Resolving neutrino mass hierarchy from supernova (anti)neutrino-nucleus reactions

We introduce a hybrid method to determine neutrino mass hierarchy by simultaneous measurements of detector responses induced by antineutrino and neutrino fluxes from accretion and cooling phase of type II supernova. The (anti)neutrino-nucleus cross sections for $^{12}$C, $^{16}$O, $^{56}$Fe and $^{208}$Pb are calculated in the framework of relativistic nuclear energy density functional and weak Hamiltonian, while the cross sections for inelastic scattering on free protons, $p(\bar{\nu}_{e},e^{+})n$, are obtained using heavy-baryon chiral perturbation theory. The simulations of (anti)neutrino fluxes emitted from a protoneutron star in a core-collapse supernova include collective and Mickheev-Smirnov-Wolfenstein effects inside star. The emission rates of elementary decay modes of daughter nuclei are calculated for normal and inverted neutrino mass hierarchy. It is shown that simultaneous use of (anti)neutrino detectors with different target material and time dependence of the signal allow to determine the neutrino mass hierarchy from the ratios of $\nu_e /$ $\bar{\nu}_e$ induced particle emissions. The hybrid method favors detectors with heavier target nuclei ($^{208}$Pb) for the neutrino sector, while for antineutrinos the use of free protons and light nuclei ($\text{H}_2\text{O}$ or $\text{-CH}_2\text{-}$) represent appropriate choice.Comment: 4 pages, 2 figures, 1 tabl

Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons

Background: Magnetic dipole (M1) excitation is the leading mode of nuclear excitation by the magnetic field, which couples unnatural-parity states. Since the M1 excitation occurs mainly for open-shell nuclei, the nuclear pairing effect is expected to play a role. As expected from the form of operator, this mode may provide the information on the spin-related properties, including the spin component of dineutron and diproton correlations. In general, the sum rule for M1 transition strength has not been derived yet. Purpose: To investigate the M1 excitation of the systems with two valence nucleons above the closed-shell core, with pairing correlation included, and to establish the M1 sum rule that could be used to validate theoretical and experimental approaches. Possibility to utilize the M1 excitation as a tool to investigate the pairing correlation in medium is also discussed. Method: Three-body model, which consists of a rigid spherical core and two valence nucleons, is employed. Interactions for its two-body subsystems are phenomenologically determined in order to reproduce the two-body and three-body energies. We also derive the M1 sum rule within this three-body picture. Conclusion: The introduced M1 sum rule can be utilized as a benchmark for model calculations of M1 transitions in the systems with two valence nucleons. The total sum of the M1 transition strength is related with the coupled spin of valence nucleons in the open shell, where the pairing correlation is unnegligible. The three-body-model calculations for 18 O, 18 Ne, and 42 Ca nuclei demonstrate a significant effect of the pairing correlations on the low-lying M1 transitions. Therefore, further experimental studies of M1 transitions in those systems are on demand, in order to validate proposed sum rule, provide a suitable probe for the nuclear pairing in medium, as well as to optimize the pairing models.Comment: 10 pages, 3 figures, 4 tables. Revised for re-submission to Phys. Rev.

Stellar electron-capture rates calculated with the finite-temperature relativistic random-phase approximation

We introduce a self-consistent microscopic theoretical framework for modelling the process of electron capture on nuclei in stellar environment, based on relativistic energy density functionals. The finite-temperature relativistic mean-field model is used to calculate the single-nucleon basis and the occupation factors in a target nucleus, and $J^{\pi} = 0^{\pm}$, $1^{\pm}$, $2^{\pm}$ charge-exchange transitions are described by the self-consistent finite-temperature relativistic random-phase approximation. Cross sections and rates are calculated for electron capture on 54,56Fe and 76,78Ge in stellar environment, and results compared with predictions of similar and complementary model calculations.Comment: Physical Review C, accepte

Mathematical properties and algorithm for fast calculation of full Wick’s contractions in quantum many-body fermion systems

Wick’s contractions, also related to Wick’s theorem, represent important mathematical technique used in quantum many-body theory to simplify calculations involving creation and annihilation operators. In this work we study the properties of full Wick’s contractions and discuss in details corresponding graph and group theory aspects. We observed isomorphism between graph-like objects which are in fact contained in the full Wick’s contractions and some geometrical objects, such as circle or regular rectangle with internal structure. We also found isomorphism between two induced groups, one which is related to permutations of one end of Wick’s lines and the second which corresponds to rotations of directed lines inside geometrical object. We present fast and efficient algorithm for calculation of the expectation value of large number of creation and annihilation particle and hole operators in order to achieve different particle-hole or particle-particle terms in many-body theories, from nuclear to solid state physics or quantum chemistry. The algorithm is based on observed isomorphisms. It simplifies full Wick’s contractions to simple adjacency and geometrical relations, which are also used for sign determination. Also, we presented several illustrative examples of computation, such as calculation of the two-body particle-hole terms in Hartree-Fock’s theory and the Random phase approximation

Mathematical properties and algorithm for fast calculation of full Wick’s contractions in quantum many-body fermion systems

Wick’s contractions, also related to Wick’s theorem, represent important mathematical technique used in quantum many-body theory to simplify calculations involving creation and annihilation operators. In this work we study the properties of full Wick’s contractions and discuss in details corresponding graph and group theory aspects. We observed isomorphism between graph-like objects which are in fact contained in the full Wick’s contractions and some geometrical objects, such as circle or regular rectangle with internal structure. We also found isomorphism between two induced groups, one which is related to permutations of one end of Wick’s lines and the second which corresponds to rotations of directed lines inside geometrical object. We present fast and efficient algorithm for calculation of the expectation value of large number of creation and annihilation particle and hole operators in order to achieve different particle-hole or particle-particle terms in many-body theories, from nuclear to solid state physics or quantum chemistry. The algorithm is based on observed isomorphisms. It simplifies full Wick’s contractions to simple adjacency and geometrical relations, which are also used for sign determination. Also, we presented several illustrative examples of computation, such as calculation of the two-body particle-hole terms in Hartree-Fock’s theory and the Random phase approximation