Quark Shell Model Research Articles

Blokhintsev fluctuon in the deuteron within the cluster approximation

We develop an early suggested idea that the six-quark component of NN-states in nuclei (analog of the Blokhintsev fluctuon) may turn to be a physical cause for the core on the NN-interaction. Using the quark-cluster approach and the quark translationalinvariant shell model (TISM) with oscillator potential we calculate the weight of the 6q-component in a deuteron for the configurations s6 ands4p2. How our results correspond to the earlier estimates and experimental restrictions is discussed.

Mass spectrum of L = 1 mesons in the quark shell-model

An analysis of the mass spectrum of L = 1 mesons in the quark model with SU(6) σ ⊗ O(3) symmetry is presented. An acceptable fit to the data is not possible with only spin-scalar and spin-vector operators, but the inclusion of a particular spin-tensor gives an excellent description of the spectrum and a successful prediction of mixing angles.

Baryon spectroscopy and the quark shell model (II). Numerical fitting to the data and the baryonic predictions

A shell-model description for a three-quark bound state is used with harmonic-oscillator quark-quark interactions. The baryon spectrum is associated with the energy levels of such a system which is taken to exhibit a broken SU(6) σ ⊗ O(3) symmetry. In an earlier paper, baryon states were constructed in the SU(3) ⊗ SU(2) σ ⊗ SU(3) basis of theis scheme, and a symmetry-breaking mass operator was defined as being a linear combination of two-body tensor operators, each of which has a definite transformation property under SU(6) ⊗ O(3). The matrix elements for each tensor operator were given when acting on the states associated with the N = 0, 1 and 2 harmonic-excitation bands of the model. In this paper, the eigenvalues in the mass-operator expansion are obtained by a least-squares fit of experimental data to the eigenvalues of the mass operator for each multiplet belonging to these excitation bands. The multiplets considered are (56.0 +) 0, (70,1 −) 1, (56,2 +) 2, (70,2 +) 2, (20.1 +) 2, (56,0 +) 2 and (70,0 +) 2. Constraints between the parameters associated with different multiplets previously derived are imposed in order to greatly reduce the number of available solutions. The results give assignments for known baryons and predict those required to complete the multiplets. We find that no mixing is possible among the nucleon states of the (70,1 −) 1 and that none is predicted among the non-strange states of the N = 2 excitation band. The established resonances pertinent to these multiplets are well accomodated in our scheme and the prediction of ΣD 13(1470) is given. The full predicted spectra are given.

Baryon spectroscopy and the quark shell model (I). The framework, basic formulae, and matrix-elements

Baryonic states are discussed in terms of a three-quark shell-model with SU(6) σ⊗ O(3) symmetry and harmonic oscillator wave-functions. For all states with N = 0, 1 or 2 quanta of excitation, which comprise the following supermultiplets: (56,0 +) 0, (70,1 −) 1, (56,2 +) 2, (70,2 +) 2, (56,0 +) 2, (70,0 + 2 and (20,1 +) 2, wave functions which are symmetric for permutations on the three quark labels are constructed in the SU(3)⊗ SU(2) σ⊗O(3) basis appropriate to this symmetry, and the structure of these wavefunctions in terms of two-quark substrates is made explicit. A general mass operator is considered which is a linear combination of two-body operators, each of which conserves isospin and hypercharge and transforms under SU(6) σ⊗O(3) according to an irreducible tensor representation. These operators are constructed by use of the Wigner-Eckart theorem for SU(6) σ and are written in a way which makes transparent their effect on the wavefunctions constructed. The calculation of their matrix-elements then becomes a straightforward and systematic operation, and these are tabulated for all operators which are spin-scalar (central) or spin-vector (spin-orbit) in character, and have either singlet or octet character with respect to SU(3). All 27-tuplet SU(3) operators are also given (but not their matrix-elements). Relationships are also derived between reduced matrix-elements for different supermultiplets, some depending only on the shell-model character of the wavefunctions and others depending specifically on their harmonic character, which act to constrain greatly a simultaneous fitting of all supermultiplets N ≤ 2.