Neutron-proton effective mass splitting in terms of symmetry energy and its density slope

Using a simple density-dependent finite-range effective interaction having Yukawa form, the density dependence of isoscalar and isovector effective masses is studied. The isovector effective mass is found to be different for different pairs of like and unlike nucleons. Using HVH theorem, the neutron-proton effective mass splitting is represented in terms of symmetry energy and its density slope. It is again observed that the neutron-proton effective mass splitting has got a positive value when isoscalar effective mass is greater than the isovector effective mass and has a negative value for the opposite case. Furthermore, the neutron-proton effective mass splitting is found to have a linear dependence on asymmetry β. The second-order symmetry potential has a vital role in the determination of density slope of symmetry energy but it does not have any contribution on neutron-proton effective mass splitting. The finite-range effective interaction is compared with the SLy2, SKM, f−, f0, and f+ forms of interactions.