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Experimental measurement of ultracold neutron production in superfluid 4He
Physics Letters A 308 (2003) 67–74 www.elsevier.com/locate/pla
Experimental measurement of ultracold neutron production in superfluid 4 He C.A. Baker a , S.N. Balashov a , J. Butterworth b , P. Geltenbort b , K. Green a,c , P.G. Harris c , M.G.D. van der Grinten a,c,∗ , P.S. Iaydjiev a,1 , S.N. Ivanov a,2 , J.M. Pendlebury c , D.B. Shiers c , M.A.H. Tucker c , H. Yoshiki d a Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK b Institut Laue-Langevin, B.P. 156, 38042 Grenoble, France c Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QJ, UK d Kure University, Hiroshima, Japan
Received 27 November 2002; accepted 9 December 2002 Communicated by V.M. Agranovich
Abstract The absolute production rate of ultracold neutrons (UCN) produced by the interaction of a cold neutron beam with superfluid helium has been measured over an incident energy range of 0.7 to 4 meV. The neutrons are reduced in energy to become UCN by creating phonon(s) in the superfluid. The separate roles played by single and multi-phonon emission processes have been identified. Detection and identification of UCN, those neutrons with energies less than ∼ 250 neV and which can be stored in material bottles, were carried out using solid-state silicon detectors set within the superfluid helium. With a cold neutron flux of 2.62 × 107 neutrons cm−2 s−1 Å−1 at 8.9 Å in the superfluid, the single-phonon production rate of UCN was measured to be (0.91 ± 0.13) cm−3 s−1 , a value close to theoretical prediction. Multi-phonon emission processes for UCN production by higher energy neutrons were also observed and, in the beam used for this work at ILL, they contributed (24 ± 2)% to the overall UCN production rate. 2003 Elsevier Science B.V. All rights reserved.
1. Introduction There is currently considerable interest in new and improved sources of ultracold neutrons (UCN). Such neutrons have energies that are typically less than a
* Corresponding author.
E-mail address: [email protected] (M.G.D. van der Grinten). 1 On leave of absence from INRNE, Sofia, Bulgaria. 2 On leave of absence from PNPI, St. Petersburg, Russia.
few hundred neV, and they can be trapped and stored inside vessels made from materials with sufficiently high Fermi potentials (VF ). Stored UCN have been used to study the fundamental properties of the neutron [1] and, in particular, to measure with increasing precision the electric dipole moment (EDM) of the neutron. The current neutron EDM measurement by the RAL/Sussex/ILL group [2], which uses UCN from a cold, thermally moderated neutron source at the research reactor at the ILL in Grenoble, is now approaching its statistical limit. Further progress in ex-
0375-9601/03/$ – see front matter 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0375-9601(02)01773-5
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C.A. Baker et al. / Physics Letters A 308 (2003) 67–74
ploring in this way the nature of CP symmetry violation and particle physics beyond the Standard Model will soon need a more intense source of UCN. One of the most promising candidates for a new source of UCN at high densities is a super-thermal one [3], which exploits the properties of superfluid 4 He. UCN can be produced when superfluid 4 He is irradiated with cold neutrons, which then lose energy by each creating one or more phonons in the superfluid. The UCN produced survive well in the superfluid since the cross section for absorption of neutrons on 4 He is identically zero and, provided the temperature of the helium is low enough (< 0.7 K), the inelastic up-scattering of the UCN by phonons is very improbable.
2. Theoretical background Production of UCN by the emission of a single phonon occurs with cold neutrons having energy and momentum at the intersection of the energy– momentum relation for the free neutron and the phonon–roton dispersion curve for liquid helium. The cold neutrons and the phonons produced both have energies of E ∗ ∼ 1.0 meV and the neutron has a wavelength λ∗ ∼ 8.9 Å. The production rate RI for UCN created within 4 He (VF = 18.5 neV) and stored within beryllium walls (VF = 252 neV) has been calculated [3,4] to be −8 dΦ RI = (4.55 ± 0.25) × 10 (1) cm−3 s−1 , dλ λ∗ where dΦ/dλ|λ∗ is the differential flux in neutrons cm−2 s−1 Å−1 . The 4 He neutron-scattering cross section for the single-phonon UCN production in the superfluid is non-zero over a cold neutron energy range of only ∼ 10 µeV; a range which is determined by the kinematics of the process and by the small ranges of energies and momenta of the UCN produced that can be trapped. Cold neutrons with energies outside this range can also be down-scattered to UCN energies, but only by the emission of two or more phonons in one scattering event [5]. Several experiments [7–10] have in the past been carried out with the intention of measuring these UCN production rates but, because they all had neutron detectors at room temperature far outside the liquid he-
lium where the UCN were being produced, the interpretation of their data was difficult. In particular, it was difficult to estimate the severe attenuation, by a factor of ten or more, of the numbers of UCN as they emerged through the several windows needed for containment and radiation shielding. In this experiment, we have immersed the detectors in the superfluid helium so that the UCN produced can then pass directly to the detectors without passing through any intervening windows.
