T. Oda

Nuclear structure calculation ofβ+β+,β+/EC and EC/EC decay matrix elements

Nuclear matrix elements for double positron emisson (β+β+), positron emission/electron capture (β+/ EC) and double electron capture (EC/EC) in the 2νββ decay mode and forβ+β+ andβ+/EC decay in the 0νββ mode are calculated for the experimentally most promising isotopes58Ni,78Kr,96Ru,106Cd,124Xe,130Ba and136Ce within pn-QRPA. We point out that the matrix element for the 2νβ+/EC decay differs from the 2νβ+β+ matrix element, an effect not considered previously. For the neutrino accompanied decays our calculation predicts for theβ+/EC and the EC/EC mode half lives which are shorter typically by 4–7 orders of magnitude than those for the double positron emission. However, even for the best candidates typical values for 2νβ+/EC (2ν EC/EC) are still in the range of ∼1022 ((some) 1021) years. For 0νββ decay we have calculated all matrix elements relevant for both, the mass mechanism and the right-handed currents for the first time complete. A detailed discussion of the differences between the 0νβ+β+, the 0νβ+/EC and 0νβ−β− decay is given.

Proton-neutron quasiparticle RPA with separable Gamow-Teller forces

A comprehensive representation is presented of a generalized form of the proton-neutron quasiparticle RPA model, originally introduced by Halbleib and Sorensen almost thirty years ago. The model uses separable Gamow-Teller forces, including, in addition to the particle-hole force of the former model, the particle-particle force, which is of decisive importance for β+ decay andββ decay. The above model has further been extended to the treatment of odd-odd nuclei. An extension is also made to transitions from nuclear excited states. This is essential for calculations of nuclear weak transition rates in the high-temperature interior of massive stars. Complementing the discussion of Halbleib and Sorensen on the particle-hole force, the structure of the RPA dispersion relation is discussed with emphasis on effects of the particle-particle force.

Microscopic calculation of the rates of electron captures which induce the collapse of O+Ne+Mg cores

Abstract The rates of electron captures which induce the collapse of the stellar cores composed of 16 O, 20 Ne and 24 Mg are calculated microscopically using the shell model wave functions of Wildenthal. Since these are the best wave functions available for sd-shell nuclei, the capture rates calculated in this paper are at present the most reliable ones. Our electron capture rates differ up to an order of magnitude from those previously calculated with the gross theory and FFN. The difference of the capture rates is analyzed and the effects on the evolution of the O + Ne + Mg core are discussed. In the appendix, we tabulate the capture rates as well as the associated neutrino energy loss rates and γ-ray heating rates in the form available for the calculation of the evolution of the O + Ne + Mg core.

The orbital current for the 0gr+→1+ M1 excitations in the even-even f72 shell nuclei

Abstract The role of orbital current for the 0 gr + →1 + M1 excitations in the even-even f 7 2 shell nuclei is studied in the full f 7 2 n +f 7 2 n−1 (f 5 2 p 3 2 p 1 2 ) 1 configuration space. Most of the orbital contribution is concentrated in the lowest 1 + state. The first order correction term enhances appreciably the orbital-to-spin ratios compared with the pure f 7 2 model. The observed orbital-to-spin ratio for the 0 gr + →1 1 + M1 transition in 46 Ti is well reproduced.

Shell-model study of the Gamow-Teller giant resonance in 208Bi

Abstract The Gamov-Teller giant resonance observed in the 208 Pb(p,n) 208 Bi reaction is studied in terms of shell model. 2p−2h excitations are taken into the model space in addition to 1p-1h on the doubly closed 208 Pb core.The giant resonance is well reproduced and the Gamow-Teller strength is highly fragmented among a number of 1 + states in the resonance region.

Isospin-forbidden beta decays in 1s0d-shell nuclei

Abstract The matrix elements of the isospin-symmetry-breaking interactions are calculated in 1s0d-shell nuclei. The diagonal matrix elements are obtained to provide the systematics of the data of the mass shifts of isospin multiplets. The calculated off-diagonal matrix elements are consistent with the experiments of isospin-forbidden beta decays available in the 1s0d-shell, and predictions for other 514 isospin-forbidden beta decays are made. The isospin-symmetry-breaking terms of nuclear force are found to contribute greatly to the off-diagonal matrix elements.

Charge-symmetry-breaking nucleon-nucleon interaction in the 1s0d-shell nuclei

Abstract The nuclear charge-symmetry-breaking forces due to the ϱ 0 − ω and π 0 − η mixings are evaluated in the isovector mass shifts of isospin multiplets and the isospin-mixing matrix elements relevant to the isospin-forbidden beta decays, in the 1s0d-shell nuclei. We find that the calculated mass shifts represent the state dependence of experimental ones, and find a large contribution of the meson-mixing in the isospin-mixing matrix elements.

Systematics of the total strength and the contribution of orbital current for the M1 excitations in the even-even sd-shell nuclei

It is shown that the total M1 excitation strengths of the even-even sd-shell nuclei calculated in the full (sd)n basis are about 50% of the jj-coupling single-particle limit. Compared with the calculated values, the observed M1 strengths are reduced by typically 20%. It is found that the orbital current contribution is almost independent of the mass number, in contrast to the spin current. A large orbital-to-spin ratio for 20Ne is explained from the viewpoint of supermultiplet SU(4) symmetry. The total strength of Gamow-Teller excitation is also calculated.

Effective isospin non-conserving interaction and isospin-forbidden beta decays in the 1 s0d shell

Abstract An effective isospin non-conserving interaction is determined for a 1s0d shell full space calculation. The interaction parameters are determined by requiring the interaction to reproduce the observed energy splittings of isobaric multiplets. We introduce a new mass dependence of the parameters, which significantly improves the quality of agreement. Applying the obtained interaction, the isospin mixing matrix elements are calculated. The calculation has reproduced existing experimental values deduced from isospin-forbidden beta decays.

Extended operator expansion method for neutrinoless double beta decay

Reliable calculations of nuclear matrix elements are a prerequisite for the determination of the effective neutrino mass and other particle physics parameters from neutrinoless double beta decay. Here, the operator expansion method is improved by including Coulomb, tensor and central interactions simultaneously. Furthermore, the formalism of the OEM is extended to those matrix elements necessary to extract the right-handed parameters 〈λ 〉 and 〈η 〉 from 0νββ decay. OEM includes the dependence of the nuclear matrix elements on the intermediate states implicitly and can therefore be understood as a step beyond the closure approximation. Numerical studies are carried out for the isotope76Ge combining the OEM expressions with ground-state wave functions calculated within a proton-neutron quasiparticle Random Phase Approximation (pn-QRPA) model. The influence and relative importance of central, tensor and Coulomb interactions is investigated. Within the OEM, contributions from the Coulomb force are found to be negligible in 0νββ decay, while the tensor force leads to a moderate change of the results, of the order of (10–30)%, giving a better agreement between sets of calculations which employ different NN-interactions. Generally, results of the OEM+QRPA calculation are similar to previous calculations of 0νββ decay matrix elements, indicating that 0νββ decay is not sensitive to model approximations and might therefore be more accurately calculated than the strongly suppressed 2νββ decay matrix elements.