Measurement of the occupation number of metastable atoms in the hyperfine-substate β$_3$ in an atomic hydrogen beam

Abstract

After its discovery in 1947 by Willis Eugene Lamb and Robert C. Retherford the Lamb shift was used to create Lamb shift polarimeter to separate the $2S_{1/2}$ $\alpha_{1}$ and $\alpha_{2}$ hyperfine substates of hydrogen as well as the $\alpha_{3}$ substate of deuterium. But for a new project at the Technical University of Munich, investigation of the bound-beta decay of a neutron into a hydrogen atom and a neutrino, a Lamb shift polarimeter is needed that is also capable of separating the $\beta_{3}$ substate of hydrogen. Unfortunately, our first attempt to use a Sona transition unit to exchange the occupation numbers between $\alpha_{1}$ and $\beta_{3}$ failed, because of the unexpected complexity of the transitions in this unit [1]. The second idea of using a new kind of spinfilter which uses two radio frequencies to separate all four hyperfine substates of hydrogen also failed. Our third attempt is now to build a transition unit that can induce magnetic dipole transitions between $\alpha_{2}$ and $\beta_{3}$ as well as between $\alpha_{2}$ and $\beta_{4}$ ($\pi$ transitions, i.e. an exchange of the occupation numbers of these states). This is a similar transition to what is used in atomic beam sources, in this case not for ground state atoms but for metastable atoms, which requires a much lower radio frequency. Another difference of this new idea is the smaller interaction time of the atoms with the photons inside the transition unit due to their much higher velocity of roughly $2\cdot10^5$ m/s compared to velocities of about $10^3$ m/s in an atomic beam source.