Losses and depolarization of ultracold neutrons on neutron guide and storage materials

At Institut Laue-Langevin (ILL) and Paul Scherrer Institute (PSI), we have measured the losses and depolarization probabilities of ultracold neutrons on various materials: (i) nickel-molybdenum alloys with weight percentages of 82/18, 85/15, 88/12, 91/9, and 94/6 and natural nickel Ni100, (ii) nickel-vanadium NiV93/7, (iii) copper, and (iv) deuterated polystyrene (dPS). For the different samples, storage-time constants up to $\sim 460\mathrm{s}$ were obtained at room temperature. The corresponding loss parameters for ultracold neutrons, $\eta$, varied between $1.0\times {10}^{-4}$ and $2.2\times {10}^{-4}$. All $\eta$ values are in agreement with theory except for dPS, where anomalous losses at room temperature were established with four standard deviations. The depolarization probabilities per wall collision $\beta$ measured with unprecedented sensitivity varied between $0.7\times {10}^{-6}$ and $9.0\times {10}^{-6}$. Our depolarization result for copper differs from other experiments by 4.4 and 15.8 standard deviations. The $\beta$ values of the paramagnetic NiMo alloys over molybdenum content show an increase of $\beta$ with increasing Mo content. This is in disagreement with expectations from literature. Finally, ferromagnetic behavior of NiMo alloys at room temperature was found for molybdenum contents of 6.5 at.% or less and paramagnetic behavior for more than 8.7 at.%. This may contribute to solving an ambiguity in literature.

Figure 1

Calculated loss coefficients $\eta$ vs the material optical potential $V_{\mathrm{f}}$ [Eq. (1)] of materials commonly used for storage of UCN (high potential, low losses) and UCN guides. The material optical potential of diamond-like carbon (DLC) is between that of diamond and that of carbon depending on the graphite/diamond ratio of the crystal structure. The data have been calculated from Eq. (1); see also Refs. [37, 41].

Figure 2

Experimental apparatus for the investigation of materials for the storage of ultracold neutrons: 1, neutron guide guide from the UCN source; 2, beam-line shutter; 3, UCN detector; 4, UCN switch between UCN guide from source to sample and sample to UCN detector; 5, vacuum pumping ports; 6, vertical UCN guide (sample) below magnetic field region; 7, magnet yoke; 8, magnet coils; 9, holding field coils; 10, vacuum port to prepump; 11, vacuum port to prepump; 12, vacuum pump (turbo pump); 13, extension vacuum tube; 14, vacuum sensor; 15, UCN absorber with variable height; 16, vertical UCN guide (sample) above magnetic field region (storage volume); and 17, magnetic field lines at $I=300$ A in the air gap of the split-coil magnet. Solid lines: $B=2.7$ T in the 3-cm air gap. Dotted lines: $B=1.52$ T in the center of the bore for the vertical UCN guide ($z=0$, $r=0$).

Figure 3

Potential energy calculated from the known distribution of the magnetic field in the storage volume during UCN storage as a function of height. At small heights, the potential is mainly determined from the magnetic field in the air gap of the magnet. The slight kink around $z=150\mathrm{mm}$ originates from saturation effects in the iron where the bore diameter increases from 81 to 121 mm. The gravitational potential energy rises linearly with height and dominates at larger $z$ values.

Figure 4

Detector counts for the sequence filling ($-120$ to $-100$ s), cleaning ($-100$ to +120 s), storing, and emptying for storing times $t=0\mathrm{s}$ (top) and $t_{370}-t_{120}$ = 250 s (bottom); $N_{120}$, $N_{370}$, and $N_{\mathrm{sp}}$ are the neutron counts at $t_{120}$, $t_{370}$, and the spin-flipped neutrons, respectively. The data are from the NiMo 88/12 sample with the absorber at 90 cm. The events during storage are attributed to (i) spin-flip events of the LFS, (ii) approximately half of the spin-flipped events of the HFS, namely those which are emitted downward toward the detector; the other half is accelerated upward into the LFS region where they are stored, and (iii) background (BG). As mentioned in the text, the cleaning time depends on the absorber position. The magnetic field B at $z=0$, $r=0\mathrm{as}$ a function of time is also shown. It is ramped from 90% of the current to 100% at $t=0$.

