Impact of a Reflecting Material on a Search for Neutron--Antineutron Oscillations using Ultracold Neutrons

TL;DR

This work analyzes neutron--antineutron oscillations using ultracold neutrons stored in a one-dimensional bottle, focusing on how wall reflections modify the antineutron amplitude and the experimental sensitivity. By formulating a minimal-approximation, semi-classical model with complex wall potentials, it derives the antineutron time evolution and an annihilation-based Figure of Merit (FoM) that depends on the complex reflection amplitude $\tilde{R}$ and the magnetic splitting $\Delta E$. A key result is that maximizing sensitivity favors closely matched real parts of the neutron and antineutron pseudopotentials, thereby minimizing the relative phase $|\Delta\varphi|$, and hence enhancing the annihilation signal. The paper also outlines experimental paths to constrain the elusive antineutron scattering lengths—via precision antiprotonic-atom X-ray spectroscopy and low-energy antineutron–nucleus scattering—and discusses extending the framework to three-dimensional, gravity-influenced storage geometries with realistic surface effects.

Abstract

We investigate neutron--antineutron oscillations of ultracold neutrons in a storage bottle represented by a one-dimensional potential. The experimental sensitivity is determined by the annihilation rate of antineutrons. Its dependence on the antineutron reflectivity and the relative phase shift between the neutron and the antineutron wavefunctions by a reflection from the wall is derived. Optimization of the antineutron pseudopotential was found crucial to maximize the sensitivity of the experiment. Furthermore, methods are discussed for determining the antineutron pseudopotential, which has only been studied indirectly thus far.

Figures (4)

• Figure 1: Antineutron appearance probability $P_{\bar{n}}(t)=|\psi_{\bar{n}}(t)|^2$ for different conditions of $\Delta E$ and $\tilde{R}=R_{\bar{n}}\exp(i\Delta\varphi)$. The lines show numerical results using the Runge--Kutta method, and the dots represent values from Eq. (\ref{['nbar_appearance_prob2']}). We set $T=1\,\mathrm{sec}$ and $\delta m=\hbar/(10^8\,\mathrm{sec})$.
• Figure 2: Antineutron annihilation rate for different conditions of $\tilde{R}=R_{\bar{n}}\exp(i\Delta\varphi)$. We set $T=1\,\mathrm{sec}$, $\delta m=\hbar/(10^8\,\mathrm{sec})$, and $\Delta E\,T=0.01\hbar$.
• Figure 3: The reflectivity and phase shift caused by a pseudopotential of $V_0-iW_0$.
• Figure 4: Dependence of $\tilde{R}=R_{\bar{n}}\exp(i\Delta\varphi)$ on the antineutron pseudopotential strength $V_0-iW_0$ for $50\,\mathrm{neV}$ UCNs reflecting from a material with $U_n=100\,\mathrm{neV}$. A contour plot of the FoM in case of $\Delta E=0$ is overlaid in gray.