The correlative method of unsymmetrized self-consistent eld CUSF is used to study dynamical characteristics of a strongly anharmonic crystal with body-centered cubic lattice, namely, the interatomic and mean square relative displacements. We present the general formulae for crystals with anharmonicity, including the strong one, up to fourth anharmonic terms. Taking into account the second order of the method we calculate correlations in this lattice between the nearest, second, third, fourth and fth neighbors. The in uence of more distant i n teractions is discussed. The results are compared with those obtained previously for an weakly anharmonic BCC crystal. We use the Schi potencial for Na and also Lennard-Jones potentials for comparison.
I IntroductionThe quadratic correlation moments of atomic positions QCM as well as their mean square relative displacements MSRD expressing the e ective amplitude of the atomic vibrations are the most important features of lattice dynamics 1, 2 .Using the dynamical theory of crystal lattice, QCM and MSRD have been calculated in the harmonic approximation 2 . However, this approximation is not more valid at high temperatures due to anharmonic e ects which are of considerable importance. Here the correlative method of unsymmetrized self-consistent eld CUSF 3, 4 , 5 , 6 , 7, 8 is used to study the inuence of anharmonic e ects on the QCM and MSRD 9, 10 , including strongly anharmonic ones. The general expressions for QCM and MSRD are presented taking into account anharmonic terms up to the fourth order. Recently, they have been applied to weakly anharmonic crystal with face-and body centered cubic lattices 11, 12 and also to strongly anharmonic FCC crystal 13 . In the present paper we study a strongly anharmonic BCC crystal, namely solid Na.
II General RelationsIn CUSF, the mean square relative displacements between two atoms i and j in a crystal, can be written as c D aa ij = q ia , q ja 2 = q 2 ia + q 2 ja , 2C aa ij ; 1 where a denotes the Cartesian components of atomic displacements and C aa ij = q ia q ja is the correlation moment.We consider a perfect crystal with pairwise central interactions U r; :::;r N = 1 2 X i6 =j jr i ,r j j : 2