Figure 5

Same as Fig. 4. The absorber position is 50 cm and the cleaning time is 170 s.

Figure 6

Same as Fig. 4. Here, the absorber position is 30 cm and the cleaning time 100 s.

Figure 7

Counts of UCN as a function of the absorber height $z_{\mathrm{a}}$ after 20 s of filling and 220 s of spectral cleaning. The sample is NiMo82/18. Black dots, measured integral UCN distribution; and open squares, differential UCN distribution. The differential distribution was obtained from the differences in count rate at $z\left(i\right)$ and $z$($i-1$), where $z(i-1)=z\left(i\right)-20$ cm. The integral distribution was fitted with a function $N_{120}\left(z\right)=N_{120}\left(30\mathrm{cm}\right)+P_1{(z-P_2)}^{3/2}$ and is plotted as the line through the data points. Here, $P_1=2.47\pm 0.09$ is a normalization factor, $P_2=33.4\pm 1.0$ is the minimum of the potential energy, and $N_{120}\left(30\mathrm{cm}\right)=49.1$ is the measured number of HFS at $z_{\mathrm{a}}=30\mathrm{cm}$. The ${\chi }^2$ of the fit is 1.2 for one degree of freedom. The line through the experimental differential data is the derivative of $N_{120}$ with respect to $z$, $d{N}_{120}/dz=3.7{(z-33.4)}^{1/2}$. The agreement between the fitted value for $P_2$ and the calculated one from the magnetic field distribution (23 cm) is only fair but good enough for our purposes.

Figure 8

Result for the differential frequency of wall collisions $d\nu /dz$ for LFS, obtained with a MC code (black line with black dots), and a comparison with a theoretical model, using the kinetic gas theory for UCN (black line with open squares). The absorber was set to $z_{\mathrm{a}}=90\mathrm{cm}$.

Figure 9

Collision rates $\nu \left(z\right)$ of UCN as a function of the absorber height. The black line is calculated from kinetic gas theory. The Monte Carlo simulations are as follows: (i) open circles, Ref. [85]; (ii) black circles, Ref. [86]; (iii) diamonds, Ref. [87]; and (iv) black triangles, Ref. [88].

Figure 10

Detector counts during data taking at different absorber positions: 90, 70, 50, 30, and 0 cm. The sample is NiMo88/12.

Figure 11

Neutron spectra at absorber positions 30 and 20 cm. The sample was NiMo 82/18 and the holding time is 270 s. The counts for $N_{\mathrm{sp}}$ and $N_{270}$ averaged over all runs are 15.6 $\pm$ 0.9 and 21.1 $\pm$ 1.1 for $z=30$ cm and 13.0 $\pm$ 2.5 and 19.5 $\pm$ 3.1 for $z=20\mathrm{cm}$.

Figure 12

Neutron counts with emptying from $t=20\mathrm{s}$ to $t=370\mathrm{s}$. The sample is NiMo 88/12, with absorber height 90 cm. $N_{\mathrm{sp}}^{*}$, spin-flipped LFS plus half of the spin-flipped HFS plus background during storing, $N_{\mathrm{sp}}^{*}=N_{\mathrm{sp}}\left(\mathrm{LFS}\right)+0.5N_{\mathrm{sp}}\left(\mathrm{HFS}\right)+BG;N_{\mathrm{i}}$, UCN in the emptying peak after storage for $t_{\mathrm{i}}=20$, 70, 120, 170, 270, 320, and 370 s. For the determination of $\beta$ and $\eta$ values, the data at $t_{\mathrm{i}}=20$ and 70 s were not used.

Figure 13

Time spectrum of UCN for a holding time of $370-$ 120 = 250 s. The sample is NiMo88/12 and the absorber height is 90 cm. An exponential was fitted to the data for $t=-20\mathrm{s}$ to $t=+40\mathrm{s}$ with the result ${\tau }_{\mathrm{cl}}=(59.\pm 13.8)$ s. This is appreciably smaller than the storage-time constant ${\tau }_{\mathrm{st}}=(282.2\pm 7.6$) s. Therefore, in the analysis, the spectral cleaning was increased from 100 s to 220 s, i.e., from $t=-100\mathrm{s}$ to $t=+120$ s.

