Role of atomic electron excitations in detection of the neutrinoless β-decay

  Miron Ya Amusia [1, 2]  ,  E. G. Drukarev [3]  ,  L. V. Chernysheva [2]  
[1] The Racah Institute of Physics, the Hebrew University of Jerusalem, Jerusalem 91904, Israel
[2] A. F. Ioffe Physical-Technical Institute, St. Petersburg 194021, Russian Federation
[3] National Research Center "Kurchatov Institute" B. P. Konstantinov Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300, Russia

The excitations of the electron shell in neutrinoless double beta decay shifts the limiting energy available for ejected electrons. We present the general equations for this shift and make computations for the decays of two nuclei - germanium and xenon.

The neutrinoless double β decay (0νββ) cannot take place in the framework of the Standard Model of electroweak interactions since it requires violation of the lepton quantum number. The process becomes possible if the electron neutrino is a Majorana particle, which coincides with its own antiparticle, having also a nonzero mass. This increased the interest to the (0νββ) decay. If there are massive Majorana neutrinos, the mechanism of the process is quite simple. Two W⁻ bosons are produced in two successive β-decays of the nucleus (A,Z). They interact by the exchange of neutrino, producing two electrons. The (0νββ) process has not been observed yet.

In the neutrinoless decay (0νββ) the electrons are always ejected with the energy equal to the difference of nuclei with masses MN and charges Z and (Z+2), correspondingly: E=MN,Z+2- MN,Z, leading to a monochromatic peak in the sum of the electron energies. The actual experiments are carried out for the β-decays of atoms but not of the bare nuclei. Therefore, one has to take into account the change of energy of electrons that originates from the alteration of the nuclear charge due to β-decay, as well as the excitation of electrons in the final state, i.e. in the Z+2 ion, and its possible ionization.

The typical energies of β-decay electrons are much bigger than the atomic electron energy. This permitted to apply the shake-off approximation. Therefore, we managed to perform summation over all atomic electrons excited (ionization) states analytically using the so-called closure approximation. As a result we have presented the energy shift of the total β-decay electrons as the difference between ground state electron energy of the atom Z and ion Z+2, to which it is necessary to add the atomic excitation energy. We express the atomic excitation energy via the mean Coulomb energy of electrons in the field of the atom Z.

We carry out the necessary computations employing our Hartree-Fock codes. It is of crucial importance that we must use the nonrelativistic functions. In the relativistic case the observable states of the system of Z electrons with positive energies only do not compose the complete set, since the latter includes the negative energy states also.

We found the energy shift as big as 351 eV for the double β-decay of germanium (Z=32). For the double β-decay of xenon (Z=54) we obtained δ=414 eV. Corrections to the shake-off approximation caused by the final state interactions between the β electron and the electron shell add about 1 eV to these values. These data can help in planning experiments in the field of double β-decay studies.