3. Experimental apparatus The experiment was carried out using the H53 coldneutron guide [11] at the Institut Laue-Langevin in Grenoble. The neutrons were transported from the reactor through 80 m of 58 Ni coated glass guides to the experimental area where the helium cryostat was mounted. A velocity selector, installed close to the primary guide exit, enabled the wavelength of the transmitted neutrons to be chosen with a resolution of ∼ 12% FWHM. Between the neutron guide and the cryostat the beam was reduced in size from its initial cross-sectional area of 72 cm2 by a series of collimators made from 6 LiF and boron loaded plastics spread over a horizontal distance of 3.85 metres. A final circular aperture of diameter 30 mm set close to the inlet flange of the cryostat and 55 cm from the centre of the UCN production volume, helped to define the input beam to the cylindrical, 67 mm diameter, superfluid target volume. The capture flux (Φc ), averaged over the area of the circular aperture, was measured by gold foil activation to be (1.30 ± 0.18) × 109 cm−2 s−1 without the velocity selector and (1.47 ± 0.20) × 108 cm−2 s−1 with the selector set to transmit 9 Å neutrons. Before the cryostat was put in place, the velocity spectrum of the broadband incident neutron beam was measured using timeof-flight techniques that recorded the capture flux over a flight path of 1.845 m (Fig. 1). The intensity distributions were also measured with the velocity selector set to a number of nominal settings; these distributions were then characterised using Gaussian fits to the data, which gave a central value λ and standard deviation σλ for each wavelength transmitted. This fit to a Gaussian distribution was found to be a very good approximation to the data, which, without
C.A. Baker et al. / Physics Letters A 308 (2003) 67–74
acceptance corrections, might have been expected to be purely triangular. In the case of the 9 Å nominal setting the beam was measured to have
Fig. 1. The spectrum of the cold neutron beam guided into the cryostat.
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a central wavelength of λ = 8.90 Å and a standard deviation σλ = 0.41 Å. At this setting the flux was measured using gold foil activation to be dΦ/dλ = (2.88 ± 0.39) × 107 neutrons cm−2 s−1 Å−1 . After allowing for a measured reduction factor of (1.10 ± 0.05) in beam intensity as the beam passed through the windows of the cryostat, the predicted UCN production rate from single phonon emission using Eq. (1) is RI = (1.19 ± 0.18) UCN cm−3 s−1 . The experimental arrangement of the 4 He-based UCN source is shown in Fig. 2. The ‘T’-shaped central volume of 6 litres, which contained the horizontal 1.1 litre UCN production volume, was cooled to T ∼ 0.5 K by a circulating 3 He expansion system. It was filled with superfluid 4 He from the main helium reservoir via a superleak: this decreased the atomic concentration of 3 He, a strong neutron absorber, from its natural level of 10−6 within liquid helium to below 10−12 .
Fig. 2. A sketch of part of the cryostat. A cold neutron beam is guided into the horizontal UCN production volume, which is filled with pure superfluid 4 He. After a dwell period of about 10 s the UCN that are produced escape through a 10 mm diameter hole into the vertical guide tube, at the bottom of which they reach the detector assembly.
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An outer vessel of copper and stainless steel confined the superfluid, whilst an inner vessel confined the UCN. The inner vessel consisted of a horizontal and a vertical stainless steel tube, each of internal diameter 67 mm and coated with 2500 Å of beryllium metal on the inner surface. The horizontal tube was closed at either end with a 0.25 mm thick Be foil clamped to the tube. Any neutrons which scattered from the 4 He at large angles, and with energies too great to be trapped, were absorbed and attenuated by 6 LiF loaded plastic, 1.2 mm thick and 67% 6 LiF by weight, wrapped around the outside of the horizontal tube. Neutrons trapped by the Fermi potential of the horizontal tube could escape via a 10 mm diameter aperture leading to the vertical tube and to the detectors.
4. Neutron detectors The results presented in this Letter were obtained using ORTEC ULTRA silicon detectors [12] that had 600 µg/cm2 6 LiF evaporated onto the detecting surface. The 6 LiF layer was sandwiched between aluminium layers of thickness 200 Å on top, for protection, and 2000 Å beneath for bonding to the detector. Three such detectors, each of 300 mm2 area, were mounted separately as an array in a horizontal plane at the lower end of the vertical tube, the remainder of the plane being covered with a neutron absorbing layer of 6 LiF on aluminium. The pre-amplifiers were outside the cryostat, at room temperature. The detectors were thus set 59 cm below the bottom of the horizontal tube so that gravity would accelerate the slowest UCN to energies greater than the Fermi potential of the Al and 6 LiF layers. Neutrons that entered the 6 LiF layer react according to the process n + 6 Li → α + 3 H + 4.78 MeV. These reaction products are emitted back to back, so that a single charged particle of energy at least 2.05 MeV strikes the silicon for every UCN that reacts. In separate experiments at room temperature [13], using stored UCN from the ILL PF2 source, we measured the overall efficiency for one 300 mm2 ULTRA detector to be (82 ± 1)% after optimising the thickness of the 6 LiF layer at 600 µg/cm2 . The performance of ULTRA detectors has been tested as a function of temperature and was found to show no change from room temperature down to 85 mK [14]. In the cryogenic experiment
reported here the signal spectrum from the alpha particles partially overlapped with the electronic noise, so only the peak due to tritons was used in order to ensure maximum reproducibility of the UCN detection process. The detector efficiency was then (41 ± 1)% for the purpose of these measurements.
5. Data-taking procedure Data were taken for 25 days in March 2001 using the broad-band cold neutron beam of H53 in ILL, and again for 25 days during March 2002 using the same beam but this time with a neutron velocity selector [15] in place. The measurement cycle began by opening a shutter in the cold neutron beam for a filling time of 40 s, this being about four times the storage time for UCN in the beryllium-coated containment vessel with its 10 mm diameter exit aperture. During this period the neutron beam passed through the cryostat, and UCN were produced in the superfluid. Following the filling the shutter was closed for 100 s, allowing the stored UCN to leave the horizontal tube through the aperture and to fall under gravity to be counted in the silicon detectors. The arrival times, relative to the cycle start, of the counts in the UCN detectors were recorded using a PC-based multi-scaler system with a time resolution of 136 ms per channel. The above cycle was repeated some hundreds of times to accumulate the spectrum of counts as a function of time with good statistics.
