It was pointed out that the potential acting on an election at the boundary of an atom inside a solid should not vanish in a TF model of calculation. A strict deduction shows that it approaches to the value -e2/r0. When this term is taken into account, the calculated pressure values lie near those measured in a large range of compressions-Thus, equations of states for the metals U, Pb, Au, Ag, Cu, Fe, K, Al, Na and Li can be derived for the compression ratios from 1 to 10 at the temperature of absolute zero. Results are in good agreement with the corresponding current calculations in the high pressure limit. In the low pressure range, the agreement between calculated and observed ones are good within 10%. Particularly, for high-Z atomic number, for instance, the elements U and Ag, the agreement is excellent and at v=v0, P(v0)=0.Nevertheless, large deviations arise in the low-Z elements. This is due to the quantum effects of the Brillouin zones. As a recipe, normally a pseudo-potential is introduced. Accordingly, we do the same for the potential near the boundary of the atom-This leads to a better agreement within 10% again for all the elements mentioned above.In this paper, the method of numerical iteration for fitting the boundary conditions is improved by means of a new transformation of parameters. The accuracy in the numerical computation is thereby raised to 10-8.
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