Narrow Results

In this paper, we outline a theory for the thermodynamic properties of ³He–⁴He mixtures in the neighborhood of the critical line and the tricritical point (TCP). The theory utilizes the Cheng–Schick (CS) lattice gas model where both the ³He and ⁴He atoms are treated as quantum particles on a lattice. The analysis is based on Green's function approach. Results are presented for the ordering susceptibility and the thermal averages of the occupation numbers of ³He and ⁴He atoms. We derive a self-consistent equation for the ordering susceptibility and use it to calculate the critical line and locate the TCP. Our findings are compared with the predictions obtained from high temperature series expansions, mean field theory and the random phase approximation (RPA).

In order to understand the structure of the X(3872), we have studied the effects of the core state coupling to the multi-hadronic states such as , ρ J/ψ etc. We have calculated the transition strength S(E) using the Green's function approach with the simple solvable interactions. We have also studied the S(E) in the case of no core state, namely, the molecule. Since the calculated shapes of the transition strengths are different from each other, we shall be able to determine the degree of the mixing of the state in the X(3872) from the shape of the energy spectrum.

In order to understand the structure of the X(3872), we have studied the effects of the core state coupling to the multi-hadronic states such as , p J/ψ, etc. We have calculated the transition strength S(E) using the Green's function approach with the simple solvable interactions. We have also studied the S(E) in the case of no core state, namely the molecule. Since the calculated shapes of the transition strengths are different from each other, we shall be able to determine the degree of the mixing of the state in the X(3872) from the shape of the energy spectrum.