.1038/ncomms2787 )), first demonstrated in the original ALPHA apparatus, and perform a precise measurement of antimatter gravitational acceleration with the aim of achieving a test of the weak equivalence principle at the 1% level. The design of this apparatus has drawn from a growing body of experience on the simulation and verification of antihydrogen orbits confined within magnetic-minimum atom traps. The new experiment, ALPHA-g, will be an additional atom-trapping apparatus located at the ALPHA experiment with the intention of measuring antihydrogen gravitation. This article is part of the Theo Murphy meeting issue ‘Antiproton physics in the ELENA era’.

A new method of calculating interplanar spacing: the position-factor method

When the formulae for calculating the interplanar spacingd′hklfor the seven primary lattices among the 14 Bravais lattices are used for crystal structures containing an additional atom,d′hklmust be corrected by multiplying by a correction coefficient. Based on a simple principle of analytical geometry, a new position-factor method has been developed to calculate these correction coefficients. The position factorP[whereP=hx+ky+lz=s+m/q, the scalar product of the position (x, y, z) of an additional atom in a unit cell and any plane (hkl) passing through the additional atom] indicates the following characteristics of the (hkl) plane: whether there is an additional plane (m≠ 0) or not (m= 0), what the correction coefficient (m/q) is for the interplanar spacing ifm≠ 0, and what the distance [(s+m/q)d′hkl] is from the plane to the origin. In order to provide two examples of calculations usingP, six possible interplanar spacings were obtained for a hexagonal close-packed crystal, and four possible interplanar spacings and the structure factor were obtained for a diamond crystal. In addition, the 12 undetermined plane indices in X-ray diffraction card 1-1249 (PDF-2, ICDD, Newtown Square, PA, USA) for diamond were determined using the new calculation.