Description of even-even Ti isotopes within IBM-1 model

Abstract

In this work, the some collective properties of even-even Ti isotopes in the A50 mass region were studied by using the interacting boson model-1 (IBM-1). This study includes calculations of the energy levels and the electromagnetic transition rates of [44][45][46][47][48] Ti and [52][53][54][55][56][57][58][59][60] Ti isotopes. The neutron number 50 Ti isotope is 28, the magic number, and this isotope was excluded from the IBM-1 calculations. First, the energy ratios were analyzed by comparing the typical values of U(5), SU(3), O(6) dynamical symmetries and E(5), X(5) critical point symmetries. Later model Hamiltonian was constructed according to the behavior of given isotopes. The low lying energy levels of each Ti isotopes were calculated by using the fitted parameters of Hamiltonian. B(E2) values were also calculated by using the corresponding electromagnetic transition operator in the IBM-1. The calculation results were compared with experimental data and they are in good agreement with each other. Finally, R 4/2 = E(4 1 + )/E(2 1 + ), R 0/2 = E(0 2 + )/E(2 1 + ) energy ratios and B(E2: 4 1 + → 2 1 + )/B(E2: 2 1 + → 0 1 + ), B(E2: 0 2 + → 2 1 + )/ B(E2: 2 1 + → 0 1 + ) ratios were analized to see the behavior of given isotopes. According to obtained results, Ti isotopes show E(5) behavior along the transition path from spherical to deformed -unstable region. Overall analysis indicates that these isotopes can be good example for the quantum shape phase studies along the isotopic chain.