PHYSICAL REVIEW C 95, 054323 (2017) Triaxiality in the proton emitter 109 I Swati Modi, M. Patial, * and P. Arumugam † Department of Physics, Indian Institute of Technology Roorkee, Roorkee 247667, India E. Maglione Dipartimento di Fisica e Astronomia “G. Galilei”, and Istituto Nazionale di Fisica Nucleare, Via Marzolo 8, I-35131 Padova, Italy L. S. Ferreira Centro de Física e Engenharia de Materiais Avançados CeFEMA, and Departmento de Física, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais, P1049-001 Lisbon, Portugal (Received 20 March 2017; published 25 May 2017) We study the role of triaxial deformation in the proton-emitting nucleus 109 I. We analyze the rotational spectrum as well as the decay width within the nonadiabatic quasiparticle approach. The parent nuclear wave functions are calculated using a modified rotation-particle coupling where the matrix elements of the Hamiltonian representing the rotational states of the parent nucleus are written in terms of the rotational energies of the daughter nucleus. The measured spectrum of the daughter nucleus 108 Te suggests a strong role of either triaxial or vibrational degrees of freedom which is applicable for 109 I also. With these results we successfully explain the spectra of the parent and daughter and also the decay width in a unified way which enables us to establish the configuration of the rotational bands and the decaying state. DOI: 10.1103/PhysRevC.95.054323 I. INTRODUCTION The spontaneous proton emission from 109 I was observed for the first time in 1984 [1]. 109 I lies near the double shell closure ( Z = N = 50), which forms the island of α and proton emission. 109 I is preponderantly a proton emitter [1,2], but it has also a small branch (1.4 ± 0.4) × 10 −4 [3] of α emission. The interpretation of these decays and the knowledge of the nuclear structure properties of 109 I will be quite important to the understanding of astrophysical events [3]. Knowledge of the Q value for the α decay of 109 I allows the determination of the Q value of proton emission from 105 Sb [3]. 105 Sb takes part in the Sn-Sb-Te cycle, which burns hydrogen through the rapid proton-capture process and gives rise to type 1 x-ray bursts. 109 I is proposed to be a ground-state proton emitter, but the exact proton decaying state is not assigned yet. Many of the theoretical calculations within the strong coupling limit have suggested the  π = 1/2 + [4–6] state of the g 7/2 orbital as the ground state, where  is the z projection of the total angular momentum of the single particle. Microscopic calculation [6] of the half-life for proton emission from 109 I in the strong coupling limit and the nonadiabatic method based on the coupled-channel Schrödinger equation [7] also predicted the same decaying state, but with a slightly different quadrupole deformation of β 2 = 0.14 and β 2 = 0.10, respec- tively. Within the relativistic Hartree-Bogoliubov model the proton decaying state is calculated as the  = 3/2 + [8] state of the d 5/2 orbital. On the experimental side, from the observation and measurements of the energy levels and half-life for proton emission, it was suggested that the 5/2 + state [3,9,10] coming * Present address: Department of Physics, Worcester Polytechnic Institute, Worcester, Massachusetts 01609, USA. † Corresponding author: p.arumugam@gmail.com from the d 5/2 is the ground state. The γ transitions proposed in Refs. [11,12] show some discrepancies but the positive and negative parity yrast bands were further revised in [10,13]. This revision of γ transitions [10] and further analysis with the cranked shell model suggested a triaxial deformation, also consistent with the predictions of macroscopic-microscopic calculations [14]. So far, the role of triaxiality has been ignored while calculating the proton emission half-life of 109 I. Here we apply the nonadiabatic quasiparticle approach [15] in which the structure and decay properties of triaxially deformed proton emitters can be investigated by the coupling of the rotor energies directly with the particle states. This is a modified form of the conventional particle-rotor model (PRM) [16–19] where the rotor spectrum may deviate from the rotational spectrum of a rigid rotor. In the following sections, we discuss our theoretical framework and its application to studying proton emission from 109 I and its rotational spectra. II. THEORETICAL FRAMEWORK The properties of a triaxial proton emitter is studied with the microscopic nonadiabatic coupling of the quasiparticle (in a triaxial mean field) and the triaxial rotor. The total Hamiltonian for the particle-plus-rotor system is given by H = H avg + H pair + H rot , (1) where H avg and H pair correspond to the deformed mean field of the particles and the pairing interaction, respectively. H avg + H pair gives the quasiparticle energy and H rot is the triaxial rotor Hamiltonian given by H rot =  k=1,2,3 ¯ h 2 2I k R 2 k . (2) Here I k and R k are the moments of inertia and angular momenta, respectively, in the three directions (1,2,3). The rotor 2469-9985/2017/95(5)/054323(7) 054323-1 ©2017 American Physical Society