We describe a spin-echo method for ultracold neutrons (UCNs) confined in a precession chamber and exposed to a $|B_0|=1~text{mu T}$ magnetic field. We have demonstrated that the analysis of UCN spin-echo resonance signals in combination with knowledge of the ambient magnetic field provides an excellent method by which to reconstruct the energy spectrum of a confined ensemble of neutrons. The method takes advantage of the relative dephasing of spins arising from a gravitationally induced striation of stored UCN of different energies, and also permits an improved determination of the vertical magnetic-field gradient with an exceptional accuracy of $1.1~text{pT/cm}$. This novel combination of a well-known nuclear resonance method and gravitationally induced vertical striation is unique in the realm of nuclear and particle physics and should prove to be invaluable for the assessment of systematic effects in precision experiments such as searches for an electric dipole moment of the neutron or the measurement of the neutron lifetime.
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