Neutrinoless double-electron capture

Direct determination of the neutrino mass is at the present time one of the most important aims of experimental and theoretical research in nuclear and particle physics. A possible way of detection is through neutrinoless double-electron capture, $0\nu \mathrm{ECEC}$. This process can only occur when the energy of the initial state matches precisely that of the final state. We present here a calculation of prefactors (PFs) and nuclear matrix elements (NMEs) within the framework of the microscopic interacting boson model (IBM-2) for ${}^{124}\mathrm{Xe}$, ${}^{152}\mathrm{Gd}$, ${}^{156}\mathrm{Dy}$, ${}^{164}\mathrm{Er}$, and ${}^{180}\mathrm{W}$. From the PF and NME we calculate the expected half-lives and obtain results that are of the same order as those of $0\nu {\beta }^{+}{\beta }^{+}$ decay, but considerably longer than those of $0\nu {\beta }^{-}{\beta }^{-}$ decay.

Figure 1

Schematic representation of neutrinoless double-electron capture.

Figure 2

Neutrinoless double-electron capture where $\nu =\overline{\nu }$ can be either a light or heavy neutrino.

Figure 3

Energetics of ${}^{152}\mathrm{Gd}$$\to {}^{152}$Sm double-electron capture.

Figure 4

Comparison between calculated and experimental low-lying spectra for ${}^{152}\mathrm{Gd}$$\to {}^{152}$Sm.

Figure 5

Comparison between calculated and experimental low-lying spectra for ${}^{164}\mathrm{Er}$$\to {}^{164}$Dy.

Figure 6

Comparison between calculated and experimental low-lying spectra for ${}^{180}\mathrm{W}$$\to {}^{180}$Hf.

Figure 7

Comparison between calculated and experimental low-lying spectra for ${}^{124}\mathrm{Xe}$$\to {}^{124}$Te.

Figure 8

Comparison between calculated and experimental low-lying spectra for ${}^{156}\mathrm{Dy}$$\to {}^{156}$Gd.

Figure 9

Expected half-lives for light-neutrino exchange with $〈m_{\nu }〉=1$eV, $g_A=1.269$. The figure is in semilogarithmic scale.

Figure 10

Expected half-lives for heavy-neutrino exchange with $m_p\langle m_{{\nu }_h}^{-1}\rangle =2.75\times {10}^{-7}$, $g_A=1.269$. The figure is in semilogarithmic scale.