Coherent pair state of the pion in the constituent quark model

Abstract

A coherent state of pions is introduced to the nonrelativistic quark model. The coherent pair approximation is employed for the pion field in order to maintain the spin-isospin symmetry. In this approximation the pion is localized in the momentum space, and the vertex form factor in the pion-quark interaction is derived from this localization. The nucleon masses and wave functions are calculated using this model, and our results are compared to those of the quark model with the one pion exchange potential. Similar result is obtained for the mass spectrum, but there exists a clear difference in the internal structure of nucleon resonances.

Quark Spin Couplings for Baryons - Revisited

“…( 1) -is really due to the superposition of a pseudoscalar and massive vector field, rather than a massless gauge field. Similar mixings for OPE have also been obtained elsewhere [12], however the emphasis on the independence from spectral data is missing.…”

“…The total Hamiltonian sums over all three quark pairs, and since the wavefunctions in Eq. ( 3) are symmetric under all permutations, we can pick a single pair of quarks H (12) and multiply the result by three. The computation of these matrix elements are simple but a little tedious.…”

Triply excited symmetric rotor states:ldistributions

“…We have found that significant population of states with high single-electron angular momenta can be expected and that the distribution depends on the symmetry of the states considered. We have also shown that our symmetric rotor gives rise to a classification of the triply excited states in agreement with the molecular picture derived by Lin and co-workers [21][22][23].…”

“…The energy levels of triply excited states have been classified by Lin, Watanabe and Morishita [21][22][23], who identified molecular-like normal mode solutions of the correlated electron problem with the D 3h group symmetry. Our rotor ansatz has this symmetry by construction, and in this section we shall identify explicitly the terms allowed by symmetry constraints.…”

“…As an example, consider the quartet states with |M I | mod 3 = 0. The antisymmetrized symmetric rotor is given by (see equation (23))…”