6. Analysis of the data 6.1. Data taken in 2001 During 2001 data were taken on the production of UCN at a series of liquid 4 He temperatures between 0.43 K and 2.05 K. The results at the lowest temperature (0.43 K) and at the highest temperature (2.05 K) are shown in Fig. 3. Both sets are the accumulation of 500 filling and emptying cycles. With the cryostat at 0.43 K, the lowest temperature achievable in the present configuration, the results are qualitatively and quantitatively different from those at 2.05 K. At 0.43 K, the neutron count-rate initially increases with time after the shutter is opened and
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Fig. 4. Experimental measurement of the temperature dependence of UCN storage lifetime, together with the theoretical expectations [6] from two models of phonon and roton interactions.
Fig. 3. (a) Neutron counts accumulated from 500 data-taking cycles, where the cold neutron beam is introduced into the liquid helium at zero time and then switched off again at 40 s. The symbols represent UCN production (#) at 430 mK, and () at 2.05 K where UCN are immediately lost by interaction with thermal phonons in the liquid He. Graph (b) is an expanded view of the tail of (a), showing the characteristic storage time of the UCN in the production cell.
decreases exponentially with time after it is closed. The initial rise is a build-up of the population of stored UCN as they are produced whilst the beam is on. This is superimposed upon a background of higher energy neutrons that cannot be trapped and which are scattered into the detector from the incident broad band beam as it passes through the helium. The fall in count rate when the incident beam is turned off shows a decrease in the population of stored UCN as they diffuse out of the horizontal containment tube to the detectors. This emptying curve can be fitted very well to a single exponential with a time constant of ∼ 10 s, and the resultant average total number of
counts from one filling and emptying cycle is N0 = (65.5 ± 1.0) UCN. We present these data as a very clear demonstration of the production, storage and detection of UCN within the liquid helium. Fig. 4 shows our results for the characteristic temperature dependence of UCN storage in liquid helium. This is very similar to the results reported by Kilvington et al. [9] and demonstrates clearly that at T = 2.05 K no UCN from the horizontal tube reach the detector because of the fast up-scattering rate in the superfluid. 6.2. Data taken in 2002 In order to see separately the single- and multiphonon processes in the production of UCN, further data were taken in March 2002 with a velocity selector in the incident neutron beam. The superfluid helium in the cryostat was kept at 0.7 K, and a series of 18 data runs took place with the wavelength of the incident neutron beam in each run being selected from within the range 4.5 Å to 11 Å. Fig. 1 shows the spectra of transmitted neutrons for various settings of the velocity selector. The wavelength acceptance was typically 12% FWHM. The UCN detection was carried out as before, within the superfluid helium, using 300 mm2 silicon neutron detectors. The emptying curves of all of the data sets could again be very well fitted to a single exponential with a
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Table 1
Fig. 5. The UCN detector counts as a function of time, with the velocity selector set to 9 Å.
Fig. 6. The UCN count rate recorded at wavelengths between 4 Å and 11 Å.
Nominal wavelength setting λ (Å)
Standard deviation σλ (Å)
UCN/ cycle
Error
UCN/ 0.5 Å
Error
4.50 4.99 5.49 5.99 6.53 6.99 7.49 8.01 8.25 8.50 8.65 8.80 9.01 9.20 9.50 9.75 10.00 10.52
0.25 0.26 0.28 0.29 0.32 0.33 0.35 0.37 0.38 0.39 0.40 0.41 0.41 0.41 0.42 0.43 0.44 0.47
1.68 3.06 4.06 5.05 5.57 3.77 1.6 2.74 11.97 28.88 41.84 49.57 48.51 37.58 21.65 9.31 1.75 0.05
0.08 0.11 0.12 0.13 0.14 0.1 0.08 0.08 0.47 0.5 0.7 0.65 0.66 1.1 0.39 0.38 0.07 0.05
1.36 2.38 2.93 3.52 3.52 2.31 0.92
0.06 0.09 0.09 0.09 0.09 0.06 0.05
Table 1. The ten data sets that constitute a scan over the range 7.5 Å to 10.5 Å have been fitted to a Gaussian distribution, yielding as parameters a peak value of N0 = (52.4 ± 0.4) UCN/cycle at a wavelength of λ = 8.86 Å and a standard deviation of σλ = 0.39 Å. The latter is in very close agreement with σλ = 0.41 Å the wavelength resolution of the incident beam. This is clear evidence that a peak in the production of UCN is occurring at ∼ 8.9 Å with a width which is much less than the wavelength range of the incident beam.
