First observation of trapped high-ﬁeld seeking ultracold neutron spin states

material walls. Low-ﬁeld seeking neutrons were axially conﬁned above the magnetic ﬁeld. High-ﬁeld seeking neutrons are trapped inside the magnetic ﬁeld. They can systematically shift the measured neutron lifetime to lower values in experiments with magnetic conﬁnement.


Introduction
The free neutron interacts via all known forces. While the weak interaction is responsible for the decay of the neutron, e.g., n → p + e − + ν e , strong interaction, gravity, and electromagnetic interaction can be used to store very slow neutrons with velocities v n 7 m/s in bottles. These neutrons are termed ultracold neutrons, UCN, because a neutron gas with such neutron velocities has a temperature below 3 mK.
The coherent strong interaction potential arises in the theoretical treatment of the interaction of very low energy neutrons (with their corresponding large neutron wave length) with materials in terms of refraction, see, e.g., Ref. [1]. As a consequence, the interaction of neutrons with material surfaces [2][3][4] can be described by a potential, V f = V − iW . Here, V and W depend on the nuclear properties of the surface atoms: where, m denotes the neutron mass, N the scattering centre density, b the bound coherent nuclear scattering length, σ the loss cross section per atom of the surface material,h Planck's constant, and v the neutron velocity. For neutrons being reflected from a material surface the real part of the potential, V , sets the critical velocity, v c = √ 2V /m, for total reflection and the imaginary part, W , determines the reflection loss [5,6]. Ultracold neutrons interact with the gravitational field of the Earth. Their potential energy per height, E pot /h = m · g, is equivalent to 102 neV/m. That means a UCN of 250 neV corresponding to a velocity of about 7 m/s can rise against the Earth's gravitational field to about 2.5 m. When a neutron enters a magnetic field B it is reflected if the orientation of its magnetic moment is antiparallel to the direction of the magnetic field and if its kinetic energy is E E B = |1.91 · μ N · B| = 60 neV/T · B, with μ N the nuclear magneton. Because of the repulsion, neutrons with this spin orientation are generally termed low-field seekers, LFS. Neutrons with the orientation of the magnetic moment parallel to the field are accelerated into the magnetic field with the force F m = −∇[μ · B] = |μ|∇|B| and are therefore termed high-field seekers, HFS. This assumes that the neutron's motion is so slow that its magnetic moment always keeps the same orientation with respect to the magnetic 0370 2693 -field (adiabatic case). The condition for this is that the time variation, i.e., the rotation rate of the magnetic field B seen by the neutron as it moves through the inhomogeneous field is much less than the Larmor frequency, ω L , of the neutron spin: (2) Here, d B ⊥ /dx is the magnetic field gradient perpendicular to B, |dx/dt| the neutron velocity, and μ n the neutron magnetic moment, μ n = −1.91 · μ N .
Ultracold neutron storage in a multipole magnetic field has been used in the past to measure the lifetime of the free neutron [7,8]. Because of discrepancies in the most precise neutron lifetime measurements [9][10][11], new experiments with magnetic confinement in order to avoid losses on wall collisions are in discussion worldwide.

