First the structure function of the many fermion systems is written in terms of the fluctuation of the target density and too the value of this function at very small momentum transfer is calculated. It is shown that the values of the structure function of these systems at very small momentum transfer calculated from two different ways which one is the mathematical straight way and other way is the sum rules of the quantum fluids, are not equal. This topic transparently is a paradox for the many-fermion systems and must be considered. Finally for removing this paradox, we offer a new defination for the response function or the structure function of the many fermion systems.


1- O. Benhar,A. Fabrocini and S. Fantoni, Phys.Rev.Lett., 87, (2001) 052501-4.
2- M. Modarres and Y. Younesizadeh, Nucl.Phys.A, 789, (2007), 82-93
3-J. J. Sakurai, Modern Quantum Mechanics, chap.7, 1994.
4-M. Modarres and Y. Younesizadeh, Int. J. Theor. Phys. 49, (2010), 413.
5- E. Feenberg, Theory of Quantum Fluids, Academic Press, New York, chap.1, (1969).

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