Determination of the neutrino mass hierarchy via the phase of the disappearance oscillation probability with a monochromatic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mover accent="true"><mml:mi>ν</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>e</mml:mi></mml:msub></mml:math>source

The neutrino mass hierarchy can be determined, in principle, by measuring a phase in the disappearance oscillation probability in vacuum, without relying on the matter effect, using a single channel. This phase is not the same for the normal and inverted neutrino mass spectra. In this paper, we give a complete description and physics understanding of the method. The key feature of the method is to detect advancement (normal) or retardation (inverted) of the phase of the atmospheric-scale oscillation relative to the solar-scale oscillation. We then show that this method can be realized with the recently proposed resonant $\bar��_{e}$ absorption reaction enhanced by M��ssbauer effect. The unique feature of this setup is the ultra-monochromaticity of the observed \bar��_{e}'s. Because of this feature the phase advancement or retardation of atmospheric-scale neutrino oscillation is detectable after 20 or more oscillations if the source and the target are made sufficiently compact in size. A quantitative estimate of the sensitivity to mass hierarchy resolution is given. We have also examined how a possible continuation of such experiment can be carried out in order also to achieve high precision (few %) determination of the solar-scale oscillation parameters ��m^2_{21} and ��_{12}.

23 pages, 10 figures, final published version, title changed