A Deformable Bag Model of Hadrons. I

Abstract

As a generalization of the MIT spherical bag model, we construct the spheroidal bag model of hadron with an arbitrary eccentricity. This generalization is made by slightly modifying the MIT linear boundary condition: The linear boundary condition is examined in detail. Our model always satisfies two necessary requirements of the MIT bag model --i. e., n-j=O, no quark colour flux leaves the bag, and ijq =0, the scalar density of quark should vanish on the bag surface-- and it reduces to the MIT spherical bag model in the limit of zero-eccentricity. Lagrangian formalism of our model is briefly described. The eigenfrequencies of a single massless quark confined in this spheroidal bag are numer­ ically calculated. We obtain the level-splitting of the excited quark orbits, which is just analogous to the well-known Nilsson's splitting of single particle orbits in deformed nuclei. By using the numerical results of the lowest orbit, the effect of the bag-deformation on the mass of low-lying hadrons is estimated. It is found that, although the spherical bag is stable, tbe quark bag is extremely soft against the quadrupole deformation. Brief discussions are added on the mechanisms which make the spherical bag more stable.