Mon·Jan 2, 2017Monday·January 2, 2017

1. 01*

   Solving Dirac equations on a 3D lattice with inverse Hamiltonian and spectral methods

   Z.X. Ren🇨🇳 · S.Q. Zhang🇨🇳 · J. Meng🇨🇳

   A new method to solve the Dirac equation on a 3D lattice is proposed, in which the variational collapse problem is avoided by the inverse Hamiltonian method and the fermion doubling problem is avoided by performing spatial derivatives in momentum space with the help of the discrete Fourier transform, i.e., the spectral method. This method is demonstrated in solving the Dirac equation for a given spherical potential in 3D lattice space. In comparison with the results obtained by the shooting method, the differences in single particle energy are smaller than $10^{-4}$~MeV, and the densities are almost identical, which demonstrates the high accuracy of the present method. The results obtained by applying this method without any modification to solve the Dirac equations for an axial deformed, non-axial deformed, and octupole deformed potential are provided and discussed.

   ↳ nucl-thnucl-exPRC(2017)·61 citations
2. 02*

   Semirelativistic approximation to the ${\gamma }^{\ast }N\to N(1520)$ and ${\gamma }^{\ast }N\to N(1535)$ transition form factors

   G. Ramalho🇧🇷

   The representation of the wave functions of the nucleon resonances within a relativistic framework is a complex task. In a nonrelativistic framework the orthogonality between states can be imposed naturally. In a relativistic generalization, however, the derivation of the orthogonality condition between states can be problematic, particularly when the states have different masses. In this work we study the $N(1520)$ and $N(1535)$ states using a relativistic framework. We considered wave functions derived in previous works, but impose the orthogonality between the nucleon and resonance states using the properties of the nucleon, ignoring the difference of masses between the states (semirelativistic approximation). The $N(1520)$ and $N(1535)$ wave functions are then defined without any adjustable parameters and are used to make predictions for the valence quark contributions to the transition form factors. The predictions compare well with the data particularly for high momentum transfer, where the dominance of the quark degrees of freedom is expected.

   ↳ hep-phhep-exhep-latnucl-ex+1PRD(2017)·30 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.