| Based on the quantum-chemical theory and ab initio self-consistent- field calculation method, the various many-body correlations among atoms in condensed helium have been investigated. Over a large volume and temperature range of 7.5-1.5 cm3/mol and 0-21000 K, the equation of state (EOS) of helium is given, and the density and temperature dependence of the effective pair potential are revealed. Our work includes four parts:(1) To investigate the importance of various many-body effects in crystal helium on its compression properties, the crystal cohesive energy is expanded as the sum of the two- to six-body potentials in present work. The results indicate that the many-body expansion formula is an altered series, in which two-, four-, and six-body terms are positive, whereas three- and five-body terms are negative. When the specific volume values from 7.5 to 1.5 cm7mol, the expansion series is convergent. According to such an expansion of crystal cohesive energy, the isothermal EOS at 0 K is obtained. It is found that the incorporation of three-body interaction can only satisfactorily describe EOS between 1-5 GPa, and give a much lower theoretical curve at higher pressures. Adding the four-body contribution greatly improves the theoretical curve, but only reproduces measurements up to -25 GPa. In the compression region 1-58 GPa, which has been covered by the recent experimental techniques, it shows that the many-body expansion series of crystal energy can be truncated at five-body term, and such a truncation treatment is sufficient to fit all available experimental data. At higher pressures, six-body effects become significant, and the inclusion of its contribution can extend the theoretical prediction from 60 to 180 GPa, where the empirical Vinet EOS give a lower prediction by 6-14%.(2) Many-body expansion treatment and ab initio self-consistent-field calculations have also been performed to fcc, bcc crystal and fluid helium. A newformula for short-range potential energy Es has been deduced from our calculations. It means that the total short-range repulsive energy ofcondensed matter can be calculated by an appropriate interpolation between the total two-body interactions U2(M) and atomic potential Vn(M). We find that the value of ft is about 0.5 for condensed helium. The formula can give almost the same numerical values of Es as those given by exact many-body expansion series, so it greatly reduces the computation time. It makes it possible to deal with many-body effects in fluid helium, where the configuration of atomic cluster, composed of an given atom and its neighbors, randomly varies by the influence of temperature.(3)The equation of state (EOS) of helium is obtained in the temperature range of 300 ~ 21000K, and in the density range of 7.5 to 1.5 cmVmol, by a newly developed semi-empirical self-consistent-fleld molecular dynamics, a computational method that combines Hartree-Fock self-consistent field technique with a classical molecular dynamics method to solve the electronic structure of atomic clusters, which are sampled during simulation. The Gruneisen coefficient y and heat capacity at constant volume Cv are also calculated for fluid helium. The density and temperature dependence of the pair potential is firstly discussed.(4) According to the approximation of pair-wise additivity, the total potential energy may be obtained by summing the interaction potential between all pairs of atoms in the condensed matter. We assume that the repulsive pair potential can be expressed by such a formula, , then short-range part of the potential energy fromthe central atomic contribution can be written as For agiven temperature and density, an appropriate quantity of atomic configurations are investigated, and the short-range part of the total potential energy from the central atomic contribution can also be calculated with equation The magnitude of coefficients (A, ) isdetermined by making a weighted least-square fit to values of Es obtained from the two different ways. The obtained pair potentia...
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