Momentum and density dependence of the isospin part of nuclear mean field and equation of state of asymmetric nuclear matter

Momentum and density dependence of the isospin part of nuclear mean field uτ(k,ρ) which is still, in part, the open problem of the old Lane potential is analysed using density dependent finite range effective interactions. The behaviour of uτ(k=kf,ρ) around the Fermi momentum kf is found to be related to the density dependence of nuclear symmetry energy Jτ(ρ) and nucleon effective mass M∗(k=kf,ρ)/M in symmetric nuclear matter. The momentum dependence of uτ(k,ρ) is separated out in terms of a simple functional uτex(k,ρ) which vanishes at k=kf and involves only the finite range parts of the exchange interactions between pairs of like and unlike nucleons. Depending on the choice of the parameters of these exchange interactions two conflicting trends of momentum dependence are noticed which lead to two opposite types of splitting of neutron and proton effective masses. The equation of state of asymmetric nuclear matter and the high density behaviour of nuclear symmetry energy Jτ(ρ) are studied by constraining the additional parameters involved on the basis that pure neutron matter should not be predicted to be bound by any reasonable nuclear interaction. Emphasis is also given on the need of experimental data sensitive to the differences between neutron and proton transport properties in highly asymmetric dense nuclear matter and its analysis to constrain the high density behaviour of nuclear symmetry energy as well as to resolve the controversy on the two opposite types of splitting of neutron and proton effective masses.