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

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.

💡 Research Summary

The paper presents a comprehensive theoretical study of neutron–antineutron (n‑={n}) oscillation searches using ultracold neutrons (UCNs) stored in a material bottle. The authors model the bottle walls as a one‑dimensional step potential, assigning a real‑plus‑imaginary “pseudopotential” (U_n = V_0 - iW_0) for neutrons and a generally different complex potential (U_{\bar n}=V’0 - iW’0) for antineutrons. Because UCN kinetic energies (∼100 neV) are below the real part of the neutron potential, neutrons are totally reflected; the reflected wave acquires only a phase shift (\phi_n). Antineutrons, however, experience both reflection and absorption, characterized by a reflection coefficient (R{\bar n}=|R{\bar n}|e^{i\phi_{\bar n}}) and a relative phase (\Delta\phi=\phi_{\bar n}-\phi_n).

The free‑space oscillation dynamics are described by a two‑state Hamiltonian that includes the magnetic‑field‑induced energy splitting (\Delta E = \mu_n B) and the transition amplitude (\delta m). In realistic laboratory fields (\Delta E) far exceeds (\delta m), so the authors adopt the “quasi‑free” approximation (\Delta Et \ll \hbar), under which the antineutron appearance probability grows quadratically, (P_{\bar n}(t)\simeq (t/\tau_{n\bar n})^2) with (\tau_{n\bar n}= \hbar/\delta m).

Inside the storage bottle the neutron wavefunction is unchanged by each wall collision (only a global phase), whereas the antineutron wavefunction is multiplied by a complex factor (\tilde R = R_{\bar n} e^{i\Delta\phi}) at every reflection. By solving the Schrödinger equation between collisions and applying the recurrence relation for the antineutron amplitude, the authors derive an analytic expression for the antineutron probability after (N) wall traversals (time (t = NT), where (T = \ell/v) is the round‑trip time):

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