A dynamic algebra for rotation-vibration spectra of complex molecules

Calculation of some of the nuclear properties of even-even 172-176Hf isotopes using IBM-1

“…The stimulation energies of collective quadrupole nuclei are strongly dependent on the number of nucleons outside the closed shell (Abdul & Mushtaq, 2011). The interacting boson model constitutes a simple Hamiltonian capable of describing collective nuclear properties across a wide range of nuclei, based on general algebraic group theoretical techniques, which have found applications in problems in atomic, molecular, and high energy physics (Kellman & Herrick, 1980;Van Roosmalen et al, 1982). In the interacting boson model (IBM-1), proton and neutron-boson degrees of freedom are not distinguished.…”

Finite-size corrections in the bosonic algebraic approach to two-dimensional systems

“…[10], is an algebraic model based on the spectrum generating algebra U (4). This approach is appropriate for the modelling of three-dimensional systems and has been mostly employed to model rotational and vibrational molecular spectra of diatomic [10,11] and polyatomic [12,13] molecular species, treating molecular degrees of freedom as collective excitations in a bosonic space (vibrons) [3]. The one-dimensional (1D) limit of the model [14] has been used to decouple vibrations from rotations, permitting to take full advantage of the discrete molecular symmetry [15].…”

Recoupling coefficients of group SO(4) and their application to linear tetratomic molecules

“…Majorana operators and Casimir operators play an important role in the algebraic Hamiltonian, and they represent an important interaction between two bonds of a triatomic or tetratomic molecule. In this paper we first prove the general expressions for recoupling coefficients of SO (4) and then give the special case corresponding to linear tetratomic molecules. In Section 3 the matrix elements of C and M operators are calculated using recoupling coefficients of SO (4).…”