Microscopic calculation of the ?- decays of 151Sm, 171Tm, and 210Pb with implications to detection of the cosmic neutrino background

The electron spectral shapes corresponding to the low -Q beta--decay transitions 151Sm(5/2-g.s.) -> 151Eu(5/2+g.s.), 151Sm(5/2-g.s.) -> 151Eu(7/2+1), 171Tm(1/2+g.s.) -> 171Yb(1/2- g.s.), 171Tm(1/2+g.s.) -> 171Yb(3/2-1), 210Pb(0+g.s.) -> 210Bi(1-g.s.), and 210Pb(0+g.s.) -> 210Bi(0- 1 ) have been computed using beta -decay theory with several refinements for these first-forbidden nonunique (ff-nu) beta- transitions. These ff-nu beta- transitions have non-trivial electron spectral shapes with transition nuclear matrix elements (NMEs) computed by using the microscopic Interacting Boson-Fermion Model (IBFM-2) for the decays of 151Sm and 171Tm, and the nuclear shell model (NSM) for the decay of 210Pb. Within the respective Q windows, the computed ff-nu electron spectral shapes deviate maximally at sub-percent level from the universal allowed shape, except for the transition 210Pb(0+g.s.) -> 210Bi(1-g.s.), where the maximal deviation is some 2.7%. This confirms that the so-called xi approximation is fairly good for most of these low -Q beta- transitions and thus the allowed shape is a rather good first approximation. Our computed spectral shapes could be of interest for experiments aiming to measure the cosmic neutrino background (C nu B), like the PTOLEMY experiment. We have also derived C nu B cross sections for the ground-state transitions of the considered nuclei at the beta endpoint. Our findings indicate that more work on the atomic mismatch correction is needed in the future in order to extract reliable and precise C nu B cross sections for any nuclear target.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/). Funded by SCOAP3.