Ultracold-neutron production and up-scattering in superfluid helium between 1.1 K and 2.4 K

Ultracold neutrons (UCNs) were produced in superfluid helium using the PF1B cold-neutron beam facility at the Institut Laue-Langevin. A 4-liter beryllium-coated converter volume with a mechanical valve and windowless stainless-steel extraction system were used to accumulate and guide UCNs to a detector at room temperature. At a converter temperature of 1.08 K the total storage time constant in the vessel was $(20.3\pm 1.2)\mathrm{s}$ and the number of UCNs counted after accumulated was $91700\pm 300$. From this, we derive a volumetric UCN production rate of $(6.9\pm 1.7){\mathrm{cm}}^{-3}{\mathrm{s}}^{-1}$, which includes a correction for losses in the converter during UCN extraction caused by the short storage time, but not accounting for UCN transport and detection efficiencies. The up-scattering rate of UCNs caused by excitations in the superfluid was studied by scanning the temperature between $1.2$ K and $2.4\mathrm{K}$. Using the temperature-dependent UCN production rate calculated from inelastic neutron scattering data, the only UCN up-scattering process found to occur was from two-phonon scattering. Our analysis for $T<1.95\mathrm{K}$ rules out the contributions from roton-phonon scattering to $<29\%$ (95% C.I.) and from one-phonon absorption to $<47\%$ (95% C.I.) of their predicted levels.

Figure 1

The sizes of the three main processes contributing to the up-scattering of UCNs by excitations in superfluid helium from Eq. (1) derived in Ref. [46]. The thickness of the ${\tau }_{2-\mathrm{ph}}^{-1}$ line covers the range of values for $T<1\mathrm{K}$ owing to the different values of $B$ (see text). The dotted lines are used to indicate that the up-scattering rates are only approximate for $T\gtrsim 1\mathrm{K}$ due to temperature dependencies in the $A, B$, and $C$ coefficients.

Figure 2

The experimental installation at the PF1B CN beamline. For clarity, extraneous elements of the original photograph are erased. The added labels indicate $①$ main cooling tower; $②$ horizontal helium connection; $③$ converter volume; $④$ mechanical UCN flap valve actuator; $⑤$ UCN extraction guides; and $⑥$ UCN detector. The direction of the CN beam is shown as the blue arrow. Additional lead shielding surrounding the apparatus was added later.

Figure 3

Cross section of the superfluid helium converter volume and UCN extraction system. $ⓐ$ Isolation vacuum window; $ⓑ$ outer radiation shield window; $ⓒ$ inner radiation shield window; $ⓓ$ superfluid containment vessel (shown transparent); $ⓔ$ front beryllium sheet; $ⓕ$ beryllium-coated aluminum sidewalls; $ⓖ$ beryllium-coated copper end section; $ⓗ$ beryllium UCN flap valve; $ⓘ$ back beryllium sheet; $ⓙ$ pulley of UCN flap valve mechanism; $ⓚ$ polished stainless-steel conical guide; $ⓛ$ polished stainless-steel UCN guide; $ⓜ$ thermal anchoring to second-stage radiation shield; and $ⓝ$ UCN guide adapter (50- to 66-mm i.d.). The directions of the incoming CN beam (blue arrow) and the remaining UCN guides to the detector (red arrow) are also shown. (The concentric cylindrical sidewalls of the radiation shields and vacuum vessel are not shown.)

Figure 4

View of the converter vessel before the superfluid containment vessel is mounted. The added labels and arrows indicate: screws for assembling the sidewalls; claw clamps for mounting the front sheet to the sidewalls; claw clamps for mounting the sidewalls to the copper end section; and wiring for thermometer at the front end of converter volume.

Figure 5

The mechanical UCN flap valve viewed from the incoming direction of the CN beam. The axle and wires supporting the flap can be seen, as well as the exit for UCNs at the bottom of the stainless-steel conical guide section.

Figure 6

UCN count rate during the 1.08 K accumulation measurement. At $187\mathrm{s}$ ($\equiv t_0$) the UCN valve was opened and CN beam switched off. At $258\mathrm{s}$ the UCN valve was closed again, before all the UCNs were emptied from the converter volume. The fits of the buildup and emptying curves, details of which are described in the text, are shown as solid lines.

Figure 7

Continuous measurements for selected temperatures to demonstrate the changes in the buildup, saturation, and emptying. The duration the CN beam is left on is not the same between the measurements. The last 50–$60\mathrm{s}$ before the CN beam is switched off is used to determine ${\dot{N}}_{\mathrm{c}}\left(T\right)$.

Figure 8

(Bottom) The saturated count rates from continuous measurements ${\dot{N}}_{\mathrm{c}}$ between $1.16\text{K}\text{and}2.40$ K. The region around $T_{\lambda }$ is shown magnified. The solid green line is the fit for $T<T_{\lambda }$ using ${\tau }_{\mathrm{up}}^{-1}\left(T\right)={\tau }_{2-\mathrm{ph}}^{-1}$. ${\dot{N}}_{\mathrm{c}}\left(T\right)/P_{\mathrm{rel}}\left(T\right)$ is being fitted in the analysis, but ${\dot{N}}_{\mathrm{c}}\left(T\right)$ is shown here. See text for details. (Top) The relative error of each ${\dot{N}}_{\mathrm{c}}\left(T\right)/P_{\mathrm{rel}}\left(T\right)$ point and the residuals (fit minus data) of the ${\tau }_{\mathrm{up}}^{-1}\left(T\right)={\tau }_{2-\mathrm{ph}}^{-1}$ fit are also shown. $T_{\lambda }$ is marked by the vertical dashed lines.

Figure 9

The relative UCN production rate $P_{\mathrm{rel}}\left(T\right)$ calculated using inelastic neutron scattering data and an analytic approximation of the PF1B CN beam spectrum (see the Appendix for details of the calculations). The solid green line is the interpolation between the points with Eq. (23) used in the data analysis.

Figure 10

The PF1B CN capture flux $d{\varphi }_{\mathrm{c}}/d{\lambda }_{\mathrm{n}}, s\left({\lambda }_{\mathrm{n}}\right)$ [Eq. (A2)], and the differential UCN production rate $P(T,{\lambda }_{\mathrm{n}})$ used for the calculations of $P_{\mathrm{rel}}\left(T\right)$, at selected temperatures. Each separate quantity plotted is in the same arbitrary units for all temperatures, but the plots for incrementally increasing temperatures are offset by $-0.3$ (arbitrary units) from the previous. Details of the calculations are described in the text.