Directed Neutrino Beam with Electron Capture Beta Decay

We suggest generation of directed neutrino beams using electron capture beta decay sources. The basic idea is the following. Consider a Gamov-Teller transition with a decrease of nuclear spin I of one unit: $I\to I-1$. Assume that the nuclear spins are highly polarized by a magnetic field at low temperature. In this case the z-component of the total angular momentum before decay is $F_z =I$. The electron capture beta decay produces an unpaired electron with spin $S=\frac{1}{2}$ and a neutrino with spin $V=\frac{1}{2}$. From conservation of the z-component of the angular momentum we obtain after the decay $I_z =I-1, S_z =\frac{1}{2}, V_z =\frac{1}{1}.$ From the helicity requirement, the emitted neutrino momentum is opposite to the direction of its spin. Thus, the considered source generates a directed neutrino beam propagating in the negative z-direction. We show an opportunity for experimental detection of the average recoil force produced by the neutrino emission with a conventional technique of atomic force microscopy.