  By comparing experimental results obtained in the study of the electron
transport and magnetic properties of samples of lightly strontium-substituted
lanthanum cuprates and the results of a previously published numerical analysis
in the reduced elastic scattering space (RPS) of the elastic scattering
cross-section, we construct a phenomenological classical self-consistent
strong-binding energy density profile in the superconducting
$La_{2-x}Sr_xCuO_4$ cuprate. It is found that the imaginary part of the reduced
phase scattering space can be zero, almost constant, or strongly
self-consistent, depending on the Sr substituted concentration. If the Sr
atomic concentration is dilute, a constant imaginary part of the elastic
scattering cross-section brings a sub-melted coalescent superconducting
metallic profile similar to the one with a constant scattering lifetime in the
metallic state of normal metals, except for the unitary narrow, sharp peak at
zero frequency. A self-consistent broadening of this peak occurs for a higher
concentration of Sr atoms, and finally, for very small amounts of nonmagnetic
dirt, only the narrow unitary peak prevails around the zero frequency.
