Geometric phases in electric dipole searches with trapped spin-1/2 particles in general fields and measurement cells of arbitrary shape with smooth or rough walls

The important role of geometric phases in searches for a permanent electric dipole moment of the neutron, using Ramsey separated oscillatory field nuclear magnetic resonance, was first noted by Commins and investigated in detail by Pendlebury et al. Their analysis was based on the Bloch equations. In subsequent work using the spin density matrix Lamoreaux and Golub showed the relation between the frequency shifts and the correlation functions of the fields seen by trapped particles in general fields (Redfield theory). More recently we presented a solution of the Schr\"odinger equation for spin-$1/2$ particles in circular cylindrical traps with smooth walls and exposed to arbitrary fields [Steyerl et al.] Here we extend this work to show how the Redfield theory follows directly from the Schr\"odinger equation solution. This serves to highlight the conditions of validity of the Redfield theory, a subject of considerable discussion in the literature [e.g., Nicholas et al.] Our results can be applied where the Redfield result no longer holds, such as observation times on the order of or shorter than the correlation time and non-stochastic systems and thus we can illustrate the transient spin dynamics, i.e. the gradual development of the shift with increasing time subsequent to the start of the free precession. We consider systems with rough, diffuse reflecting walls, cylindrical trap geometry with arbitrary cross section, and field perturbations that do not, in the frame of the moving particles, average to zero in time. We show by direct, detailed, calculation the agreement of the results from the Schr\"odinger equation with the Redfield theory for the cases of a rectangular cell with specular walls and of a circular cell with diffuse reflecting walls.Comment: 20 pages, 8 figure

Surface roughness effect on ultracold neutron interaction with a wall and implications for computer simulations

We review the diffuse scattering and the loss coefficient in ultracold neutron reflection from slightly rough surfaces, report a surprising reduction in loss coefficient due to roughness, and discuss the possibility of transition from quantum treatment to ray optics. The results are used in a computer simulation of neutron storage in a recent neutron lifetime experiment that re-ported a large discrepancy of neutron lifetime with the current particle data value. Our partial re-analysis suggests the possibility of systematic effects that were not included in this publication.Comment: 39 pages, 9 figures; additional calculations include

Ultracold neutron depolarization in magnetic bottles

We analyze the depolarization of ultracold neutrons confined in a magnetic field configuration similar to those used in existing or proposed magneto-gravitational storage experiments aiming at a precise measurement of the neutron lifetime. We use an extension of the semi-classical Majorana approach as well as an approximate quantum mechanical analysis, both pioneered by Walstrom et al. [Nucl. Instr. Meth. Phys. Res. A 599, 82 (2009)]. In contrast with this previous work we do not restrict the analysis to purely vertical modes of neutron motion. The lateral motion is shown to cause the predominant depolarization loss in a magnetic storage trap. The system studied also allowed us to estimate the depolarization loss suffered by ultracold neutrons totally reflected on a non-magnetic mirror immersed in a magnetic field. This problem is of preeminent importance in polarized neutron decay studies such as the measurement of the asymmetry parameter A using ultracold neutrons, and it may limit the efficiency of ultracold neutron polarizers based on passage through a high magnetic field.Comment: 18 pages, 6 figure

Spin flip loss in magnetic storage of ultracold neutrons

We analyze the depolarization of ultracold neutrons confined in a magnetic field configuration similar to those used in existing or proposed magneto-gravitational storage experiments aiming at a precise measurement of the neutron lifetime. We use an approximate quantum mechanical analysis such as pioneered by Walstrom \emph{et al} [Nucl. Instrum. Methods Phys. Res. A 599, 82 (2009)]. Our analysis is not restricted to purely vertical modes of neutron motion. The lateral motion is shown to cause the predominant depolarization loss in a magnetic storage trap.Comment: 12 pages, 3 figures, for Proceedings of Neutron Lifetime Worksho

Comment on "Giant absorption cross section of ultracold neutrons in Gadolinium"

Rauch et al (PRL 83, 4955, 1999) have compared their measurements of the Gd cross section for Ultra-cold neutrons with an exptrapolation of the cross section for thermal neutrons and interpreted the discrepancy in terms of coherence properties of the neutron. We show the extrapolation used is based on a misunderstanding and that coherence properties play no role in absorption.Comment: 2 pages, 1 postscript figure, comment on Rauch et al, PRL 83,4955 (1999

Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schr\"odinger equation

Pendlebury $\textit{et al.}$ [Phys. Rev. A $\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schr\"odinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.Comment: 11 pages, 4 figure

Localization of Ultra-Cold Particles over Rough Substrates

Localization and diffusion parameters are calculated for particles adsorbed over inhomogeneous substrates for discrete and quasicontinuous spectra of the adsorbed states. The results are expressed via the angular harmonics of the correlation function of surface roughness. The problem is solved analytically in the limiting cases of longwave particles and large correlation radii of surface inhomogeneities. Elsewhere, the problem is solved numerically for Gaussian correlation of inhomogeneities. Applications to electrons on helium films, mobile adsorbed hydrogen atoms and molecules, ultra-cold neutrons in gravitational or magnetic field, etc., are discussed

Observation of Quasibound States of the Neutron in Matter

Quasistationary states of ultracold neutrons have been observed in a double-hump potential barrier. This potential barrier was created by sandwiching a thin film of aluminum between two thin copper films. Measurements of reflection from and transmission through such composite films displayed clear resonances. The resonance positions and widths are in agreement with calculations

Neutron Lifetime Measured with Stored Ultracold Neutrons

The neutron lifetime has been measured by counting the neutrons remaining in a fluid-walled bottle as a function of the duration of storage. Losses of neutrons caused by the wall reflections are eliminated by varying the bottle volume-to-surface ratio. The result obtained is τβ=887.6±3 s