  The differential cross-section of elastic proton-proton collisions is studied
at ISR and LHC energies, utilizing a quark-diquark model, that generalizes
earlier models of Bialas and Bzdak, and, in addition, a model of Glauber and
Velasco. These studies suggest that the increase of the total pp cross-section
is mainly due to an increase of the separation of the quark and the diquark
with increasing energies. Within the investigated class of models, two simple
and model-independent phenomenological relations were found, that connect the
total pp scattering cross-section to the effective quark, diquark size and
their average separation, on one hand, and to the position of the dip of the
differential cross-section, on the other hand. The latter t(dip) sigma(tot) ~
const relation can be used to predict t(dip), the position of the dip of
elastic pp scattering for future colliding energies, and for other reactions,
where sigma(tot) is either known or can be reliably estimated.

High Energy Physics - Phenomenology;High Energy Physics - Experiment;Nuclear Experiment