Two-oscillator basis expansion for the solution of relativistic mean field equations

In the relativistic mean field (RMF) calculations usually the basis expansion method is employed. For this one uses single harmonic oscillator (HO) basis functions. A proper description of the ground state nuclear properties of spherical nuclei requires a large (around 20) number of major oscillator shells in the expansion. In halo nuclei where the nucleons have extended spatial distributions, the use of single HO basis for the expansion is inadequate for the correct description of the nuclear properties, especially that of the surface region. In order to rectify these inadequacies, in the present work an orthonormal basis composed ot two HO basis functions having different sizes is proposed. It has been shown that for a typical case of (A = 11) the ground state constructed using two-HO wave functions extends much beyond the second state or even third excited state of the single HO wave function. To demonstrate its usefulness explicit numerical RMF calculations have been carried out using this procedure for a set of representative spherical nuclei ranging from ¹⁶O to ²⁰⁸Pb. The binding energies, charge radii and density distributions have been correctly reproduced in the present scheme using a much smaller number of major shells (around 10) in the expansion.