Starting from a point - like two - and three - particle interaction the kinetic equation is derived. While the drift term of the kinetic equation turns out to be determined by the known Skyrme mean field the collision integral appears in two - and three - particle parts. The cross section results from the same microscopic footing and is naturally density dependent due to the three - particle force. By this way no hybrid model for drift and cross section is needed for nuclear transport. Besides the mean field correlation energy the resulting equation of state has also a two - and three - particle correlation energy which are both calculated analytically for the ground state. These energies contribute to the equation of state and lead to an occurrence of a maximum at 3 times nuclear density in the total energy.

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