Loss and spinflip probabilities for ultracold neutrons interacting with diamondlike carbon and beryllium surfaces

The storage of ultracold neutrons (UCN) in a combined magnetic, gravitational, and material trap is described. Wall materials investigated were diamondlike carbon (DLC) coatings on solid and flexible foil substrates as well as beryllium coatings on solid substrates. The loss coefficient per wall collision, η, and the depolarization probability β were measured simultaneously as a function of temperature (from 70 to 400 K) and energy (from 30 to 80 neV). The results at 70 K are $\eta =(0.7\pm 0.1)\times {10}^{-4},\beta =(15.4\pm 1.0)\times {10}^{-6}$ for DLC on polyethyleneterephtalate (PET) foil and $\eta =(1.7\pm 0.1)\times {10}^{-4},\beta =(0.7\pm 0.3)\times {10}^{-6}$ for DLC on aluminum foil. At room temperature the loss coefficients are larger by a factor of about 2 whereas the depolarization probabilities are found to be independent of temperature. The corresponding values for Be at room temperature are $\eta ~5\times {10}^{-4},\beta ~10\times {10}^{-6}$. The DLC results for β and for the temperature-dependent part of the loss coefficient, ${\eta }_T$, are interpreted in terms of incoherent scattering by hydrogen. The hydrogen admixture was measured independently by elastic recoil detection analysis to be about $1\times {10}^{16}$ atoms/cm${}^2$. The data do not support the hypothesis of hydrogen being chemically bound within the top layers of the DLC. Using two different models with a thin waterlike film on top of the substrate we obtain consistency between the temperature-dependent loss contribution and the measured hydrogen contamination.

Figure 1

Experimental apparatus: 1: Nickel-coated neutron guide from the turbine; 2: beam-line shutter; 3: stainless steel neutron guide; 4: neutron switch; 5: detector; 6: vacuum pumping port; 7: vacuum separation foil; 8: vertical neutron guide; 9: sample; 10: magnet yoke; 11: magnet coils with poles (horizontal); 12: insulation vacuum; 13: vacuum pumping port; 14: sensor feedthroughs; 15: holding field coils; 16: vacuum separation membrane; 17: thermal shield (copper); 18: vacuum pump; 19: clean sample vacuum; 20: sensor feedthrough; 21: flexible thermal copper connections; 22: 10 K cold stage; 23: 70 K stage; 24: vibration decoupling; 25: cryo cooler.

Figure 2

Measurement sequence for the standard procedure: detector counts for the sequences “filling” (0–15 s), “cleaning” (15–115 s), “holding,” and “emptying” for different holding times $t_i,t_1-t_0=20$ s (top) and $t_2-t_0=220$ s (bottom); $N_1,N_2$, and $N_{\mathrm{sp}}$ are the neutron counts at $t_1,t_2$, and the spinflipped neutrons, respectively. For each case the magnetic field $B$ during cleaning and storage is also shown.

Figure 3

Measurement sequence for the complementary procedure: detector counts (top) and magnetic field amplitude (bottom). Spinflipped neutrons are accumulated between $t_0$ and $t_1$, cleaned at the 90% magnetic field level for 100 s between $t_1$ and $t_2$, and emptied at $t_3$. In this example the field is successively lowered to zero in two distinct steps, allowing for a measurement of β for two different energy ranges. The counts between $t_0$ and $t_1$ are caused by leakage through the neutron switch.

Figure 4

Foil samples, coated with DLC. Left: Al-foil sample viewed from the bottom, where the neutrons enter. The foil is clamped by two aluminum strips and contained within two aluminum half-shells of inside diameter (ID) of 70 mm. Right: PET-foil sample viewed from the top. Here, the foil was clamped directly with the two aluminum half-shells. The aluminum shells are mounted within a copper tube (which serves as thermal shielding) via teflon spacers. Below, the two geometries are shown as they were used in the simulation.

Figure 5

Simulated time evolution of losses from the storage bottle, originating from the different loss processes: region 1—escape from the top; region 2—escape through the magnetic field; region 3—“wrong” spin population, escaping through the magnetic field; region 4—losses from wall collisions; region 5—losses from neutron β decay; region 6—spinflip following wall reflections and subsequent escape through the magnetic field. Time zero corresponds to end of filling. After 60 s the field is raised from 90 to 100%. For a detailed description see the text.