Experimental apparatus
Our apparatus for the storage of UCN takes advantage of all interactions (except the weak interaction) neutrons participate in, (i) the coherent strong interaction of neutrons with a material wall, (ii) gravitation and (iii) the electromagnetic force. The apparatus is shown in Fig. 1 and described in detail in Ref. [12].
We have recently performed an experiment to measure the depolarisation of UCN in neutron guides [13] at the beam line PF2/EDM [14,15] of the Institute Laue-Langevin (ILL), Grenoble. Ultracold neutrons from the UCN turbine [16] enter the experimental apparatus from the right through a UCN guide (1, Fig. 1) and a rotatable shutter (2, Fig. 1) in open position. With the UCN switch (4, Fig. 1) in filling position, UCN are deflected into a cylindrical vertical neutron guide (6 and 16, Fig. 1) which is placed in a bore through the centre of the iron yokes and poles of the magnet. It is 1.5 m long, has an outer diameter of 80 mm, an inner diameter of 70 mm, and is coated with a 500 nm thick layer of materials with high optical potential, e.g. Ni/Mo alloy with a weight ratio of 85% Ni and 15% Mo (NiMo 85/15). This alloy is non-magnetic [17] and has an optical potential of 238 neV [5] which makes it well suited for the transport of polarised as well as unpolarised UCN.
Our coordinate system is defined as follows: The origin is placed in the midplane of the air gap and the center of the bore in the H-type split coil magnet, with the height z = 0 and the radius r = 0. The upper 900 mm of the sample tube (16, Fig. 1) are above the air gap of the H-type split coil magnet, i.e., at z > 0, and serve as a storage volume for UCN. The H-type split coil magnet is used to make a dipole field at the lower end of the storage volume. Ultracold neutrons are filled into the storage volume with the magnetic field switched off. After 20 s of filling, equilibrium neutron density in the storage volume is reached and the magnetic field in the air gap is switched on for the storage of UCN. The field is raised within about 2 s to 90% of the maximum electric current resulting in a magnetic field strength of 1.45 T and corresponding to a UCN kinetic energy of 87 neV at the origin of the coordinate system. Then, the mechanical neutron switch (4, Fig. 1) is moved from filling position to emptying position into the detector (3, Fig. 1) blocking UCN from the turbine. The beam line shutter (2, Fig. 1) is closed for improved background suppression.
After switching on the magnetic field, the stored UCN spectrum is "cleaned" by waiting without any action over a time of 100 s. This period was found by Monte Carlo calculations using GEANT4UCN [18] and by experimentally varying this time span. With the absorber position at 890 mm during this cleaning period, all UCN in the storage volume above the magnetic field with kinetic energies higher than 87 neV at z = 0 have been either  After the spectral cleaning time of 100 s, the magnet current is raised in a split second (t ∼ 0.3 s) to 100%, resulting in 1.52 T and UCN are stored over holding times reaching from 20 to 370 s. Neutrons which have been spin-flipped during these holding times, e.g., by interaction with the wall material during a wall bounce, can now pass the magnetic shutter and are registered in the neutron detector. After storage, the magnetic field is rapidly switched off (t < 2 s) and the remaining UCN are detected over an emptying time of 45 s. Fig. 2 shows the detector counts over time from filling (detector closed), spectral cleaning, storage and emptying. With this procedure, the wall loss and depolarisation probabilities of UCN interacting with the material of the wall can be determined, cf. Refs. [19,20].

