The impurity-induced charge density in jellium is calculated by solving the Schrödinger equation self-consistently. The resulting phase shifts have been used to estimate the value of residual resistivity for dilute Zr-H system, which comes out to be 0.50 µΘ cm/at.%. An alternative form of one-parameter-screened Coulomb potential, which is more suitable than the customary Thomas-Fermi potential, is suggested. The calculated self-energy by using new potential is found close to its value obtained by Darbyet al.

We have derived a new equation of state (EOS) based on the Eulerian finite scheme utilizing the 3/2th power of edge length by pressure. By truncating the order of finite strains in the expression of the Helmholtz free energy, we have derived new expressions for second- and third-order EOSs, as well as expressions for bulk modulus and its first pressure derivative. We have considered four materials, viz. CaO, Bi, NaCl and Fe$_2$SiO$_4$ to test the applicability and validity of the derived EOS. The feature of this EOS shows more validity than other prominent EOSs and corresponds well with the available experimental results.