Magnetic Trapping of Ultracold Neutrons

C. R. Brome*, J. S. Butterworth*, K. J. Coakley§, M. S. Dewey†, S. N. Dzhosyuk*, R. Golub‡, G. L. Greene¶, K. Habicht‡, P. R. Huffman*†, S. K. Lamoreaux¶, C. E. H. Mattoni*, D. N. McKinsey*, F. E. Wietfeldt*†, J. M. Doyle*

* Harvard University, Cambridge, MA 02138, USA.
§ National Institute of Standards and Technology, Boulder, CO 80303, USA.
† National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
‡ Hahn-Meitner-Institut, Berlin, Germany.
¶ Los Alamos National Laboratory, Los Alamos, NM 87545, USA.

Overview

Our method of trapping neutrons employs the interaction of the magnetic moment of the neutron (|µ_n| = 1.9µ_N = 0.7 mK/T) with a static but spatially varying magnetic field. Low field seeking states (m_s = +1/2) are trapped in a potential well surrounding a magnetic field minimum in free space. Axial confinement is provided by two solenoids with the same current sense. Radial confinement is provided by four current bars parallel to the beam axis which together form a quadrupolar field. This defines a cylindrical confinement region centered around the beam axis.

In order to magnetically trap a neutron, its total energy must be reduced to less than the trapping potential while it is located inside the confinement region. The superthermal technique for UCN production, as proposed by Golub and Pendlebury, satisfies this requirement. The neutron dispersion curve (Q²/2m) intersects the Landau-Feynman dispersion curve for elementary excitations in superfluid ⁴He at an energy of 0.95 meV (11 K or a neutron wavelength of 0.89 nm). Neutrons close to this energy can scatter to near rest by emission of a single phonon. The rate for the inverse process, upscattering by absorption of a phonon, is suppressed by the Boltzmann factor e^-11K/T, where T is the temperature of the superfluid helium bath. This allows neutrons with energies less than the trap depth (~1 mK) to remain out of thermal equilibrium with the warmer liquid helium for times much longer than the neutron lifetime.

When a trapped neutron decays, the resulting electron recoils through the liquid helium, producing ionization tracks less than 1.5 cm long. Ionized helium recombines to form He₂* molecules, in both singlet and triplet states. Molecules in the singlet states decay promptly, emitting extreme ultraviolet (EUV) photons in a broad peak centered around 80 nm. The combined process of ionization leading to EUV radiation is very efficient; roughly 15 prompt EUV photons are emitted per keV of beta energy.

Although in principle it is possible to detect the EUV light di"RECT"ly, such an approach is impractical due to experimental difficulties in using EUV detectors at low temperatures and in the presence of neutrons. Furthermore, the absence of materials for transmitting and reflecting such radiation precludes the use of room temperature EUV detection. Therefore we frequency downconvert the EUV light to the visible before transporting it out of the cryostat and into a photomultiplier tube (PMT) at room temperature.

Apparatus

A picture of our apparatus is shown above. The key requirement for the apparatus is to allow a cold neutron beam to pass through the center of the trapping region while this region is filled with < 250 mK superfluid helium. In addition, neutron-induced activation and luminescence of surrounding materials must be kept to a minimum.

The entire cryogenic apparatus resides within a dewar which is shaped like an inverted-"T". The dewar has two sections: a vertical section which houses a 400 µW (cooling power at 100 mK) dilution refrigerator and a horizontal section attached below which holds the magnetic trap and detection system. The two sections are assembled independently and joined using an arrangement of sliding seals. Neutrons enter the apparatus through a series of teflon windows, which form vacuum seals and transmit neutrons with low scatter. Beryllium foils at 77 K and 4 K prevent heating from blackbody radiation.

Neutron Trapping Data

Ultracold neutrons have been magnetically trapped for the first time.

Neutron trapping data from four weeks of running are shown at right in figures a and c. The neutron beam passes through the cell for 22 minutes following which scintillation events are recorded for one hour. Data are collected either with the magnetic field on for the entire run ("trapping runs") or with the magnetic field off during the loading phase but on during observation ("non-trapping runs"). The results shown are obtained by pooling the data and subtracting the trapping runs from the non-trapping runs. This technique minimizes contributions from time dependent backgrounds, such as luminescence and activation.

While taking trapping data, the trapping region is filled with isotopically pure ⁴He (less than 1 part in 10^{15 3}He). In order to confirm that the observed signal is due to trapped neutrons, additional data were taken with a small amount of ³He (1 part in 10⁷) doped into the isotopically pure ⁴He. This amount of ³He absorbs less than 1 % of the neutron beam but results in a trap lifetime of less than 1 second. The difference of trapping and non-trapping runs with ³He doped into the bath is shown at right in figures b and d. The exponential decay from the trapped neutron events is absent.

