We derive nonstrange baryon-baryon scattering amplitudes in the nonrelativistic quark model using the "quark Born diagram" formalism. This approach describes the scattering as a single interaction, here the one-gluon-exchange (OGE) spin-spin term followed by constituent interchange, with external nonrelativistic baryon wave functions attached to the scattering diagrams to incorporate higher-twist wave-function effects. The short-range repulsive core in the NN interaction has previously been attributed to this spin-spin interaction in the literature; we find that these perturbative constituent-interchange diagrams do indeed predict repulsive interactions in all I, S channels of the nucleon-nucleon system, and we compare our results for the equivalent short-range potentials to the core potentials found by other authors using nonperturbative methods. We also apply our perturbative techniques to the NA and AA systems: Some AA channels are found to have attractive core potentials and may accommodate "molecular" bound states near threshold. Finally we use our Born formalism to calculate the NN differential cross section, which we compare with experimental results for unpolarized proton-proton elastic scattering. We Gnd that several familiar features of the experimental differential cross section are reproduced by our Born-order result.PACS number(s): 21.30. +y, 24. 10.i
We present Monte Carlo results for the energies of static holes in the t-J model. We consider the cases of zero, one, two, and four holes on square lattices of side L=4, 6, and 8 and extrapolate these results to give estimates for the bulk limit. We And that the hole energies and finite-size effects are in good agreement with spin-wave theory. Our results are consistent with phase separation in the static limit of the t-J model, but indicate that the incorporation of long-range Coulomb repulsion between holes prevents phase separation. We find that hole pairs alone are bound for a certain range of dielectric constant e, which is 52&@&104 in the static limit of a t-J-e model with 1/r Coulomb repulsion, given the currently accepted value of J. The large observed value of the inplane dielectric constant of LazCu04, a=30+3, is not far from the lower limit of this theoretical pairing range, so the t-J-e model may provide a useful approximate description of the mechanism of hole pairing in the high-temperature superconductors.Hole Cooper pairs that act as mediators of high-temperature superconductivity may thus arise from a competition between the large antiferromagnetic coupling J, which encourages hole clustering, and the e-suppressed hole Coulomb repulsion, which restricts hole binding to pairs.
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