Dealing with the shifted and inverted Tietz-Hua oscillator potential using the J-matrix method

The tridiagonal J-matrix approach has been used to calculate the low and moderately high-lying eigenvalues of the rotating shifted Tietz-Hua (RSTH) oscillator potential. The radial Schrödinger equation is solved efficiently by means of the diagonalization of the full Hamiltonian matrix, with the Laguerre or oscillator basis. Ro-vibrational bound state energies for 11 diatomic systems, namely H2, HF, N2, NO, CO, O2, O2+, Cl2, N2+, I2, and NO⁺, are calculated with high accuracy. Some of the energy states for molecules are reported here for the first time. The results of the last four molecules have been introduced for the first time using the oscillator basis. Higher accuracy is achieved by calculating the energy corresponding to the poles of the S-matrix in the complex energy plane using the J-matrix method. Furthermore, the bound states and the resonance energies for the newly proposed inverted Tietz-Hua IRSTH-potential are calculated for the H₂-molecule with scaled depth. A detailed analysis of variation of eigenvalues with n, l quantum numbers is made. Results are compared with literature data, wherever possible.