Magnetic effects in heavy-ion collisions at intermediate energies

Abstract

The time evolution and space distribution of internal electromagnetic fields in heavy-ion reactions at beam energies between 200 and 2000 MeV/nucleon are studied within an isospin-dependent Boltzmann-Uhling-Uhlenbeck transport model (ibuu11). While the magnetic field can reach about $7\ifmmode\times\else\texttimes\fi{}{10}^{16}$ G, which is significantly higher than the estimated surface magnetic field ($\ensuremath{\sim}$$1\ifmmode\times\else\texttimes\fi{}{10}^{15}$ G) of magnetars, it has almost no effect on nucleon observables because the Lorentz force is normally much weaker than the nuclear force. Very interestingly, however, the magnetic field generated by the projectilelike (targetlike) spectator has a strong focusing and defocusing effect on positive and negative pions at forward (backward) rapidities. Consequently, the differential ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio as a function of rapidity is significantly altered by the magnetic field, whereas the total multiplicities of both positive and negative pions remain about the same. At beam energies above about 1 GeV/nucleon, while the integrated ratio of total ${\ensuremath{\pi}}^{\ensuremath{-}}$ to ${\ensuremath{\pi}}^{+}$ multiplicities is not, the differential ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio is sensitive to the density dependence of nuclear symmetry energy ${E}_{\mathrm{sym}}(\ensuremath{\rho})$. Our findings suggest that magnetic effects should be carefully considered in future studies of using the differential ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio as a probe of the ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ at suprasaturation densities.