![]() ![]() The transition between the parent and daughter even-even nuclei goes through a virtual odd-odd nucleus. Although there is no one-to-one correspondence between M 2ν and M 0ν, this experimental input is essential for M 0ν evaluation, which in turn is crucial for pinning down the New Physics parameters responsible for full lepton number violation.įigure 5 shows a nuclear-level diagram of the double- β decay transition for the isotope of 100Mo. Considering that making such a calculation involves mapping out all possible transitions between the two complex multibody systems (initial and final nuclei), it is not surprising that this is a difficult task.Īs mentioned above, 2νββ allows one to experimentally verify nuclear models used for the M 2ν calculation. NMEs are notoriously difficult to calculate even in the case of a single-β decay. NMEs define the nuclear-structural part of the probability for the double-β transition between the parent and daughter nuclei. The results for light nuclei (such as 48Ca and 76Ge) are consistent with previous calculations, whereas those for heavy nuclei (such as 136Xe and 150Nd) are ∼30% lower than previous values. The results are particularly interesting for heavy nuclei, in which relativistic and screening corrections play a major role. The phase-space factors were recalculated for most β −β − nuclei of interest ( 4) by taking advantage of modern developments in the numerical evaluation of the Dirac wave function for electrons. The contribution of the NME to the shape of the energy and angular distribution is small, and it affects primarily the absolute value of the transition probability.Īn exhaustive list of phase-space factors can be found in Reference 11. ![]() The angle between the two electrons follows the 1− β 1 β 2distribution for 0 +→ 0 + transitions and the 1+ β 1 β 2/3 distribution for 0 +→ 2 + transitions (here β= p/ E). To first order, the phase-space factor determines the shape of the electron spectra as well as their angular distribution. For the two-neutrino mode, these leptons are the two electrons and the two (anti)neutrinos: The phase-space factor is obtained by integration over all possible energies and angles of the leptons emitted in the decay. General methods for phase-space factor calculations in double-β decay have been developed ( 6– 8). The nuclear models used for M 2ν calculations can therefore be directly probed. The formula for Γ 2νshows that once 2νββ is observed, the experimental value of the corresponding NME can be extracted. Any experimental input into these models is, of course, important. We have to rely on nuclear models to do that. Unfortunately, there is no direct experimental observation available to independently pin down M 0ν. Knowledge about M 0ν is clearly necessary to extract the New Physics parameters. The most-discussed mechanism involves a light Majorana mass exchange,, but there are many other possibilities (see, e.g., Reference 5 for a relevant discussion). Where 〈η〉 2 is the lepton number–violating parameter that represents New Physics. Weizsäcker ( 3) made the first successful attempt to describe the mass of a nucleus in what is widely known as the semiempirical mass formula (SEMF): The stability of the nucleus is determined by its binding energy or, equivalently, its mass. 2. PHENOMENOLOGY OF TWO-NEUTRINO DOUBLE-BETA DECAY 2.1. Double-Beta Decay in Nuclei We discuss the implications of 2νββ in Section 7 and conclude in Section 8. Key backgrounds that have to be considered when searching for this rare process are discussed in Section 5, and Section 6 reviews the main results obtained during 60 years of experimental research. Section 4 describes experimental methods, both direct and indirect, that are used to search for 2νββ decay. Various models used to calculate the aforementioned NMEs are briefly reviewed and compared in Section 3. We review criteria for its occurrence and the basic formulae determining its probability. Section 2 is dedicated to the phenomenology of the 2νββ transition. Also, knowledge about 2νββ rates and the spectral shapes of electron energies emitted in the decay can mitigate this ultimate background for 0νββ. In particular, it provides experimental access to the values of nuclear matrix elements (NMEs) that can then be used to inform NME calculations for the 0νββ mode, which in turn is necessary to extract the particle physics parameters responsible for lepton number violation. Importantly, 2νββ provides vital information for the 0νββ search. ![]() The study of this process is important in its own right because it provides a tool for testing a possible higher-order Standard Model process and provides insights into nuclear structure. This review focuses on the version of the process that is allowed in the Standard Model: 2νββ ( Figure 1 b). ![]()
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