constant background: N(t) = N0 exp(−t/τ ) + B,
7. Calculation of UCN production rate
with τ = 8.82 ± 0.16 s and a background B of (2.2 ± 0.2) × 10−2 counts/second. Fig. 5 shows the data obtained with the velocity selector set to 9.0 Å. The background arising from neutrons scattered from the liquid helium during the filling period, with energies > E ∗ and which are not trapped, is now also negligible compared with the contribution from the UCN counts since kinematic restrictions force these scattered neutrons into the forward hemisphere and away from the detector arrangement [4]. The results from the data sets taken at different incident wavelengths are shown in Fig. 6 and in
The full UCN production rate in the horizontal containment tube can now be calculated after making allowances for inefficiencies in the detection arrangement. The number of neutrons detected is not the true number produced because the detector only covers a small fraction of the area at the end of the detector guide tube, the remainder of the end-face having been made totally absorbent to neutrons by coating it with 6 LiF. Also, some UCN are lost through small gaps around the edges of the beryllium end windows of the horizontal vessel and through interactions with the vessel walls. We estimate the compensating (mul-
C.A. Baker et al. / Physics Letters A 308 (2003) 67–74
tiplicative) factors to be: Fractional detection area correction: 11.75 ± 0.04 Losses in the horizontal vessel: 1.42 ± 0.15 Additionally, in separate calibration measurements, with the storage cell at room temperature, and using UCN from the PF2 turbine source at the ILL, we have measured (i) the UCN detection efficiency, which is 41% when only tritons are detected, (ii) the radial distribution of UCN across vertical cylindrical guide tubes, and (iii) the effect of the detector surroundings in reflecting UCN to the detectors. The corresponding multiplicative correction factors to obtain the true UCN current from the detected UCN rate are: Detector efficiency (when only tritons are detected): 2.44 ± 0.04 UCN distribution across the vertical guide tube: 0.87 ± 0.08 Reflection of UCN from the detector surroundings: 1.00 ± 0.02 Once the net correction factor of (35.4 ± 5.0) from the five correction factors listed above has been applied to the (equilibrium) rate of detection of UCN the result represents the rate of production within the superfluid helium. 7.1. UCN production rate from a narrow-band neutron beam around 9 Å The fit to the one phonon peak of Fig. 6 showed that it was centred on a wavelength of λ = 8.86 Å with a peak UCN detection rate of 5.94 ± 0.17 s−1 . After multiplying by the correction factor of 35.4 ± 5.0, this yields a total UCN production rate of 210 ± 31 s−1 . Given a superfluid helium length of 326 mm in the direction along the beam, and a circular beam of diameter 30 mm, this gives a UCN production rate of (0.91 ± 0.13) cm−3 s−1 . This is to be compared with the predicted single-phonon production rate of (1.19 ± 0.18) UCN cm−3 s−1 from Eq. (1).
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peak in production centred about 8.86 Å is that expected for single-phonon production broadened by the limited resolution of the velocity selector, whilst the broader peak covering the range of incident neutron wavelengths from 4.0 Å to 7.5 Å is that expected from UCN production via multi-phonon processes. Our observed ratio of two-phonon to one-phonon production rates, after allowing for the broadening of the very narrow one-phonon peak, is RII /RI = (0.32 ± 0.01). This is to be compared with a theoretical calculation [5] of 1.13 for a pure Maxwell–Boltzmann distribution at 300 K, and 0.37 at 30 K. 8. Conclusions We have observed a UCN production rate in superfluid 4 He of (0.91 ± 0.13) cm−3 s−1 from a wavelength-selected cold neutron beam at 8.86 Å; this figure is close to theoretical expectations for UCN production by single-phonon emission between the cold neutron beam and superfluid 4 He. This agreement between experiment and prediction for the UCN production rates confirms the view that earlier experiments on UCN production from helium suffered severe losses as UCN travelled to the detectors at room temperature and that the theoretical treatment of neutron helium interactions is adequately described at these low neutron energies. In addition, we have demonstrated experimentally the role played by multi-phonon emission processes in superthermal UCN production. In general, the relative rates of single- to multi-phonon production processes in UCN production depend upon the spectrum of the cold neutron beam used. In our particular case— that of the end position of the H53 beam at ILL— the contribution of multi-phonon processes to UCN production is (24 ± 2)%. This is the first time that ultracold neutrons have, to our knowledge, been both produced and directly detected within superfluid 4 He. We expect that the techniques used and described here will open the way to a new generation of cryogenic neutron EDM measurements.
7.2. UCN production rate from a broad-band neutron beam
Acknowledgements
Table 1 and Fig. 6 show clear evidence for two different mechanisms of UCN production. The sharper
The authors would like to acknowledge the technical support and encouragement received from the In-
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stitut Laue-Langevin in the provision of the neutron facilities for this research. We are also grateful for the financial support received from our funding agencies, namely PPARC in the UK and the Grant-in-Aid for Specially Promoted Research (1) No. 10101001 in Japan.
References [1] J.M. Pendlebury, Annu. Rev. Nucl. Part. Sci. 43 (1993) 687. [2] P.G. Harris, C.A. Baker, K. Green, P. Iaydjiev, S. Ivanov, D.J.R. May, J.M. Pendlebury, D. Shiers, K.F. Smith, M. van der Grinten, P. Geltenbort, Phys. Rev. Lett. 82 (1999) 904. [3] R. Golub, J.M. Pendlebury, Phys. Lett. A 62 (1977) 337. [4] H. Yoshiki, Comput. Phys. Commun. (2002), in press. [5] E. Korobkina, R. Golub, B.W. Wehring, A.R. Young, condmat/0204635. [6] R. Golub, Phys. Rev. A 72 (1979) 387. [7] P. Ageron, W. Mampe, R. Golub, J.M. Pendlebury, Phys. Lett. A 66 (1978) 469.
