Based on an equation of motion approach the single impurity Anderson model(SIAM) is reexamined. Using the cluster expansions the equations of motion of Green functions are transformed into the corresponding equations of motion of connected Green functions, which provides a natural and uniform truncation scheme. A factor of two missing in the Lacroix's approximation for the Kondo temperature is gained in the next higher order truncation beyond Lacroix's. A quantitative improvement in the density of states at the Fermi level is also obtained.The single impurity Anderson model(SIAM) 1 is one of the most fundamental and probably best understood models in the field of strongly correlated electronic systems. It was proposed to describe the properties of magnetic impurities in non-magnetic metallic hosts (for a review see e.g. Ref.2). Yet, the SIAM has been used widely to imitate mixed valence and heavy fermion systems. [3][4][5][6] Since the SIAM was proposed, a variety of standard techniques have been applied to it and new methods have been developed to study its static and dynamical properties, basically in the whole parameter space. ( For a recent review see, e.g. Ref. 7.) The method of equations of motion(EOM) of Green functions(GFs) is one of the most important tools to solve the model Hamiltonian problems in condensed matter physics. One of its most appealing features is that it can work in the whole parameter space. Many authors have applied the EOM approach to the SIAM for finite U 1,8,9 or infinite U . [10][11][12][13][14] In order to close the chain of equations it is usual to introduce the conventional Tyablikov decoupling scheme. 15 Lacroix employed thus decoupling scheme for higher order GFs. 12,13 In the limit of strong intra-atomic Coulomb interaction he did not get the correct expression of Kondo temperature from his high-and/or intermediate-temperature solutions 12 at his approximation level.In the present paper we shall go beyond Lacroix's approximation in a slightly different way. In the following we use the correlation dynamics approach 17 to treat the problem. After writting down the hierarchy of EOM of the GFs the Tyablikov decoupling scheme is not applied directly. Instead systematic cluster expansions are employed, which express the higher order GFs in terms of same order connected GFs and lower order GFs, the hierarchy of EOM of the usual GFs is thus transformed into that of EOM of the connected GFs. The connected GFs are defined such that they can not be reduced to the low order ones by any way of decoupling. The hierarchy of equations of the connected GFs provides a natural and uniform truncation scheme. Our formalism, which is essentially equivalent to the Tyablikov decoupling scheme, is more systematic. The well known results like mean field theory, 1 Hubbard-I approximation, 11 twopeak solutions, 16 and Lacroix's results 12,13 are recovered exactly in successively higher levels of truncation. To go beyond Lacroix we introduce even higher order truncation. The Kondo temperature obtained i...

Using an isospin-dependent quantum molecular dynamics, nuclear stopping in intermediate heavy ion collisions has been studied. The calculation has been done for colliding systems with different neutron-proton ratios in beam energy ranging from 15 MeV/ u to 150 MeV/ u. It is found that, in the energy region from above Fermi energy to 150 MeV/ u, nuclear stopping is very sensitive to the isospin dependence of in-medium nucleon-nucleon cross section, but insensitive to symmetry potential. From this investigation, we propose that nuclear stopping can be used as a new probe to extract the information on the isospin dependence of in-medium nucleon-nucleon cross section in intermediate energy heavy ion collisions.