Superfluid helium film may greatly increase the storage time of ultracold neutrons in material traps

We propose a method to increase both the neutron storage time and the precision of its lifetime measurements by at least tenfold. The storage of ultracold neutrons (UCN) in material traps now provides the most accurate measurements of neutron lifetime and is used in many other experiments. The precision of these measurements is limited by the interaction of UCN with the trap walls. We show that covering trap walls with liquid helium may strongly decrease the UCN losses from material traps. ${}^4\mathrm{He}$ does not absorb neutrons at all. Superfluid He covers the trap walls as a thin film, $\approx 10$ nm thick, due to the van der Waals attraction. However, this He film on a flat wall is too thin to protect the UCN from their absorption inside a trap material. By combining the van der Waals attraction with capillary effects we show that surface roughness may increase the thickness of this film much beyond the neutron penetration depth, $\approx 33\mathrm{nm}$. Using liquid He for UCN storage requires low temperature, $T<0.5$ K, to avoid neutron interaction with He vapor, while the neutron losses because of the interaction with surface waves are small and can be accounted for using their linear temperature dependence.

Figure 1

Schematic representation of the ultracold neutron potential and wave function near the trap wall, covered by He film (a) and without He film (b).

Figure 2

The neutron wave functions without (a) and with helium film of thickness $d_{\mathrm{He}}=10\mathrm{nm}$ (b) and $d_{\mathrm{He}}=28.5\mathrm{nm}$ (c) at four values of neutron wave vector, $k=0.005$ (solid blue), 0.01 (dashed green), 0.02 (dot-dashed orange), and $0.03{\mathrm{nm}}^{-1}$ (dotted magenta).

Figure 3

The reduction factor ${\gamma }_{\mathrm{He}}$ of neutron losses inside flat trap walls, made of Be (solid blue) and “ Fomblin” oil (green dashed), due to the He film of thicknesses $d_{\mathrm{He}}=10\mathrm{nm}$ (a) and $d_{\mathrm{He}}=28.5\mathrm{nm}$ (b). It illustrates the momentum dependence of ${\gamma }_{\mathrm{He}}$ given by Eq. (21). For comparison, the dot-dashed magenta curves show ${\mathrm{\Psi }}_{\mathrm{He}}^2\left(0\right)/{\mathrm{\Psi }}_s^2\left(0\right)$ determined using Eq. (1) with ${\kappa }_{\mathrm{He}}$ given by Eq. (6).

Figure 4

The squared ratio (in logarithmic scale) of neutron wave functions on the wall surface, made of Be, as a function of helium film thickness $d_{\mathrm{He}}$ at four different values of neutron wave vector: $k=0.005$ (solid blue), 0.01 (dashed green), 0.02 (dot-dashed cyan), and $0.03{\mathrm{nm}}^{-1}$ (dotted magenta). Thin solid curves of the corresponding colors show the predictions of Eq. (1).

Figure 5

The functions $d_{\mathrm{He}}\left(h\right)$ from Eq. (23) (solid blue curve) and from Eq. (26) with the parameters [53] $d_0=28.5\text{nm}$ and $1/n\approx 1/3.5$ (dashed green line) and [50] $d_0=118\text{nm}$ and $1/n\approx 0.5$ (dash-dotted magenta line).

Figure 6

The steplike roughness of the wall surface covered by liquid helium with an almost flat surface.

Figure 7

Schematic view of a furry rough wall surface covered by liquid helium.