Figure 6

Measured (full dots) and calculated (bars and histogram) neutron counts in the detector during the cleaning process (see text). The discrepancy at $t=0$ originates from the fact that the simulation only considered one spin population and neutrons with energies below 110 neV.

Figure 7

The potential energy in the sample tube during storage as a function of height for different field levels (0–4 from Table ). The uppermost curve corresponds to the maximum magnetic field (level 0); the lowermost one to level 4. At small heights the potential is mainly determined by the magnetic field; the appearance of a “kink” at higher fields is due to saturation effects in the iron yoke, where the bore diameter increases from 80 to 120 mm at a height of 180 mm. The gravitational potential rises linearly with height (straight line going through the origin).

Figure 8

The wall collision frequency distribution for neutrons with polarization antiparallel to the magnetic field orientation, ${\nu }^{-}(h)$, as a function of height in the sample and for two different neutron energies [97.5 neV: upper curve (in red); 35 neV: lower curve (in black)]. The number of collisions is normalized per centimeter of height, per second, and per neutron. Height zero corresponds to the magnet midplane (i.e., at the maximum of the vertical field component).

Figure 9

The measured differential energy spectrum of UCN in the DLC(PET-foil) sample at 70 K (filled squares and histogram), obtained at magnet level 0 120 s after filling. The small triangles are Monte Carlo data [39]; the line is to guide the eye.

Figure 10

Calibration curves for the spin-independent storage time constant ${\tau }_{\mathrm{st}}^{*}$ as a function of the loss coefficient η for the DLC-coated PET foil. The numbers 1–5 correspond to the magnetic field levels with the respective average energies $E_{\mathrm{avg}}$ given by 37.8 neV (curve 1) to 66.5 neV (curve 5) (see Table ).

Figure 11

The loss coefficient η as a function of energy for the DLC(Al-foil) sample at 70 K, measured at five different magnet levels. The values are drawn at the average energy of the corresponding energy range, $E_{i,\mathrm{avg}}$ (see Table ). The uncertainties shown are statistical only. The asymmetric error bars originate from the nonlinear behavior of the ${\tau }_{\mathrm{st}}$ vs η curve (see Fig. 10). For the weighted average over the five measurements (solid line, with $1\sigma$ bounds represented by dashed lines) standard error propagation was used with an averaged error per data point.

Figure 12

The depolarization probability β for the DLC(PET-foil) at 70 K, extracted from measurements with different neutron energy ranges. The full squares correspond to the results obtained with the standard method and the open squares to the measurement at 57 and 79 neV with the complementary method deduced from stepwise emptying (see Sec. 4b). The solid line corresponds to the weighted mean of the standard method results; the dotted lines denote the 1σ uncertainty.

Figure 13

Mechanical misalignment of the sample for the first series of measurements: The bottom end was not positioned below the magnet midplane (where the field reaches its maximum value, represented by the dash-dotted horizontal line), but by mistake at $\Delta h$ above. 1: magnet poles, 2: vacuum housing, 3: sample tube, 4: uncoated edge, 5: stainless steel guide.

Figure 14

The loss coefficient η and the depolarization probability per wall reflection, β, as a function of time and temperature (right-hand scale), measured for the DLC(PET-foil) sample. The solid line is the average temperature of the sample, the solid squares correspond to the measured values for η, and the open circles correspond to the depolarization probability β.

Figure 15

Illustration of the Debye model loss channels for DLC(PET-foil) as a function of temperature. Line 1 shows a temperature-independent contribution (${\eta }_{\mathrm{add}}=3\times {10}^{-5}$; see text), 2 the contribution from holes in the coating $({\eta }_h=5\times {10}^{-6})$, 3 the absorption on carbon (not visible on this scale), 4 the absorption on hydrogen, 5 the inelastic scattering on DLC, and 6 inelastic scattering on hydrogen, using $N_H=27\times {10}^{16}$ atoms/cm${}^2$ (see line 2 of Table ). The points with error bars are the experimental values.