A new technique for calculation of the electron gas radial distribution function g͑r 12 ͒ and the groundstate energy is developed based on the idea that the probability amplitude c͑r 12 ͒ p g͑r 12 ͒ has to satisfy a zero-energy Schrödinger equation where the effective interaction is the sum of the Coulomb force and the induced interaction y c 1 W͑r͒. In the case of electron gas with positive background we write the induced potential in the form W B 1 W e where W B ͑r͒ is the known bosonic reference potential and W e ͑r͒ is a fermionic correction determined from the fact that the Coulomb force for low r s is switched off. The coupling constant integration produces energies which agree very closely with Green's function Monte Carlo results. [S0031-9007(96)01622-5] PACS numbers: 71.10.CaDuring the past 40 years, after the milestone paper by Gell-Mann and Brueckner [1], a large quantity of research has been directed towards understanding the properties of electron gas on positive background [2][3][4]. Since the field-theoretical approach works only at the high density limit r s ! 0, coupled-cluster method (CCM)[5] and variational methods have been developed to cope with the strong electron-electron correlations. Of these particularly the Fermi hypernetted-chain method (FHNC) [6-10] should be mentioned since it provides a systematic way to improve the ground-state wave function. The main obstacle in FHNC has been the difficulty in summation of elementary diagrams, corresponding to the bridge diagrams in classical statistical mechanics. Fortunately the accuracy of analytical calculations can nowadays be checked against the Green's function Monte Carlo (GMC) results which are "exact" for Bose systems but are still plagued to some extent by the Slater determinant nodes [4,11] in the fermion case.The purpose here is to devise an accurate way to sum up the elementary diagrams and, at the same time, simplify the existing FHNC method to the level of the Bose system to have only one Euler-Lagrange Schrödinger equation instead of four. This is important in generalizations of FHNC to a multicomponent system [12][13][14].To introduce the hypernetted-chain method (HNC) briefly we repeat the steps needed to calculate energy per particle of the Coulomb gas. The density parameter r s is defined as the volume taken by one particle n 21 4͞3 p͑r s a 0 ͒ 3 where n is the number density and a 0 h 2 ͞ me 2 is the Bohr radius. Another relevant quantity is the radial distribution function g͑r 12 ͒, which gives the relative probability of finding another particle at r 2 if there is one at r 1 . For a uniform liquid g͑r 12 ͒ g͑r 12 ͒, independent of angles. The corresponding probability amplitude c͑r͒ is p g͑r͒. With the Coulomb interaction y c the potential energy can be calculated exactly fromprovided that function g͑r 12 ͒ is calculated from exact ground-state wave function C bywhere N is the number of particles and dt d 3 r 1 d 3 r 2 dt 2 . For other interactions y͑r͒ the integrand in Eq.(1) should be g͑r͒ y͑r͒. The reason for ͑g 2 1͒ y c...

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