2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125470Recently, quantum states of ultra-cold neutrons in the Earth's gravitational field have been observed for the first time. From the fact that they are consistent with Newtonian gravity on the 10 %-level, analytical limits on alpha and lambda of short-range Yukawa-like additional interactions are derived between lambda = 1 micrometer and 1 mm. We arrive for lambda > 10 micrometer at alpha < 2 \cdot 10^11 at 90 % confidence level. This translates into a limit g_s g_p / (\hbar c) < 2 \cdot 10^{-15} on the pseudo-scalar coupling of axions in the previously experimentally unaccessible astrophysical axion window.9 pages, 2 figures, LaTeX, uses RevTeX 4High Energy Physics - PhenomenologyAnalytically derived limits on short-range fifth forces from quantum states of neutrons in the Earth's gravitational fieldtext