Neutron scattering in the hole-doped cuprate superconductors

The occurrence of a neutron resonance energy is a common feature of unconventional superconductors. In turn, the low-temperature incommensurate sharp peaks observed in the inelastic neutron scattering of La${}_{2-x}$Sr${}_x$CuO${}_4$ (LSCO) correspond to four rods symmetrically distributed around $[\pi ,\pi ]$. Here it is shown that within the virtual-electron pair quantum liquid recently introduced the neutron resonance energy and the LSCO low-temperature incommensurate sharp peaks are generated by simple and closely related spinon processes. Our results indicate that in LSCO the neutron resonance energy either does not occur or corresponds to a lower energy $\approx 17$ meV.