Deformation properties of the even–even rare-earth Er–Os isotopes for N = 100

The energies of the ground, [Formula: see text] and [Formula: see text] bands as well as the associated [Formula: see text] values have been calculated using interacting boson model (IBM). We have developed a new method called “new empirical equation” for each even–even rare-earth Er–Os for [Formula: see text]. Also, the relation of the gamma energy over spin as a function of the spin [Formula: see text] (E-GOS) has been drawn. The ratio between the energies of the [Formula: see text] and [Formula: see text] states as a function of [Formula: see text] has been drawn to determine the property of the ground-state band, these curves indicated that these isotopes have a rotational property SU(3), with the [Formula: see text] property for [Formula: see text]Os isotopes. The contour plots of the potential energy surface for Er–Os for [Formula: see text] are studied using the simplified form of interacting boson model with an intrinsic coherent state. The critical points have been determined for [Formula: see text]Os isotopes. The behaviors of energy and [Formula: see text] ratios in the ground-state band are examined.