PHYSICAL REVIEW C 78, 064311 (2008) Structure of A = 82 analogs and isospin-symmetry-breaking effects on superallowed Fermi β decay A. Petrovici, 1,2 K. W. Schmid, 2 O. Radu, 1 and Amand Faessler 2 1 National Institute for Physics and Nuclear Engineering, R-077125 Bucharest, Romania 2 Institut f ¨ ur Theoretische Physik, Universit¨ at T ¨ ubingen, D-72076 T¨ ubingen, Germany (Received 23 July 2008; published 17 December 2008) We study the effects of the isospin-symmetry breaking on the superallowed Fermi β decay of the ground state of 82 Nb to 82 Zr. Results on the analog as well as nonanalog β -decay branches are self-consistently obtained within the complex excited VAMPIR approach. The 82 Nb → 82 Zr β decay to the first two excited 0 + states with significant strength is predicted to coexist with the superallowed decay. The structure and electromagnetic properties of the analog and nonanalog low- and high-spin states in 82 Nb and 82 Zr are compared with the available experimental data. DOI: 10.1103/PhysRevC.78.064311 PACS number(s): 21.10.−k, 21.60.−n, 23.40.−s, 27.60.+j I. INTRODUCTION The investigation of the structure and dynamics of exotic nuclei around the N = Z line in the A ≃ 80 mass region is one of the most exciting challenges in low-energy nuclear physics today. Apart from displaying some rather interesting nuclear structure effects, the superallowed 0 + → 0 + Fermi β decay of these nuclei is a valuable tool in probing many properties of the weak interaction. Superallowed Fermi β decays between 0 + T = 1 analog states provide tests of the validity of the conserved-vector-current (CVC) hypothesis and the unitarity of the Cabibbo-Kobayashi-Maskawa matrix (see Ref. [1] and the references therein). Since the late 1990s, intense theoretical effort has been devoted to the investigation of the superallowed Fermi β decay [1–6] and several experimental programs have been initiated to measure the half-lives and branching ratios for the decays of odd-odd N = Z nuclei with A  62 where the charge-dependent correction terms are expected to be large. The β + -decay half-life for the odd-odd N = Z nucleus 82 Nb has been measured following the fragmentation of a primary 92 Mo beam at the GANIL laboratory and the reported value is T 1/2 = 52(6) ms [7]. Extending the mass range over which the CVC hypothesis can be tested this is one of the heaviest N = Z nuclei for which superallowed Fermi β decay was established. In this study we examine the charge-symmetry-breaking effects on the superallowed Fermi β decay of 82 Nb to 82 Zr using the complex excited VAMPIR variational approach. The charge independence of nuclear forces requires that the energy spectra in pairs of mirror nuclei are identical. Small differences between energy levels could then be interpreted as isospin-symmety-breaking effects. To illustrate these effects at low and high spins and to test the quality of the complex excited VAMPIR description of the properties of these states we investigated the even-spin positive-parity states up to 20 + in the mirror nuclei 82 Zr and 82 Nb. Calculations based on the variational approaches of the VAMPIR family have been successfully performed for the description of a variety of nuclear structure phenomena in the A = 60–90 mass region, not only in nuclei along the valley of β -stability but also in some exotic nuclei close to the proton drip line [8–16]. The complex excited VAMPIR approach allows for a unified description of low- and high-spin states, including in the projected mean fields neutron-proton correlations in both the T = 1 and T = 0 channels and general two-nucleon unnatural-parity correlations. The oblate-prolate coexistence and mixing, the variation of the deformation with mass number, increasing spin, as well as excitation energy have been compared with the available experimental information. Because the VAMPIR approaches enable the use of rather large model spaces and of general two-body interactions, large-scale nuclear structure studies going far beyond the abilities of the conventional shell-model configuration-mixing approach are possible. Our previous investigations on microscopic aspects of shape coexistence in N ≃ Z nuclei in this mass region indicated the presence of a strong competition between particular configurations based on large and small oblate and prolate quadrupole deformations. Furthermore, as expected, because in N ≃ Z nuclei neutrons and protons fill the same single particle orbits, the neutron-proton pairing correlations were found to play an important role [9]. However, the theoretical results suggest that certain properties of these nuclei are extremely sensitive to small variations of particular parts of the effective Hamiltonian [10,11]. We briefly describe the complex excited VAMPIR vari- ational procedure and define the effective Hamiltonian in the next section. In Sec. III we then discuss the results on isospin-symmetry-breaking corrections for superallowed Fermi β decay of 82 Nb to 82 Zr. Results on the low- and high-spin states, including electromagnetic properties, will be compared for the 82 Zr and 82 Nb with the available data in Sec. IV. Finally we present some conclusions in Sec. V. II. THEORETICAL FRAMEWORK The complex excited VAMPIR approach uses Hartree- Fock-Bogoliubov (HFB) vacua as basic building blocks, which are restricted only by time reversal and axial symmetry. The underlying HFB transformations are essentially complex and do mix proton with neutron states as well as states of different parity and angular momentum. The broken symmetries of these vacua (nucleon numbers, parity, total angular momentum) are restored by projection techniques 0556-2813/2008/78(6)/064311(8) 064311-1 ©2008 The American Physical Society