UCN energy distribution in the storage volume
In order to study eventual energy dependences of the UCN loss and depolarisation probabilities -the results will be presented later elsewhere in Ref. [13] -the experimental cycle shown in Fig. 2 has been performed with the absorber (15, Fig. 1) at different heights. The maximal storable UCN energy is then defined by the absorber height. Fig. 3 shows the UCN counts in the emptying period as a function of the UCN absorber height. The number of UCN counts decreases continuously between the absorber positions at z = 890 mm and z = 400 mm. Between z ∼ 300 mm and z ∼ 100 mm, the UCN counts are constant at a level of about 7% of the total counts and decrease to zero at zero height position. This means that there are no or only very few UCN in the storage volume between z ∼ 100 mm and z ∼ 300 mm, as one can easily see from the differential energy spectrum, Fig. 3. This finding is confirmed by the potential energy distribution of UCN in the apparatus, see Fig. 4. The calculation is based on magnetic field measurements along the vertical axis of the apparatus and two-dimensional rotation-symmetric field distribution calculations using the code POISSON SUPERFISH [21].
The explanation of this phenomenon is as follows: There are quite some UCN traversing the region of the magnetic field while the field is ramped rapidly. Those with their magnetic moments antiparallel to the magnetic field (LFS) are accelerated out of the magnetic field region into the storage volume and experience a gain in total energy. They can be stored if their kinetic energy after this acceleration is below 87 neV at z = 0. This energy corresponds to the 1.45 T magnetic field during the 'spectral cleaning'. spectrum; open squares: differential UCN energy spectrum. The differential spectrum was obtained by the count rate differences at z(i) and z(i − 1), where z(i − 1) = z(i) − 100 mm. The z position for the differential spectrum is then the weighted mean, z(i − 1) + 100/ √ 2 mm. High-field seekers are decelerated and trapped in the high magnetic field region if their kinetic energy at z = 0 is smaller than about 10 neV immediately after the magnetic field of 1.45 T is switched on. Further measurements have been performed using samples coated with Ni alloys which are ferromagnetic at room temperature, e.g., NiMo 91/9, NiMo 94/6, and natural nickel. These samples are probably immediately magnetised to saturation in the vicinity of the magnet air gap when the magnetic field is switched on.
For the stored HFS, the depolarisation rate is very small and almost equal to the background. At the inner radius of the cylindrical vertical neutron guide, i.e., where the material under investigation is coated onto the cylinder wall, the magnetic field in the mid-  In the case of changing the magnetic field after the cleaning period from 1.45 T to 1.52 T at the origin of the coordinate system, z = 0, r = 0, in a split second (∼0.3 s) the gradient changes from 0.55 T/m to 0.58 T/m and we obtain, e.g. at r = 0 (d B ⊥ /dt)/B = (0.03 T)/(0.3 s)/(1.52 T) = 0.07 Hz. Also here the adiabatic condition, cf. Eq. (2), is well fulfilled and no depolarisation can occur due to this change in the magnetic field value.
Above z ∼ 130 mm, the magnetic field in air in the magnet bore drops below the saturation value in the ferromagnetic Ni coating (B(air) < 0.6 T), cf. Fig. 5, and therefore the relative permeability of the ferromagnetic coating increases to μ > 1. As a consequence, the stray magnetic field entering the ferromagnetic coating is suddenly strongly bent and has a discontinuous distribution and gradient.
For a quantitative estimate, we assume that the measured stray magnetic field of 0. In case the magnetic stray and holding field at larger z values is too weak to align the Weiss domaines in the Ni coating, we assume dx to be of the order of the size of the Weiss domaines (0.01-1 μm). Here, we obtain (d B ⊥ /dt)/B ≈ 2 · 10 6 Hz (for v n = 2 m/s at z ∼ 600 mm) where the Larmor frequency, e.g., for the minimal value of the holding field, B(min) = 2.5 mT, is about 4 · 10 5 Hz. This also does not fulfill the adiabatic condition, cf.
As a consequence, all UCN stored above z ∼ 130 mm can be rapidly depolarised already during spectral cleaning and fall into the detector. This can be seen from Fig. 6 (b) and (d): the counts with the absorber at z = 890 mm and z = 100 mm agree within statistics.

Conclusion
In conclusion, with these measurements we have demonstrated for the first time that in a UCN storage trap using a switchable magnetic dipole field as a shutter, UCN with both spin orientations can be trapped: (i) Low-field seekers are accelerated away from the magnetic field and stored in the storage volume above the magnetic dipole field if their energies are below E = μ · B.
(ii) High-field seekers with energies below E = μ · B are decelerated and trapped in the region of the magnetic field if they were in this region during the ramping of the magnetic field (or if they are transported adiabatically into the magnetic field region while the field is on). This phenomenon is important for UCN experiments using magnetic confinement by means of a magnetic dipole shutter. For instance in a neutron lifetime experiment it could induce a time-dependent background which may lead to a systematic shift of the measured neutron lifetime to lower values.
As a preliminary statement concerning the depolarisation probabilities β, we can say that these values are in the order of 10 −5 per wall bounce or smaller. Details will be described elsewhere in a forthcoming publication [13].