Modelling and Systematics of $\tfrac{1}{2}[521]\,\nu$ Quasiparticle Rotational Bands in $N = 99,\;101,\;103$ Isotonic Chains

Abstract

We analyze the $\tfrac{1}{2}[521]\,\nu$ quasiparticle rotational bands along the $N = 99,\;101,\;103$ isotonic chains using semi-empirical model in which first and higher order Coriolis terms are treated perturbatively. A dedicated Python routine optimizes five parameters bandhead energy, inertia A, decoupling a, and Coriolis coefficients B and C for each nucleus. The calculations match experimental level spacings to within 5 keV. Staggering keeps a common phase across the three chains yet grows with spin and, on average, with both neutron and proton number. The inertia parameter rises smoothly with Z (e.g., A for N = 99: 10.6 to 12.4 keV), signaling a decrease in the moment of inertia as axial deformation weakens. Decoupling parameter a increases and then saturates for N = 99 and 103, indicating purer K = 1/2 structure at high Z; the N = 101 chain shows the opposite trend, pointing to stronger configuration mixing. The first order Coriolis term B becomes increasingly negative with Z, whereas the higher order term C shows chain specific sign changes. The present work, explore the dynamics of various physical parameters associated with {\nu}1/2[521] quasiparticle rotational bands and helps to understand observed signature effects.