Two sets of background subtracted trapping data were collected: set I with a trap depth of 0.76 mK (a) and set II with a lower trap depth of 0.50 mK (c). (The lower trap depth was used due to problems with the magnet.) Most of the run-to-run variation in background rate is eliminated by excluding the first two pairs of runs in which the background rate is changing quickly due to activation of materials with lifetimes > 12 hours. The remaining 23 pairs in set I (from about five days of running) and 120 pairs in set II (from about three weeks of running) are pooled and modeled as:

W₁ = a₁ e^-t/Tau+C₁,     W₂ = a₂ e^-t/Tau+C₂.

The subscripts refer to sets I and II, a_i = E N_i/t, N_i is the initial number of trapped neutrons, E is the detection efficiency, and Tau is the lifetime of neutrons in the trap. The constant C_i is present to account for the possible remaining effect of the changing background rate due to long-lived activation. However, in all of our fits the value of C_i is consistent with zero. The fit is performed simultaneously on the two data sets, minimizing the total Chi² while varying five parameters: a₁, a₂, C₁, C₂ and Tau. The only parameter connecting the two data sets is Tau. The best fit values indicate N_I = 560 ± 160 and N_II = 240 ± 65. Calculations using the known beam flux, trap geometry and the theory of the superthermal process predict N_I = 480 ± 100 and N_II = 255 ± 50, in good agreement with the measured values. The best fit value for the lifetime, Tau = 750 +330/-200 s is consistent with the presently accepted value of the neutron beta-decay lifetime of 886.7 ± 1.9 s. All of the errors quoted correspond to a 68 % confidence interval.

This work demonstrates the loading, trapping, and detection techniques necessary for performing a neutron lifetime measurement using magnetically trapped UCN. Another important result is the di"RECT" confirmation of the theoretical prediction of the UCN density in the trap. Our value for the number of trapped neutrons at a 0.76 mK trap depth corresponds to a density of 2 UCN/cm³, compared to the density of 1 UCN/cm³ obtained in UCN material bottle experiments with a comparable UCN cut-off energy and higher flux reactor. Our measured density is consistent with previous measurements of the UCN production rate based on observation of upscattered UCN at higher temperatures.

Future Di"RECT"ions

We are currently limited by statistics and are in the process of building a larger and deeper trap in addition to implementing minor upgrades to the neutron collimation and detection system. We expect these improvements to ulitimately yield a factor of 200 increase in the number trapped neutrons. With this new apparatus, we expect to make a lifetime measurement with significantly higher precision than the present world average.

There are four principal sources of systematic error due to neutron loss, all of which are controllable to our desired precision. First, ³He dissolved in the superfluid bath can absorb neutrons. We find that ultra-pure ⁴He with a fractional ³He content of 5 x 10^-16 gives an absorption loss time of greater than 2.8 years. (This ultra-pure helium is obtainable by employing the heat flush technique developed by Hendry and McClintock.) Second is inelastic upscattering of the UCN. The dominant process at temperatures less than 1 K is two-phonon upscattering. The one-phonon upscattering rate is negligible. The two-phonon rate depends on temperature as 10²T^-7 s^-1, where T is measured in Kelvin. A negligible upscattering lifetime requires T < 250 mK. The third possibility is that neutrons with total energy greater than the trap depth may be temporarily contained within the trap in semi-stable orbits. We have shown, both analytically and through simulations, that it is possible to remove these neutrons by lowering the depth of the trap for a short time and then raising it again. A fourth possibility is loss by Majorana or spin-flip transitions in low-field regions. The use of a fixed-bias Joffe trap configuration with no zero-field regions greatly reduces such losses. An axial field of B_z > 0.2 T will suppress the rate of Majorana transitions below our expected statistical accuracy. The reduction of trap phase space due to this field is insignificant. Several systematic effects associated with previous lifetime experiments, such as wall losses, betatron oscillations, and pulse pile-up losses are eliminated by three-dimensional magnetic trapping and continuous monitoring of the neutron decay. In addition, our technique removes dependence on detector efficiencies, requiring only that the detection threshold remain stable throughout a trapping cycle (about two hours).

Based on our current understanding of the potential systematic effects, a precision of 10^-5 in the neutron lifetime could ultimately be possible with this technique. For the foreseeable future, however, this experiment will remain statistics limited.

For more information, please see our latest publication P. R. Huffman et al., Nature, 403, 62 (2000). A complete list of publications related to this work can be found at http://www.doylegroup.harvard.edu/~neutron.