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Final results of a detailed analysis of p+p elastic scattering data arepresented, utilizing the quark-diquark model of protons in a form proposed byBialas and Bzdak. The differential cross-section of elastic proton-protoncollisions is analyzed in a detailed and systematic manner at small momentumtransfers, starting from the energy range of CERN ISR at $ \sqrt{s}= 23.5 $GeV, including also recent TOTEM data at the present LHC energies at $\sqrt{s}= 7$ TeV. These studies confirm the picture that the size of proton increasessystematically with increasing energies, while the size of the constituentquarks and diquarks remains approximately independent of (or only increasesonly slightly with) the colliding energy. The detailed analysis indicatescorrelations between model parameters and also indicates an increasing role ofshadowing at LHC energies. Within the investigated class of models, a simpleand model-independent phenomenological relation was discovered that connectsthe total p+p scattering cross-section to the effective quark, diquark size andtheir average separation. Our best fits indicate, that the relative error ofthis phenomenological relation is 10-15% in the considered energy range.

Detailed Analysis of p+p Elastic Scattering Data in the Quark-Diquark Model of Bialas and Bzdak from sqrt{s}=23.5 GeV to 7 TeV