[8] R. Golub, C. Jewell, P. Ageron, W. Mampe, B. Heckel, I. Kilvington, Z. Phys. B 51 (1983) 187. [9] A.I. Kilvington, R. Golub, W. Mampe, P. Ageron, Phys. Lett. A 125 (1987) 416. [10] H. Yoshiki, K. Sakai, M. Ogura, T. Kawai, Y. Masuda, T. Nakajima, T. Takayama, S. Tanaka, A. Yamaguchi, Phys. Rev. Lett. 68 (1992) 1323. [11] T. Bitter, F. Eisert, P. El-Muzeini, M. Kessler, E. Klemt, W. Lippert, W. Meienburg, M. Baldo-Ceolin, D. Gibin, A. Guglielmi, M. Mezzetto, G. Puglierin, D. Dubbers, Nucl. Instrum. Methods A 321 (1992) 284. [12] ORTEC ULTRATM Detectors; EG & G Nuclear Instruments, Oak Ridge, USA. [13] C.A. Baker, K. Green, M.G.D. van der Grinten, P.S. Iaydjiev, S.N. Ivanov, S. Al-Ayoubi, P.G. Harris, J.M. Pendlebury, D.B. Shiers, P. Geltenbort, Nucl. Instrum. Methods A 487 (2002) 511. [14] C.A. Baker, S.N. Balashov, K. Green, M.G.D. van der Grinten, P.S. Iaydjiev, S.N. Ivanov, J.M. Pendlebury, D.B. Shiers, M.A.H. Tucker, H. Yoshiki, P. Geltenbort, Nucl. Instrum. Methods A (2003), in press. [15] Dornier Satellitensysteme GmbH, Friedrichshafen, Germany.
Experimental measurement of ultracold neutron production in superfluid 4 He C.A. Baker a , S.N. Balashov a , J. Butterworth b , P. Geltenbort b , K. Green a,c , P.G. Harris c , M.G.D. van der Grinten a,c,∗ , P.S. Iaydjiev a,1 , S.N. Ivanov a,2 , J.M. Pendlebury c , D.B. Shiers c , M.A.H. Tucker c , H. Yoshiki d a Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK b Institut Laue-Langevin, B.P. 156, 38042 Grenoble, France c Department of Physics and Astronomy, University of Sussex, Falmer, Brighton BN1 9QJ, UK d Kure University, Hiroshima, Japan
Received 27 November 2002; accepted 9 December 2002 Communicated by V.M. Agranovich
Abstract The absolute production rate of ultracold neutrons (UCN) produced by the interaction of a cold neutron beam with superfluid helium has been measured over an incident energy range of 0.7 to 4 meV. The neutrons are reduced in energy to become UCN by creating phonon(s) in the superfluid. The separate roles played by single and multi-phonon emission processes have been identified. Detection and identification of UCN, those neutrons with energies less than ∼ 250 neV and which can be stored in material bottles, were carried out using solid-state silicon detectors set within the superfluid helium. With a cold neutron flux of 2.62 × 107 neutrons cm−2 s−1 Å−1 at 8.9 Å in the superfluid, the single-phonon production rate of UCN was measured to be (0.91 ± 0.13) cm−3 s−1 , a value close to theoretical prediction. Multi-phonon emission processes for UCN production by higher energy neutrons were also observed and, in the beam used for this work at ILL, they contributed (24 ± 2)% to the overall UCN production rate. 2003 Elsevier Science B.V. All rights reserved.
1. Introduction There is currently considerable interest in new and improved sources of ultracold neutrons (UCN). Such neutrons have energies that are typically less than a
* Corresponding author.
E-mail address: [email protected] (M.G.D. van der Grinten). 1 On leave of absence from INRNE, Sofia, Bulgaria. 2 On leave of absence from PNPI, St. Petersburg, Russia.
few hundred neV, and they can be trapped and stored inside vessels made from materials with sufficiently high Fermi potentials (VF ). Stored UCN have been used to study the fundamental properties of the neutron [1] and, in particular, to measure with increasing precision the electric dipole moment (EDM) of the neutron. The current neutron EDM measurement by the RAL/Sussex/ILL group [2], which uses UCN from a cold, thermally moderated neutron source at the research reactor at the ILL in Grenoble, is now approaching its statistical limit. Further progress in ex-
0375-9601/03/$ – see front matter 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0375-9601(02)01773-5
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C.A. Baker et al. / Physics Letters A 308 (2003) 67–74
ploring in this way the nature of CP symmetry violation and particle physics beyond the Standard Model will soon need a more intense source of UCN. One of the most promising candidates for a new source of UCN at high densities is a super-thermal one [3], which exploits the properties of superfluid 4 He. UCN can be produced when superfluid 4 He is irradiated with cold neutrons, which then lose energy by each creating one or more phonons in the superfluid. The UCN produced survive well in the superfluid since the cross section for absorption of neutrons on 4 He is identically zero and, provided the temperature of the helium is low enough (< 0.7 K), the inelastic up-scattering of the UCN by phonons is very improbable.
2. Theoretical background Production of UCN by the emission of a single phonon occurs with cold neutrons having energy and momentum at the intersection of the energy– momentum relation for the free neutron and the phonon–roton dispersion curve for liquid helium. The cold neutrons and the phonons produced both have energies of E ∗ ∼ 1.0 meV and the neutron has a wavelength λ∗ ∼ 8.9 Å. The production rate RI for UCN created within 4 He (VF = 18.5 neV) and stored within beryllium walls (VF = 252 neV) has been calculated [3,4] to be −8 dΦ RI = (4.55 ± 0.25) × 10 (1) cm−3 s−1 , dλ λ∗ where dΦ/dλ|λ∗ is the differential flux in neutrons cm−2 s−1 Å−1 . The 4 He neutron-scattering cross section for the single-phonon UCN production in the superfluid is non-zero over a cold neutron energy range of only ∼ 10 µeV; a range which is determined by the kinematics of the process and by the small ranges of energies and momenta of the UCN produced that can be trapped. Cold neutrons with energies outside this range can also be down-scattered to UCN energies, but only by the emission of two or more phonons in one scattering event [5]. Several experiments [7–10] have in the past been carried out with the intention of measuring these UCN production rates but, because they all had neutron detectors at room temperature far outside the liquid he-
lium where the UCN were being produced, the interpretation of their data was difficult. In particular, it was difficult to estimate the severe attenuation, by a factor of ten or more, of the numbers of UCN as they emerged through the several windows needed for containment and radiation shielding. In this experiment, we have immersed the detectors in the superfluid helium so that the UCN produced can then pass directly to the detectors without passing through any intervening windows.
