Five pairs of superdeformed (SD) signature partners in the mass region A~190 namely: 191Hg (SD2, SD3), 193Hg (SD1,SD2) , 193Hg (SD3,SD4), 191Tl (SD1,SD2) and 193Tl (SD1,SD2) are studied in version of particle – rotor model. We considered the odd-A nucleus as a system of three valence particles coupled to an even- even symmetric deformed core. The three extra core particles lie in high- j intruder orbital and occupy only two Nilsson levels with 1= 1 2 and 2= 3 2. There are four completely antisymmetric functions with K =  1 2 and K =  3 2 and only two basis functions . We diagonalized the 22 matrix of the total Hamiltonian and evaluated the excitation energies . Transition energies E, rotational frequencies ħ , dynamic J(2) and kinematic J(1)moments of inertia have been calculated . A very good agreement with the experimental data support the proposed model by calculating the 2. The bands exhibit the usual increasing of J(2) with ħ ω.
The I = 1 energy staggering in - ray transition energies presented in these odd- A SD nuclei has been examined by proposing a two staggering functions: the first one depending on the dipole transitions linking the two signature partners and the quadrupole transitions within each band and the second one depending only on the dipole transition energies linking the two signature partners. Our selected signature partners in Hg and Tl nuclei show large amplitude staggering pattern.