Narrow Results

We have employed the constrained variational method to study the influence of spin polarization on the ground state properties of liquid ³He. The spin polarized phase, we have found, has stronger correlation with respect to the unpolarized phase. It is shown that the internal energy of liquid ³He increases by increasing polarization with no crossing point between polarized and unpolarized energy curves over the liquid density range. The obtained internal energy curves show a bound state, even in the case of fully spin polarized matter. We have also investigated the validity of using a parabolic formula for calculating the energy of spin polarized liquid ³He. Finally, we have compared our results with other calculations.

We have used the lowest order constrained variational (LOCV) method to calculate some ground-state properties of polarized liquid ³ He at zero temperature with the spin-dependent correlation function employing the Lennard–Jones and Aziz pair potentials. We have seen that the total energy of polarized liquid ³He increases with increasing polarization. For all polarizations, it is shown that the total energy in the spin-dependent case is lower than the spin-independent case. We have seen that the difference between the energies of spin-dependent and spin-independent cases decreases by increasing the polarization. We have shown that the main contribution of the potential energy comes from the spin-triplet state.

By considering a spin dependence for the correlation function, the thermodynamic properties of normal liquid ³He have been investigated by employing a lowest order constrained variational approach. It is seen that the spin-singlet state has a smaller contribution in the potential energy of normal liquid ³He with respect to the spin-triplet state. It is seen that at high temperatures, the free energy of normal liquid ³He in cases of spin-dependent and spin-independent correlation functions are nearly identical. The equations of state of these two cases are nearly similar too.

We have used the lowest order constrained variational (LOCV) method to calculate some of the ground state properties of the polarized liquid ³He by inclusion of the three-body cluster energy contribution. It is shown that the contribution of the three-body cluster term for the ground state energy of this system is substantial, especially at high densities. It is also shown that the inclusion of the three-body energy contribution improves our result for the binding energy of the liquid ³He. It is seen that the magnitude of the three-body cluster energy decreases by increasing the polarization. The magnetic susceptibility of the liquid ³He has also been computed, showing no spontaneous ferromagnetic phase transition.

Liquid ³He injected in a carbon nanotube is of high interests due to different behavior of the liquid helium in the quasi-one-dimensional systems. In this work, a variational approach has been performed to calculate some thermodynamic properties of this quantum system. In order to do so, a single-walled carbon nanotube containing liquid ³He is considered, applying the Lennard-Jones and Stan–Cole potentials for ³He–³He and ³He–C interactions, respectively. Finally the total energy, equation of state and incompressibility of the system have been calculated. Our calculations show the high values for the incompressibility at high densities, especially for high radii.