  Based on the Rheological Paradigm, one has extended the equations of state
for relativistic spherically symmetric static neutron stars, taking into
consideration the derivative of the matter pressure along the so-called
director four-vector. The modified equations of state are applied to the model
of a zero-temperature neutron condensate. This model includes one new parameter
with the dimensionality of length, which describes the rheological type
screening inside the neutron star. As an illustration of the new approach, one
has considered the rheological type generalization of the non-relativistic
Lane-Emden theory and found the numerical profiles of the pressure for a number
of values of the new guiding parameter. One has found that the rheological type
self-interaction makes the neutron star more compact, since the radius of the
star, related to the first null of the pressure profile, decreases when the
modulus of the rheological type guiding parameter grows.
