### Abstract

We systematically investigate the new experimental method of using atoms or molecules to measure the important parameters of neutrinos that are still to be determined: the absolutemass scale, the mass hierarchy pattern (normal or inverted), the neutrino mass type (Majorana or Dirac), and the CP-violating phases, including Majorana phases. Most of these observables are difficult to measure in neutrino oscillation experiments. There are advantages to using atomic targets, such as the closeness of available atomic energies to anticipated neutrino masses, over nuclear target experiments such as the end point spectrum of β decay and two-electron line spectrum in the neutrinoless double β decay, both of which address some of the overlapping objectives with atomic/molecular experiments. A disadvantage of using atomic targets, the smallness of rates, is overcome by the macro-coherent amplification mechanism. The atomic or molecular process we use is a cooperative deexcitation of a collective body of atoms in a metastable level |e emitting a neutrino pair and a photon: |e → |g + γ + νiνj , where νi s are neutrino mass eigenstates. The macro-coherence is developed by trigger-laser irradiation of two colors, which frequently causes the two-photon process |e ↔ |g + γ + γ, |e + γ ↔ |g + γ inside the target.We discuss important aspects of the macro-coherence development in detail, by setting up the master equation for the target Bloch vector (whose components are population difference and medium polarization) and the propagating electric field. Our master equation includes the effects of phase decoherence of medium polarization and decay of population difference. The spectral rate (the number of events per unit time) of macro-coherent radiative emission of a neutrino pair has three parts, and is given by a factorized formula of the form (overall ω-independent rate denoted by 0) × (spectral shape function denoted by I (ω)) × (time-evolving dynamical factor), where ω is the photon energy. The constant factor 0 determines the overall rate in the unit of 1/time, and for Xe it is of the order of 1Hz(n/1022 cm-3)3 (V/102 cm3). The dynamical factor is time dependent and is given by the space integrated quantity, over the entire target, of the product of the magnitude squared of the coherent polarization and the field strength (in the units of the maximally extractable energy density) stored inside the target. The asymptotic value of the timeevolving dynamical factor is given by the contribution of the field condensate accompanied by macroscopic coherence, which is calculated using the static limit of the master equation. With an appropriate choice of heavy target atoms or molecules such as Xe and I2 that have a large M1 × E1 matrix element between |e and |g, we show that one can determine three neutrino masses along with distinction of the mass hierarchy pattern (normal or inverted) by measuring the spectral shape I (ω). If one uses a target of available energy of a fraction of 1 eV, the most experimentally challenging observable, the Majorana CP phases may be determined, comparing the detected rate with differences of theoretical expectations which exist at the level of several percent. The Majorana CP-violating phase is expected to be crucial to the understanding of the matter-antimatter imbalance in our universe. Our master equation, when applied to E1 × E1 transitions such as pH2 vibrational Xv = 1 → 0, can describe explosive paired superradiance events in which most of the energy stored in |e- is released in the order of a few nanoseconds. The present paper is intended to be self-contained, explaining some details of related theoretical works in the past, and reports on new simulations and the ongoing experimental efforts of the project to realize neutrino mass spectroscopy using atoms/molecules.

Original language | English |
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Article number | 04D002 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2012 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Progress of Theoretical and Experimental Physics*,

*2012*(1), [04D002]. https://doi.org/10.1093/ptep/pts066