Neutrinos are the key particle for astro-nuclear physics, particle physics and cosmology. Nuclear physics is helping to pin down the properties and sources of this ubiquitous but elusive rascal.
Neutrinos are electrically neutral elementary particles which interact extremely weakly with matter. They have been extensively studied both experimentally and theoretically for some five decades, and yet several basic questions about the neutrino remain unsolved. These include, amongst others things, the fundamental nature of the neutrino, i.e. whether it is a Majorana particle (if neutrinos are their own antiparticle) or a Dirac particle (whether neutrinos and antineutrinos are different species). Furthermore, the absolute mass scale and the mass hierarchy (mass spectrum) remain unknown.
Owing to the weak neutrino-matter interactions, the detection of neutrinos is a difficult job. On the other hand, however, neutrinos can easily escape from the places of their creation, thus enabling experimental studies of intense astrophysical sources of neutrinos like the Sun and supernovae.
Neutrino fluxes from these sources can be monitored by Earth-bound neutrino telescopes. These arrays have large active masses in order to catch some of these messengers. Due to the inherent experimental challenges, the importance of theoretical investigations of neutrino-involved processes has grown, in particular the role of atomic nuclei as femto-scale laboratories of neutrino studies. In these laboratories, the nucleons are in quantum states of good energy, spin, parity and isospin and thus the transitions between nuclear states, caused by the neutrino-nucleon interactions, are easily quantifiable.
The influence of nuclear structure on the neutrino-nucleus processes is summarised by the nuclear matrix elements (NMEs), evaluated by using nuclear wave functions obtained from a given nuclear-structure model. Our theory group at the University of Jyväskylä’s Department of Physics produces NMEs for dark-matter direct detection, for the coherent scattering of solar neutrinos in studies of the so-called ‘neutrino floor’ in future xenon-based dark-matter detectors, and for the scattering of astroneutrinos on nuclei and for nuclear muon capture. A particular topic of interest are the rare weak decays.
Nuclear double beta decay and Majorana neutrinos
Discovery of the neutrinoless double beta decay (DBD) of atomic nuclei is currently one of the top priorities in particle physics. Interest on double beta decay has been revived with the discovery of the neutrino oscillations at the end of the 20th century, about two decades ago.
Detection of DBD would imply that neutrinos are massive Majorana particles and that lepton-number conservation does not hold. In addition, the absolute mass scale and mass hierarchy of neutrinos can be studied by DBD. Past and current measurements of DBD have given only lower limits to the decay half-lives of the nuclei used as sources in the experimental installations.
Since the decay half-lives are at least a billion times the age of the Universe, the experiments have to be protected against cosmic rays in underground caverns or inside mountain masses. The DBD transition rate is extremely small because it is mediated by a second-order weak process and a tiny neutrino mass.
In order for the DBD of a nucleus to be observed, the single beta decay of the nucleus has to be forbidden by energy conservation. For this reason, only 35 potential double beta emitters exist on the neutron-rich side of the nuclear chart. On the proton-rich side, another 35 DBD nuclei are found. The potentially measured half-life of DBD can be translated to the neutrino mass through the NMEs.
These NMEs are sensitive to the details of the many-nucleon correlations and the renormalisation (quenching) of the effective weak axial-vector coupling g(A) in nuclei. The life-time of a free neutron gives g(A)=1.27 but the strenght of g(A) in atomic nuclei is largely uncertain (see below).
Shapes of electron spectra and the strength of weak axial coupling
As stated above, the DBD rate is very sensitive to the quenching of the strength of g(A) in medium-heavy and heavy nuclei. This quenching is affected by nuclear-medium effects (multiple meson exchanges of nucleons), non-nucleonic contributions (baryons heavier than nucleons) and many-nucleon correlations. Since the DBD NMEs are computed by using nuclear models based on various simplifications in the underlying many-body quantum mechanics the effects of g(A) get masked by the model inaccuracies.
This way, the deficiencies of a given nuclear model are absorbed in an effective g(A) and the quenching of g(A) becomes nuclear-model dependent. The way out from this vicious circle is to use the same nuclear models to evaluate DBD-independent processes, like the (single) beta decay. In this way, the nuclear-model-induced effects on g(A) can, at least in principle, be safely translated from one process to the other within a given nuclear-model framework.
In nuclear beta-minus decay, one neutron in a nucleus turns into a proton. This transformation is accompanied by the emission of two leptons: an electron and the corresponding antineutrino. The electron energy can be (easily) measured and it spans a continuum from zero to the endpoint energy, determined by the mass difference of the initial and final nuclei involved in the process.
This continuum is called the ‘electron spectrum’, and it has a shape which depends on the details of the decay. Many of the beta-minus decays are so-called ‘non-unique forbidden beta decays’ (NUF-BDs) in which the leptons are emitted in non-zero orbital angular momenta.
The corresponding spectral shapes of the emitted electrons depend on NMEs and lepton kinematics in a very non-trivial way. This complexity can sometimes be exploited in the determination of the quenching of g(A) since in the model calculations of the Jyväskylä theory group it has been shown that some of these decays have spectral shapes which are very sensitive to the effective value of g(A). An example is shown in Fig. 1, where the spectral shapes of the decay of Tc-98 to Ru-98 are shown for different values of g(A) in computations using advanced nuclear theory. By measuring this shape and comparing it with the theory prediction, one can access the quenching of g(A). This method has been coined the ‘spectrum-shape method’ (SSM) by our theory group.
Electron spectral shapes and the reactor antineutrino anomaly
Low-energy electron antineutrinos from nuclear reactors are used for neutrino-oscillation studies. The modern short-baseline neutrino-oscillation experiments Daya Bay in China, RENO in South Korea and Double Chooz in France have measured fluxes of antineutrinos emanating from fission products in nuclear reactors.
These reactors are used for energy production in nuclear power plants in the mentioned locations. The measured antineutrino fluxes are some 6% lower than the fluxes deduced from the data acquired from the available nuclear databases. This difference in the measured and predicted fluxes constitutes the so-called ‘reactor antineutrino anomaly (RAA)’. In addition, there is a strange unexplained ‘bump’ between 4 and 6 MeV of antineutrino energy in the measured spectrum (see Fig. 2).
The RAA has been among us already for almost a decade and no fully convincing explanation to it has been found. The anomaly has inspired a particle-physics explanation: the oscillation of part of the electron antineutrinos to ‘sterile’ neutrinos which lose their touch with the material world and thus disappear for good from the observable Universe. The nuclear physics of the fission products has been studied in order to estimate the cumulative beta spectra responsible for the theoretical antineutrino flux. The involved beta decays go partly by forbidden transitions which cannot be assessed by the present nuclear data, but instead could be calculated in a suitable nuclear-model framework.
In the so-called Huber-Mueller approximation, a standard in the field, the antineutrino flux has been estimated by assuming that the electron spectral shapes of the NUF-BDs (see the previous section) are simple and independent of the NMEs. In a recent analysis by the Jyväskylä theory group, together with collaborators from the University of Leuven, Belgium, 29 key NUF-BDs were analysed for their electron spectra by using computed nuclear wave functions and a subsequent Monte Carlo analysis for the rest of the NUF-BD electron spectra.
It was found that both the effect of the RAA and the spectral ‘bump’ can be explained by this novel approach, bringing the difference between the calculated and measured RAA and the ‘bump’ to a statistically insignificant level. This implies a nuclear-physics explanation for the RAA and the ‘bump’, possibly lifting the more appealing sterile-neutrino hypothesis nurtured by particle physicists.