Solution of Bohr Mottelson equation for modified wood Saxon potential using the hypergeometric method

The Bohr Mottelson model investigates the collective behavior of atomic nucleus [1]. The collective models are the combination of liquid drop model and shell model [2]. It is used to describes rotational and vibrational of the nucleus and also the deformed nucleus that corresponds to the excitation energy [3]. By solving the Bohr Mottelson, properties and mechanism involved in atomic nucleus can be obtained, such as energy spectrum and shape phase transitions [4]. The Bohr Mottelson has been solved for modified Davidson potential [5], Eckart potential [2], Kratzer potential [6], Killingbeck potential [7], Hulthen plus ring shape potential and three dimensional harmonic oscillator potential [8]. This study, the Bohr Mottelson equation is solved for modified Wood Saxon potential in spherical coordinates. By using hypergeometric method, the energy and the wave function of Bohr Mottelson equation were obtained. Numerically, the energy spectrum was calculated by applying energy equation in MATLAB R2013A software. While, the wave functions were investigated using hypergeometric method. The results show that the energy spectrum was increased by the increase of quantum numbers (n and L). The unnormalized wave functions were expressed in hypergeometric terms.