THE SHELL MODEL AND THE IMPULSE APPROXIMATIONS APPROACH TO THE RESPONSE FUNCTION OF 4He, 16O AND 40Ca NUCLEI
Abstract
The ambiguities proposed by Benhar et al., about the the different implementation of the impulse approximation for calculating the response function of many-fermion systems, are investigated theoretically in the frame work of simple harmonic oscillator shell model for the double closed shell nuclei, e.g. 4He, 16O and 40Ca nuclei. For each nucleus as a finite system, we evaluate the response function by using its definition in terms of the one-body spectral function and the one-body momentum distribution. It is demonstrated analytically, that there exists a sizable shift between the two schemes for each nucleus, which increases as we switch to the heavier nuclei. So one can conclude that for the nuclei with atomic number less than 4, such as 2H, 3H or 3He, it is good approximation to ignore this discrepancy. This conclusion is important for theoretical explanation of the ongoing deep inelastic scattering (DIS) experiments of 3H or 3H in the Jefferson Laboratory. However present calculation confirms the work of Modarres and Younesizadeh (2010), in which they have shown that, the above shift can be removed by imposing the impulse approximation in the same footing in the many-fermion wave-function.
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