The atomic transition from an excited state vertical bar e > to the ground state vertical bar g > by emitting a neutrino pair and a photon, i.e., vertical bar e > -> vertical bar g > + vertical bar gamma > + vertical bar nu(i)> + vertical bar(nu) over bar (j)> with i, j = 1, 2, 3, has been proposed by Yoshimura and his collaborators as an alternative way to determine the absolute scale m(0) of neutrino masses. More recently, a statistical analysis of the fine structure of the photon spectrum from this atomic process has been performed [N. Song et al. Phys. Rev. D 93, 013020 (2016)] to quantitatively examine the experimental requirements for a realistic determination of absolute neutrino masses. In this paper, we show how to improve the statistical analysis and demonstrate that the previously required detection time can be reduced by one order of magnitude for the case of a 3 sigma determination of m(0) similar to 0.01 eV with an accuracy better than 10%. Such an improvement is very encouraging for further investigations on measuring absolute neutrino masses through atomic processes.