A magneto-gravitational trap for absolute measurement of the ultra-cold neutron lifetime

Spin flip loss in magnetic confinement of ultracold neutrons for neutron lifetime experiments

“…These various approaches are semi-classical since the field B(t) acting on the neutron spin is determined by the classical motion of the particle through the field. However, the results have been shown [20,21] to be consistent also with a fully quantum mechanical analysis starting from the spin and space dependent SE. We show in the Appendix that this equivalence also holds for our extension to arbitrary field configurations.…”

“…Now we adapt this result to arbitrary 3D field models as are relevant for the Los Alamos bowl [20]. In this system the asymmetry introduced by the choice of two different radii of curvature along the rows of Halbach field magnets helps to randomize the orbits although fully mixing phase flow cannot be achieved.…”

“…As in [20] we approximate the field for the curved arrays of permanent magnets by that of the corresponding infinite planar array tangent to the bowl surface at the closest point on the bowl surface. We also use the same expressions for the flat-wall field, dubbed "smooth" [Eq.…”

“…Here c = cos (θ/2), s = sin (θ/2) and e ± = e ±iφ are given by the angles θ (polar) and φ (azimuthal) defining the direction of B(x, y, z) at the point x(t), y(t), z(t) through which the particle passes along its trajectory at time t. For example, for the Los Alamos "bowl" we choose, as in [20], the fixed Cartesian coordinate system x, y, z where z points vertically up. y (horizontal) and z define the vertical symmetry plane.…”

“…Walstrom et al [20], in 2009, pointed out that the values of D for confined, rather than freely moving, neutrons are much larger. For a particular vertical path in the field of the Los Alamos gravito-magnetic UCN trap they calculated D ∼ 10 −20 − 10 −23 , which is much larger than the Majorana estimate but still negligible in any actual or projected neutron lifetime experiment.…”