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Thick branes with a nonminimally coupled bulk-scalar field

In this paper, we investigate thick branes with a nonminimally coupled background scalar field, whose solution is a single-kink or a double-kink. The effects of the nonminimal coupling constant $ξ$ on the structure of the thick branes and the localization of gravity, fermions, scalars and vectors are discussed. It is shown that each brane will split into two sub-branes as increasing the nonminimal coupling constant $ξ$. By investigating the tensor perturbation equations of gravity and the general covariant Dirac equation of fermions, we find that both the gravity zero mode and left-chiral fermion zero mode are localized at the center of the single-kink branes and localized between the two sub-branes generated by the double-kink, which indicates that the constant $ξ$ does not effect the localization of these zero modes. However, the zero mode of scalars is localized on each sub-brane (for both single-kink and double-kink branes) when $ξ$ is larger than its critical value $ξ_0$. The effects of the nonminimal coupling constant $ξ$ on the resonances of gravity and fermions with finite lifetime on the branes are also discussed.