3. Experimental apparatus The experiment was carried out using the H53 coldneutron guide [11] at the Institut Laue-Langevin in Grenoble. The neutrons were transported from the reactor through 80 m of 58 Ni coated glass guides to the experimental area where the helium cryostat was mounted. A velocity selector, installed close to the primary guide exit, enabled the wavelength of the transmitted neutrons to be chosen with a resolution of ∼ 12% FWHM. Between the neutron guide and the cryostat the beam was reduced in size from its initial cross-sectional area of 72 cm2 by a series of collimators made from 6 LiF and boron loaded plastics spread over a horizontal distance of 3.85 metres. A final circular aperture of diameter 30 mm set close to the inlet flange of the cryostat and 55 cm from the centre of the UCN production volume, helped to define the input beam to the cylindrical, 67 mm diameter, superfluid target volume. The capture flux (Φc ), averaged over the area of the circular aperture, was measured by gold foil activation to be (1.30 ± 0.18) × 109 cm−2 s−1 without the velocity selector and (1.47 ± 0.20) × 108 cm−2 s−1 with the selector set to transmit 9 Å neutrons. Before the cryostat was put in place, the velocity spectrum of the broadband incident neutron beam was measured using timeof-flight techniques that recorded the capture flux over a flight path of 1.845 m (Fig. 1). The intensity distributions were also measured with the velocity selector set to a number of nominal settings; these distributions were then characterised using Gaussian fits to the data, which gave a central value λ and standard deviation σλ for each wavelength transmitted. This fit to a Gaussian distribution was found to be a very good approximation to the data, which, without
C.A. Baker et al. / Physics Letters A 308 (2003) 67–74
acceptance corrections, might have been expected to be purely triangular. In the case of the 9 Å nominal setting the beam was measured to have
Fig. 1. The spectrum of the cold neutron beam guided into the cryostat.
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a central wavelength of λ = 8.90 Å and a standard deviation σλ = 0.41 Å. At this setting the flux was measured using gold foil activation to be dΦ/dλ = (2.88 ± 0.39) × 107 neutrons cm−2 s−1 Å−1 . After allowing for a measured reduction factor of (1.10 ± 0.05) in beam intensity as the beam passed through the windows of the cryostat, the predicted UCN production rate from single phonon emission using Eq. (1) is RI = (1.19 ± 0.18) UCN cm−3 s−1 . The experimental arrangement of the 4 He-based UCN source is shown in Fig. 2. The ‘T’-shaped central volume of 6 litres, which contained the horizontal 1.1 litre UCN production volume, was cooled to T ∼ 0.5 K by a circulating 3 He expansion system. It was filled with superfluid 4 He from the main helium reservoir via a superleak: this decreased the atomic concentration of 3 He, a strong neutron absorber, from its natural level of 10−6 within liquid helium to below 10−12 .
Fig. 2. A sketch of part of the cryostat. A cold neutron beam is guided into the horizontal UCN production volume, which is filled with pure superfluid 4 He. After a dwell period of about 10 s the UCN that are produced escape through a 10 mm diameter hole into the vertical guide tube, at the bottom of which they reach the detector assembly.
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An outer vessel of copper and stainless steel confined the superfluid, whilst an inner vessel confined the UCN. The inner vessel consisted of a horizontal and a vertical stainless steel tube, each of internal diameter 67 mm and coated with 2500 Å of beryllium metal on the inner surface. The horizontal tube was closed at either end with a 0.25 mm thick Be foil clamped to the tube. Any neutrons which scattered from the 4 He at large angles, and with energies too great to be trapped, were absorbed and attenuated by 6 LiF loaded plastic, 1.2 mm thick and 67% 6 LiF by weight, wrapped around the outside of the horizontal tube. Neutrons trapped by the Fermi potential of the horizontal tube could escape via a 10 mm diameter aperture leading to the vertical tube and to the detectors.
4. Neutron detectors The results presented in this Letter were obtained using ORTEC ULTRA silicon detectors [12] that had 600 µg/cm2 6 LiF evaporated onto the detecting surface. The 6 LiF layer was sandwiched between aluminium layers of thickness 200 Å on top, for protection, and 2000 Å beneath for bonding to the detector. Three such detectors, each of 300 mm2 area, were mounted separately as an array in a horizontal plane at the lower end of the vertical tube, the remainder of the plane being covered with a neutron absorbing layer of 6 LiF on aluminium. The pre-amplifiers were outside the cryostat, at room temperature. The detectors were thus set 59 cm below the bottom of the horizontal tube so that gravity would accelerate the slowest UCN to energies greater than the Fermi potential of the Al and 6 LiF layers. Neutrons that entered the 6 LiF layer react according to the process n + 6 Li → α + 3 H + 4.78 MeV. These reaction products are emitted back to back, so that a single charged particle of energy at least 2.05 MeV strikes the silicon for every UCN that reacts. In separate experiments at room temperature [13], using stored UCN from the ILL PF2 source, we measured the overall efficiency for one 300 mm2 ULTRA detector to be (82 ± 1)% after optimising the thickness of the 6 LiF layer at 600 µg/cm2 . The performance of ULTRA detectors has been tested as a function of temperature and was found to show no change from room temperature down to 85 mK [14]. In the cryogenic experiment
reported here the signal spectrum from the alpha particles partially overlapped with the electronic noise, so only the peak due to tritons was used in order to ensure maximum reproducibility of the UCN detection process. The detector efficiency was then (41 ± 1)% for the purpose of these measurements.
