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The article presents brief information on the correlations and neutrinoless β βdecay nuclear matrix elements (NMEs) of p f- shell nuclei. It mentions about the determination of nuclear matrix elements (NMEs) for neutrinoless using shell model (SM) and energy density functional (EDF) methods. Topics discussed include systematic study of the radioactive decays of calcium, titanium and others, and Fermi contribution of the NMEs, is offered.

The 40Ca(α,γ)44Ti reaction is believed to be the main production channel for the radioactive nuclide 44Ti in core-collapse Supernovae. Radiation from decaying 44Ti has been observed so far for two supernova remnants, and precise knowledge of the 44Ti production rate may help improve supernova models. The 40Ca(α,γ)44Ti astrophysical reaction rate is determined by a number of narrow resonances. Here, the resonance triplet at Eα = 4497,4510, and 4523 keV is studied both by activation, using an underground laboratory for the γ counting, and by in-beam γ spectrometry. The target properties are determined by elastic recoil detection analysis and by nuclear reactions. The strengths of the three resonances are determined to be ωγ = (0.92 ± 0.20), (6.2 ± 0.5), and (1.32 ±0.24) eV, respectively, a factor of 2 more precise than before. The strengths of this resonance triplet may be used in future works as a point of reference. In addition, the present new data directly affect the astrophysical reaction rate at relatively high temperatures (above 3.5 GK). [ABSTRACT FROM AUTHOR]

The relatively short-lived radionuclide 44Ti is of considerable importance for the interpretation of nucleosynthesis in core-collapse supernova environments. Production is predominantly through the 40Ca(α,γ)44Ti reaction, which has been studied in this work over the energy range Ecm = 2.73--4.18 MeV, via direct γ counting and the 4π-summing technique, utilizing a previously characterized 12 inch × 12 inch single Nal crystal. The inferred reaction rate is compared here to both current experimental measurements and theoretical model calculations [ABSTRACT FROM AUTHOR]

Excited states of the N=32 nucleus 54Ti have been studied, via both inverse-kinematics proton scattering and one-neutron knockout from 55Ti by a liquid hydrogen target, using the GRETINA γ-ray tracking array. Inelastic proton-scattering cross sections and deformation lengths have been determined. A low-lying octupole state has been tentatively identified in 54Ti for the first time. A comparison of (p,p') results on low-energy octupole states in the neutron-rich Ca and Ti isotopes with the results of random phase approximation calculations demonstrates that the observed systematic behavior of these states is unexpected. [ABSTRACT FROM AUTHOR]