Ultracold neutron depolarization in magnetic bottles

A. Steyerl, C. Kaufman, G. Müller, S. S. Malik, and A. M. Desai

Phys. Rev. C 86, 065501 – Published 7 December 2012

Abstract

We analyze the depolarization of ultracold neutrons confined in a magnetic field configuration similar to those used in existing or proposed magnetogravitational storage experiments aiming at a precise measurement of the neutron lifetime. We use an extension of the semiclassical Majorana approach as well as an approximate quantum mechanical analysis, both pioneered by Walstrom et al. [Nucl. Instrum. Methods 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 nonmagnetic 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.

Received 28 September 2012

DOI:https://doi.org/10.1103/PhysRevC.86.065501

Authors & Affiliations

A. Steyerl^*, C. Kaufman, G. Müller, S. S. Malik, and A. M. Desai

Department of Physics, University of Rhode Island, Kingston, Rhode Island 02881, USA

^*asteyerl@mail.uri.edu

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 86, Iss. 6 — December 2012

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
For our field model, the arrows show the Halbach magnetic field $B_{H}$ as it rotates in the ( $x y$ ) plane. Its magnitude $B_{H}$ decreases exponentially with height $y$ and is represented by the arrow length using a log scale. The angle $ϕ = - K x$ of the Halbach field is also shown. The superimposed stabilization field $B_{1}$ in the $z$ direction increases slowly with $y$ as in Ref. [14] and is symbolized by the crosses of variable size.Reuse & Permissions
Figure 2
Depolarization probability, given by Eq. (34) multiplied by $m / ℏ$ , as a function of neutron position for drop heights $y_{0}$ $=$ 450 mm and 100 mm, stabilization field parameter $B_{10}$ $=$ 0.005 T, and neutron velocity component $v_{x}$ $=$ 3 m/s or zero. The sharp peak occurs in the region where the gradient of field angle $θ$ is largest.Reuse & Permissions
Figure 3
Ratio between mean depolarization rate, given by Eq. (39), and neutron $β$ -decay rate (for a lifetime of 882s), plotted as a function of vertical velocity component $v_{+}^{(n)}$ in the neutral plane (where the gravitational and magnetic forces are balanced). $v_{+}^{(n)}$ is normalized with the constant $v_{- 0}^{(n)}$ which is determined by the field magnitude in the neutral plane. The curve for $B_{10}$ $=$ 0.005 T is plotted to scale $(ν = 0)$ and the curve for $B_{10}$ $=$ 0.05 T is plotted with magnification factor $10^{1}$ $(ν = 1)$ . Their difference by about two orders of magnitude shows the strong suppression of depolarization by a stabilization field of sufficient strength. For a Maxwell spectrum, the mean height of the curves over the range of the abscissa, from 0 to 2.5 for $B_{10} = 0.05$ T and from 0 to 4.7 for $B_{10} = 0.005$ T, directly determines the average over the full spectrum (here for $- 3$ m/s $< v_{x} <$ $+ 3$ m/s and drop heights $y_{0}$ up to 450 mm).Reuse & Permissions
Figure 4
Geometry of nonmagnetic mirror conceptually placed into the magnetic storage space at various levels $y_{m}$ between the upper and lower turning surfaces at $y_{u}$ and $y_{l}$ for a given UCN energy for vertical motion. The reflected spin-flipped wave consists of the two components in Eq. (42): (a) the particular solution $β_{p}$ which is the same as for a wave moving upward from the lower turning point at II in the absence of the mirror; (b) the homogeneous wave $β_{h}$ induced at the mirror surface by the wave incident from above, starting from the upper turning level at point I. The position III of the virtual image of I below the mirror determines a phase angle.Reuse & Permissions
Figure 5
Normalized depolarization as a function of mirror position $y_{m}$ . We use Eq. (52) for the quantum treatment (QM) and Eq. (68) for the semiclassical approach. The plotted values are normalized by dividing Eq. (68) by Eq. (36), the depolarization due to the field alone, and by the ratio of duration of one bounce with and without the mirror. This figure shows a strong enhancement of depolarization due to the mirror. The enhancement factor depends on incident UCN energy (which increases with larger fall height $y_{0}$ ) and on the gradient $θ_{m}^{'}$ of field angle $θ$ at the mirror position. $θ_{m}^{'}$ is largest in the region where the curves have their peak value which is of order $10^{4}$ for $v_{x}$ $=$ 3 m/s. For the examples shown, the turning point levels are: $y_{u} = 96.86$ mm, $y_{l} = 14.31$ mm for $y_{0} = 100$ mm, and $y_{u} = 445.82$ mm, $y_{l} = 0.58$ mm for $y_{0} = 450$ mm.Reuse & Permissions
Figure 6
Depolarization current for downward motion in the magnetic field for parameters $y_{0}$ $=$ 8 cm, $B_{10}$ $=$ 0.05 T, and $v_{x}$ $=$ 3 m/s. Direct numerical integration, represented by the solid curve, coincides with the analytic result shown by the dashed curve, with a maximum deviation of 1 $%$ over the entire range from upper to lower turning point ( $y_{u} = 49.56$ mm, $y_{l} = 18.08$ mm).Reuse & Permissions

Physical Review C

covering nuclear physics