Revisiting Grodzins systematics of B(E2) values

Abstract

Using Grodzins formalism as modified by S. Raman et al., Phys. Rev. C 37 (1988) 805, and D. Habs et al., CERN Proposal INTC-P-156 (2002), we analyze systematics of our latest evaluated B(E2) data for all the eveneven nuclei in Z=2-104 range published in At. Data Nucl. Data Tables 107 (2016) 1. The analysis indicates a low predictive power of systematics for a large number of cases, and a strong correlation between B(E2) fit values and nuclear structure effects. These findings provide a strong rationale for introduction of individual or elemental (grouped by Z) fit parameters. The current estimates of quadrupole collectivities for systematics of even-even nuclei yield complementary values for comparison with experimental results and theoretical calculations. The lists of fit parameters and predicted B(E2) values are given and possible implications are discussed.

Shell model predictions forSn124double-βdecay

“…This leads us to consider this effective Hamiltonian as well suited for the description of the spectra for these initial and final nuclei involved in the ββ decay. Table I where we find very good agreement with the adopted B(E2) ↑ data [76,77].…”

“…The Q-value for the decay to the * mihai.horoi@cmich.edu † neacs1a@cmich.edu ground state (g.s. ), 2.289 MeV, is slightly smaller than those of 130 Te and 136 Xe, but it is larger than that of 76 Ge decay. As a consequence, the phase space factor (see below) for 2νββ decay of 124 Sn is about ten times larger than that of 76 Ge, while the 0νββ phase space factor of 124 Sn is about four times larger than that of 76 Ge.…”

“…), 2.289 MeV, is slightly smaller than those of 130 Te and 136 Xe, but it is larger than that of 76 Ge decay. As a consequence, the phase space factor (see below) for 2νββ decay of 124 Sn is about ten times larger than that of 76 Ge, while the 0νββ phase space factor of 124 Sn is about four times larger than that of 76 Ge. Double-beta decay modes of 124 Sn were also recently investigated experimentally by several groups [28][29][30][31], but no signal has been seen so far.…”

“…[38][39][40], in which the raw sign of the Fermi contribution was considered. The new representation clearly shows that the shell model light neutrino-exchange NME are smaller due to the dramatic cancellation between the I = 0 and I = 2 contributions, while for the heavy neutrino-exchange NME the cancellation is not as pronounced (see also the discussion of the 76 Ge case in Ref. [79]).…”

“…Table V presents our new 124 Sn light neutrinoexchange 0νββ decay NME results with two SRC parametrizations (Argonne-V18 and CD-Bonn), together with the NME of five other nuclei from our group (ISM-CMU), 48 [40,48], compared with the most recent results that were obtained with nuclear structure methods that preserve the isospin symmetry and provide NME for both mechanisms. Included in Figure 6 (but not in Table V) are also shell model light neutrino-exchange NME for 48 Ca [87], 76 Ge, and 82 Se [88] that are using the same shell model calculations but an effective transition operator obtained in many-body perturbation theory. The updated IBM-2 NME [57] are only available for the Argonne-V18 SRC.…”