Figure 14

Determination of the storage-time constants for NiMo88/12 and different absorber positions. The storage-time constants are obtained from the $N_{\mathrm{i}}$ values after different holding times ranging from $t_{\mathrm{i}}=20$ to $t_{\mathrm{i}}=370\mathrm{s}$. The background originating from HFS and ambient events was subtracted. For absorber positions 90 and 70 cm, the data at 20 and 70 s were not included in the fit. For absorber positions 50 cm, the data at 20 s was not included in the fit. At absorber position 30 cm, there are only HFS events and background; cf. Figs. 6 and 12. Here, the background measured with absorber position $z_{\mathrm{a}}=0\mathrm{cm}$ was subtracted.

Figure 15

Storage-time constants for NiMo82/18 at different absorber positions. The solid line is a fit to the data, ${\tau }_{\mathrm{st}}=A/z+B$, with $A=13094\pm 2563$ and $B=55\pm 30$, with $z$ being the variable for the absorber height.

Figure 16

Calculated values of ${\beta }_{100}$ from measured data vs $t$ for a spectral cleaning time of 100 s. The sample is NiMo88/12 and the absorber position is 90 cm. One can clearly see a dependance in time. This is supported by fitting a constant to the data points (see horizontal line). One obtains ${\beta }_{100}=(0.78\pm 0.03)\times {10}^{-5}$ with a reduced ${\chi }^2$ of 3.7. Fitting an exponential, $y=a+b$ $\exp \frac{t}{{\tau }_{\mathrm{cl}\phantom{{\mathrm{J}}_{\mathrm{j}}}}}$ in order to take into account imperfect cleaning, one obtains ${\tau }_{\mathrm{cl}}=(137\pm 107)$ s, in agreement with the ${\tau }_{\mathrm{cl}}$ values obtained in Sec. 5d. The reduced ${\chi }^2$ of this fit is 0.25.

Figure 17

The depolarization parameter ${\beta }_{220}$ for a spectral cleaning time of 220 s. The sample is NiMo88/12 and the absorber position is 90 cm. Here, the mean value is ${\beta }_{220}=(0.19\pm 0.07)\times {10}^{-5}$.

Figure 18

Depolarization probability $\beta$ for the paramagnetic NiMo alloys and for different absorber positions. (i) NiMo82/18, black circles, data taken at the ILL; black square, data taken at PSI. The average value (black line, upper line) is $\beta =(0.64\pm 0.07)\times {10}^{-5}$ with a reduced ${\chi }^2$ of 0.73. (ii) NiMo85/15, blue open circles. The average value (blue line, middle line) is $\beta =(0.38\pm 0.06)\times {10}^{-5}$ with a reduced ${\chi }^2$ of 0.59. (iii) NiMo88/12, red triangles. The average value (red line, lower line) is $\beta =(0.29\pm 0.04)\times {10}^{-5}$ with a reduced ${\chi }^2$ of 1.74. HFS, high-field seekers; LFS, low-field seekers.

Figure 19

The depolarization parameter $\beta$ as a function of the molybdenum content in NiMo alloys, (i) averaged over all holding times, $t_{\mathrm{i}}$, for absorber heights 90 cm (full dots) and (ii) averaged over all holding times and absorber heights (open circles).

Figure 20

Detector counts during data taking at absorber positions of 90, 10, and 0 cm. The sample is Ni100.

Figure 21

Loss parameter of UCN $\eta$ over absorber height. The sample is NiMo82/18. A constant was fitted to the data, $(\eta =1.6\pm 0.3)\times {10}^{-4}$. The reduced ${\chi }^2$ of the fit is 0.2. The small value of ${\chi }^2$ is partly due to correlation: The neutron lifetime and the optical potential are common to all single $\eta$ values at the different absorber heights. The red line (second horizontal line from below) is the theoretically expected value from $W/V_{\mathrm{f}}$.

Figure 22

Loss parameter of UCN $\eta$ over molybdenum content of the sample coating for different NiMo alloys. The line shows the theoretically expected values from $W/V_{\mathrm{f}}$.