5. Data-taking procedure Data were taken for 25 days in March 2001 using the broad-band cold neutron beam of H53 in ILL, and again for 25 days during March 2002 using the same beam but this time with a neutron velocity selector [15] in place. The measurement cycle began by opening a shutter in the cold neutron beam for a filling time of 40 s, this being about four times the storage time for UCN in the beryllium-coated containment vessel with its 10 mm diameter exit aperture. During this period the neutron beam passed through the cryostat, and UCN were produced in the superfluid. Following the filling the shutter was closed for 100 s, allowing the stored UCN to leave the horizontal tube through the aperture and to fall under gravity to be counted in the silicon detectors. The arrival times, relative to the cycle start, of the counts in the UCN detectors were recorded using a PC-based multi-scaler system with a time resolution of 136 ms per channel. The above cycle was repeated some hundreds of times to accumulate the spectrum of counts as a function of time with good statistics.
6. Analysis of the data 6.1. Data taken in 2001 During 2001 data were taken on the production of UCN at a series of liquid 4 He temperatures between 0.43 K and 2.05 K. The results at the lowest temperature (0.43 K) and at the highest temperature (2.05 K) are shown in Fig. 3. Both sets are the accumulation of 500 filling and emptying cycles. With the cryostat at 0.43 K, the lowest temperature achievable in the present configuration, the results are qualitatively and quantitatively different from those at 2.05 K. At 0.43 K, the neutron count-rate initially increases with time after the shutter is opened and
C.A. Baker et al. / Physics Letters A 308 (2003) 67–74
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Fig. 4. Experimental measurement of the temperature dependence of UCN storage lifetime, together with the theoretical expectations [6] from two models of phonon and roton interactions.
Fig. 3. (a) Neutron counts accumulated from 500 data-taking cycles, where the cold neutron beam is introduced into the liquid helium at zero time and then switched off again at 40 s. The symbols represent UCN production (#) at 430 mK, and () at 2.05 K where UCN are immediately lost by interaction with thermal phonons in the liquid He. Graph (b) is an expanded view of the tail of (a), showing the characteristic storage time of the UCN in the production cell.
decreases exponentially with time after it is closed. The initial rise is a build-up of the population of stored UCN as they are produced whilst the beam is on. This is superimposed upon a background of higher energy neutrons that cannot be trapped and which are scattered into the detector from the incident broad band beam as it passes through the helium. The fall in count rate when the incident beam is turned off shows a decrease in the population of stored UCN as they diffuse out of the horizontal containment tube to the detectors. This emptying curve can be fitted very well to a single exponential with a time constant of ∼ 10 s, and the resultant average total number of
counts from one filling and emptying cycle is N0 = (65.5 ± 1.0) UCN. We present these data as a very clear demonstration of the production, storage and detection of UCN within the liquid helium. Fig. 4 shows our results for the characteristic temperature dependence of UCN storage in liquid helium. This is very similar to the results reported by Kilvington et al. [9] and demonstrates clearly that at T = 2.05 K no UCN from the horizontal tube reach the detector because of the fast up-scattering rate in the superfluid. 6.2. Data taken in 2002 In order to see separately the single- and multiphonon processes in the production of UCN, further data were taken in March 2002 with a velocity selector in the incident neutron beam. The superfluid helium in the cryostat was kept at 0.7 K, and a series of 18 data runs took place with the wavelength of the incident neutron beam in each run being selected from within the range 4.5 Å to 11 Å. Fig. 1 shows the spectra of transmitted neutrons for various settings of the velocity selector. The wavelength acceptance was typically 12% FWHM. The UCN detection was carried out as before, within the superfluid helium, using 300 mm2 silicon neutron detectors. The emptying curves of all of the data sets could again be very well fitted to a single exponential with a
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Table 1
Fig. 5. The UCN detector counts as a function of time, with the velocity selector set to 9 Å.
Fig. 6. The UCN count rate recorded at wavelengths between 4 Å and 11 Å.
Nominal wavelength setting λ (Å)
Standard deviation σλ (Å)
UCN/ cycle
Error
UCN/ 0.5 Å
Error
4.50 4.99 5.49 5.99 6.53 6.99 7.49 8.01 8.25 8.50 8.65 8.80 9.01 9.20 9.50 9.75 10.00 10.52
0.25 0.26 0.28 0.29 0.32 0.33 0.35 0.37 0.38 0.39 0.40 0.41 0.41 0.41 0.42 0.43 0.44 0.47
1.68 3.06 4.06 5.05 5.57 3.77 1.6 2.74 11.97 28.88 41.84 49.57 48.51 37.58 21.65 9.31 1.75 0.05
0.08 0.11 0.12 0.13 0.14 0.1 0.08 0.08 0.47 0.5 0.7 0.65 0.66 1.1 0.39 0.38 0.07 0.05
1.36 2.38 2.93 3.52 3.52 2.31 0.92
0.06 0.09 0.09 0.09 0.09 0.06 0.05
Table 1. The ten data sets that constitute a scan over the range 7.5 Å to 10.5 Å have been fitted to a Gaussian distribution, yielding as parameters a peak value of N0 = (52.4 ± 0.4) UCN/cycle at a wavelength of λ = 8.86 Å and a standard deviation of σλ = 0.39 Å. The latter is in very close agreement with σλ = 0.41 Å the wavelength resolution of the incident beam. This is clear evidence that a peak in the production of UCN is occurring at ∼ 8.9 Å with a width which is much less than the wavelength range of the incident beam.
