No detailed calculations, but a qualitative answer: Depending on the trajectory of the impactor, the results will vary a bit, but it's clear, that the potential energy of the impactor will be transformed into a high amount of kinetic energy before the impact happens. The kinetic energy will then be transformed mainly into heat during the impact, transforming a substantial part of the mass of the impactor into x-rays and gamma rays.
The remnants of the impactor will be transformed into a plasma, with most of the electrons moving independently of their former nuclei, and dispersed mainly into the atmosphere (a thin layer of a few millimeters) of the neutron star. The energies will be high enough to trigger nuclear fusion as well as fission, together with other high-energy particle reactions. Part of the energy will be transformed into magnetic fields, which can also be very strong on neutron stars.
No much intermixing with the interior of the neutron star is to be expected in the first instant for small impactors due to the high inertia and density of the inner parts of the neutron star.
In some cases the impact could trigger the collapse of the neutron star into a black hole, depending of the mass of the neutron star, and the mass of the impactor.
More on the inner structure of neutron stars on Wikipedia.
("Matter falling onto the surface of a neutron star would be accelerated to tremendous speed by the star's gravity. The force of impact would likely destroy the object's component atoms, rendering all its matter identical, in most respects, to the rest of the star.")
More about the Chandrasekhar limit of neutron stars.