An update of the B(E2) evaluation for transitions in even–even nuclei near
Introduction
Quadrupole collectivities (reduced electric quadrupole transition rates), or B(E2) values, play an important role in nuclear physics and are in high demand for nuclear model calculations. Originally, these values were compiled by Raman et al. at the Oak Ridge Nuclear Data Project [1], [2]. Presently, this work continues within the US Nuclear Data Program (USNDP). In 2005, the Brookhaven B(E2) project website (http://www.nndc.bnl.gov/be2) was successfully launched [3]; this website currently contains an up-to-date compilation of B(E2;) experimental results and evaluated values from [2] that are widely used by scientists.
With an advent of rare isotope facilities [4] the whole nuclear landscape has been changing dramatically. These facilities have been producing rare nuclei far from the valley of stability at an increasing rate and providing researchers with unprecedented opportunities to study their properties. In many cases, B(E2) values and energies of the low-lying states have been studied for the first time. Large amount of new data, especially for the region, requires a new evaluation of quadrupole collectivities for proper interpretation and analysis of the newly obtained values. A renewed interest in B(E2) values was expressed by participants of the International Nuclear Physics Conference (INPC 2010) in Vancouver (http://inpc2010.triumf.ca) [5].
To answer the need for a new B(E2) evaluation and seek comments from the research community, new evaluations of Cr, Fe, Ni, and Zn isotopes have been completed. The complete evaluation of B(E2) for all even–even nuclei would follow thereafter based on our experience and the feedback from the users.
Section snippets
B(E2) evaluation policies
The current evaluation represents an update of B(E2) in units of , lifetimes () in ps, and deformation parameter () values for Cr, Fe, Ni, and Zn nuclei. These values are mutually related: where and are the -ray energy in keV and the total conversion coefficient, respectively, and . To introduce an additional measure of collectivity for nuclear excitations, Weisskopf units (W.u.) are added.
Adopted B(E2) values
The recommended values from the current project for Cr, Fe, and Ni isotopes are shown in Table 1. Compared to the previous evaluation of Raman et al. [2], it includes 18 new recommended values for 46, 56, 58, 60, 62Cr, 50, 52, 62, 64, 66Fe, 54, 70, 74Ni, and 72, 74, 76, 78, 80Zn. A complementary analysis of the two evaluations is presented below.
In the current evaluation, we used the latest AveTools averaging procedures [11], Band-Raman calculation of internal conversion coefficients () [13],
Shell model calculations
The 2+ excitation energies and B(E2) for transitions have been calculated in the -shell valence space using the GXPF1A effective interaction [16]. GXPF1A is a refinement of the original GXPF1 Hamiltonian [17], which was obtained starting with the G-matrix for the Bonn-C two-body potential and by further fine-tuning its matrix elements to describe the energies of about 700 selected states of -shell nuclei. The GXPF1 Hamiltonian does not describe very well the 2+ state in 54Ti ();
Experimental B(E2) values
Experimental values of B(E2), , and are shown in Table 3. To create a more comprehensive picture for each experiment we extended the scope of the previous work of Raman et al. [2] and included target, beam, beam energy, and a flag for the Coulomb barrier height into the compilation. A short review of the most recent experimental results used for the new evaluation is presented below.
Conclusion and outlook
An updated B(E2) evaluation of even–even Cr, Fe, Ni, and Zn isotopes has been performed under the auspices of the USNDP with an intention to update B(E2) values and collect nuclear data user feedback. It is a continuation of the work of Raman et al. on transition probabilities from the ground to the first-excited 2+ state of even–even nuclides [1], [2]. The update is based on all published data prior to April 2011 and includes new experimental B(E2) values for 33 out of 38 nuclei. It extends
Acknowledgments
The authors are grateful to Prof. J. Cameron (McMaster University) and V. Unferth (Viterbo University) for productive discussions and careful reading of the manuscript and useful suggestions, respectively. This work was funded by the Office of Nuclear Physics, Office of Science of the US Department of Energy, under Contract No. DE-AC02-98CH10886 with Brookhaven Science Associates, LLC. Work at McMaster University was also supported by DOE and NSERC of Canada. MH acknowledges support from NSF
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