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Register a new userHints on the quadrupole deformation of the $Delta$(1232)
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C. Fernandez-Ramirez
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The E2/M1 ratio (EMR) of the $Delta$(1232) is extracted from the world data in pion photoproduction by means of an Effective Lagrangian Approach (ELA).This quantity has been derived within a crossing symmetric, gauge invariant, and chiral symmetric Lagrangian model which also contains a consistent modern treatment of the $Delta$(1232) resonance. The textit{bare} s-channel $Delta$(1232) contribution is well isolated and Final State Interactions (FSI) are effectively taken into account fulfilling Watsons theorem. The obtained EMR value, EMR$=(-1.30pm0.52)$%, is in good agreement with the latest lattice QCD calculations [Phys. Rev. Lett. 94, 021601 (2005)] and disagrees with results of current quark model calculations.
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High-precision H(e,ep)pi0 measurements at Q2=0.126 (GeV/c)2 are reported, which allow the determination of quadrupole amplitudes in the gamma* N->Delta transition; they simultaneously test the reliability of electroproduction models. The derived quadrupole-to-dipole amplitude ratios, Rsm=(-6.5 +- 0.2{stat+sys} +- 2.5{mod}) % and Rem=(-2.1 +- 0.2{stat+sys} +- 2.0{mod}) %, are dominated by model error. Previous Rsm and Rem results should be reconsidered after the model uncertainties associated with the method of their extraction are taken into account.
We calculate the electromagnetic moments and radii of the Delta(1232) in the nonrelativistic quark model, including two-body exchange currents. We show that two-body exchange currents lead to nonvanishing Delta and N-->Delta transition quadrupole moments even if the wave functions have no D-state admixture. The usual explanation based on the single-quark transition model involves D-state admixtures but no exchange currents. We derive a parameter- free relation between the N-->Delta transition quadrupole moment and the neutron charge radius: Q(N-->Delta) = r^2(neutron)/sqrt(2). Furthermore, we calculate the M1 and E2 amplitudes for the process photon + N -->Delta. We find that the E2 amplitude receives sizeable contributions from exchange currents. These are more important than the ones which result from D-state admixtures due to tensor forces between quarks if a reasonable quark core radius of about 0.6 fm is used. We obtain a ratio of E2/M1=-3.5%.
A parametrization of octupole plus quadrupole deformation, in terms of intrinsic variables defined in the rest frame of the overall tensor of inertia, is presented and discussed. The model is valid for situations close to the axial symmetry, but non axial deformation parameters are not frozen to zero. The properties of the octupole excitations in the deformed Thorium isotopes Th-226, Th-228 are interpreted in the frame of this model. A tentative interpretation of octupole oscillations in nuclei close to the X(5) symmetry, in terms of an exactly separable potential, is also discussed.
We investigate the model dependence and the importance of choice of database in extracting the {it physical} nucleon-Delta(1232) electromagnetic transition amplitudes, of interest to QCD and baryon structure, from the pion photoproduction observables. The model dependence is found to be much smaller than the range of values obtained when different datasets are fitted. In addition, some inconsistencies in the current database are discovered, and their affect on the extracted transition amplitudes is discussed.
We discuss the pole mass and the width of the $Delta(1232)$ resonance to third order in chiral effective field theory. In our calculation we choose the complex-mass renormalization scheme (CMS) and show that the CMS provides a consistent power-counting scheme. In terms of the pion-mass dependence, we compare the convergence behavior of the CMS with the small-scale expansion (SSE).
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