In accreting neutron star (NS) low-mass X-ray binary (LMXB) systems, NS accretes material from its low-mass companion via a Keplerian disk. In a viscous accretion disk, inflows orbit the NS and spiral in due to dissipative processes, such as the viscous process and collisions of elements. The dynamics of accretion flows in the inner region of an accretion disk is significantly affected by the rotation of NS. The rotation makes NS, thus the space-time metric, deviate from the originally spherical symmetry, and leads to gravitational quadrupole, on one hand. On the other hand, a rotating NS drags the local inertial frame in its vicinity, which is known as the rotational framedragging effect. In this paper, we investigate the orbital motion of accretion flows of accreting NS/LMXBs and demonstrate that the rotational effects of NS result in a band of quasi-quantized structure in the inner region of the accretion disk, which is different, in nature, from the scenario in the strong gravity of black hole arising from the resonance for frequencies related to epicyclic and orbital motions. We also demonstrate that such a disk structure may account for frequencies seen in X-ray variability, such as quasi-periodic oscillations, and can be a potential promising tool of investigation for photon polarization.

Soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs) are two groups of enigmatic objects, which have been extensively investigated in past few decades. Based on the ample information about their timing behaviors, spectra, and variability properties, it was proposed that SGRs/AXPs are isolated neutron stars (NSs) with extremely strong magnetic fields, the so-called magnetars. Nonetheless, some alternative models are probably equally convincing such as those proposing that they are accreting NSs with a fall-back disk or rotation-powered magnetized and massive white dwarfs. The nature and nurture of SGRs/AXPs remain controversial. In this paper, we propose that SGRs/AXPs can, alternatively, originate from normal NSs in binary systems, which resorts to the reexplosion of normal NS induced by instant contraction of the massive star envelope in a Thorne-Żytkow object (TZO). The spin-period clustering is due to either the brake of a slowly rotating envelope or the frictional drag during the common-envelope phase.