Hadronic deformation energy. I. Quark-antiquark separation

The MIT bag model for hadrons is treated in the static cavity approximation in three dimensions with a definite quark number. The energy of the system is computed to second order in the gluon coupling. A constrained variational method is described which permits the calculation of the energy as a function of a collective variable. The bag cavity is permitted to assume whatever shape of a general class is necessary in order to minimize the energy for a given expectation value of the collective variable. The method is well suited for the study of the two-nucleon interaction at short range. By way of introducing the computational procedure the method is here applied to a bag containing one quark and one antiquark and the energy as a function of a measure of the separation of the quarks is evaluated.