constant background: N(t) = N0 exp(−t/τ ) + B,
7. Calculation of UCN production rate
with τ = 8.82 ± 0.16 s and a background B of (2.2 ± 0.2) × 10−2 counts/second. Fig. 5 shows the data obtained with the velocity selector set to 9.0 Å. The background arising from neutrons scattered from the liquid helium during the filling period, with energies > E ∗ and which are not trapped, is now also negligible compared with the contribution from the UCN counts since kinematic restrictions force these scattered neutrons into the forward hemisphere and away from the detector arrangement [4]. The results from the data sets taken at different incident wavelengths are shown in Fig. 6 and in
The full UCN production rate in the horizontal containment tube can now be calculated after making allowances for inefficiencies in the detection arrangement. The number of neutrons detected is not the true number produced because the detector only covers a small fraction of the area at the end of the detector guide tube, the remainder of the end-face having been made totally absorbent to neutrons by coating it with 6 LiF. Also, some UCN are lost through small gaps around the edges of the beryllium end windows of the horizontal vessel and through interactions with the vessel walls. We estimate the compensating (mul-
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tiplicative) factors to be: Fractional detection area correction: 11.75 ± 0.04 Losses in the horizontal vessel: 1.42 ± 0.15 Additionally, in separate calibration measurements, with the storage cell at room temperature, and using UCN from the PF2 turbine source at the ILL, we have measured (i) the UCN detection efficiency, which is 41% when only tritons are detected, (ii) the radial distribution of UCN across vertical cylindrical guide tubes, and (iii) the effect of the detector surroundings in reflecting UCN to the detectors. The corresponding multiplicative correction factors to obtain the true UCN current from the detected UCN rate are: Detector efficiency (when only tritons are detected): 2.44 ± 0.04 UCN distribution across the vertical guide tube: 0.87 ± 0.08 Reflection of UCN from the detector surroundings: 1.00 ± 0.02 Once the net correction factor of (35.4 ± 5.0) from the five correction factors listed above has been applied to the (equilibrium) rate of detection of UCN the result represents the rate of production within the superfluid helium. 7.1. UCN production rate from a narrow-band neutron beam around 9 Å The fit to the one phonon peak of Fig. 6 showed that it was centred on a wavelength of λ = 8.86 Å with a peak UCN detection rate of 5.94 ± 0.17 s−1 . After multiplying by the correction factor of 35.4 ± 5.0, this yields a total UCN production rate of 210 ± 31 s−1 . Given a superfluid helium length of 326 mm in the direction along the beam, and a circular beam of diameter 30 mm, this gives a UCN production rate of (0.91 ± 0.13) cm−3 s−1 . This is to be compared with the predicted single-phonon production rate of (1.19 ± 0.18) UCN cm−3 s−1 from Eq. (1).
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peak in production centred about 8.86 Å is that expected for single-phonon production broadened by the limited resolution of the velocity selector, whilst the broader peak covering the range of incident neutron wavelengths from 4.0 Å to 7.5 Å is that expected from UCN production via multi-phonon processes. Our observed ratio of two-phonon to one-phonon production rates, after allowing for the broadening of the very narrow one-phonon peak, is RII /RI = (0.32 ± 0.01). This is to be compared with a theoretical calculation [5] of 1.13 for a pure Maxwell–Boltzmann distribution at 300 K, and 0.37 at 30 K. 8. Conclusions We have observed a UCN production rate in superfluid 4 He of (0.91 ± 0.13) cm−3 s−1 from a wavelength-selected cold neutron beam at 8.86 Å; this figure is close to theoretical expectations for UCN production by single-phonon emission between the cold neutron beam and superfluid 4 He. This agreement between experiment and prediction for the UCN production rates confirms the view that earlier experiments on UCN production from helium suffered severe losses as UCN travelled to the detectors at room temperature and that the theoretical treatment of neutron helium interactions is adequately described at these low neutron energies. In addition, we have demonstrated experimentally the role played by multi-phonon emission processes in superthermal UCN production. In general, the relative rates of single- to multi-phonon production processes in UCN production depend upon the spectrum of the cold neutron beam used. In our particular case— that of the end position of the H53 beam at ILL— the contribution of multi-phonon processes to UCN production is (24 ± 2)%. This is the first time that ultracold neutrons have, to our knowledge, been both produced and directly detected within superfluid 4 He. We expect that the techniques used and described here will open the way to a new generation of cryogenic neutron EDM measurements.
7.2. UCN production rate from a broad-band neutron beam
Acknowledgements
Table 1 and Fig. 6 show clear evidence for two different mechanisms of UCN production. The sharper
The authors would like to acknowledge the technical support and encouragement received from the In-
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stitut Laue-Langevin in the provision of the neutron facilities for this research. We are also grateful for the financial support received from our funding agencies, namely PPARC in the UK and the Grant-in-Aid for Specially Promoted Research (1) No. 10101001 in Japan.
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