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Register a new userTwo-atomic potential and distortion of excitation spectrum of liquid He-4 by admixture of He-3
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The new interatomic potential g(r), providing the tunnelling of atoms, is suggested for calculating HFB phonon-roton spectrum E(p) of liquid He-4. The tunnelling enables the calculations to reproduce the experimental dependence of shifts E(p) on pressure P induced by He-3 admixture in the constant total density and volume.
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A formula for potential U of the He-4--He-4 interaction in the liquid state is obtained by the direct electromagnetic computation as a function of the interatomic distance R. The potential decreases exponentially at large R. The further development and application of the result are discussed.
Helium atoms in the metastable $2^3{S_{1}}$ state (He$^*$) have unique advantages for ultracold atomic experiments. However, there is no known accessible Feshbach resonance in He$^*$, which could be used to manipulate the scattering length and hence unlock several new experimental possiblities. Previous experimental and theoretical studies for He$^*$ have produced contradictory results. We aimed to resolve this discrepancy with a theoretical search for Feshbach resonances, using a new close-coupled model of He$^*$ collisions in the presence of an external magnetic field. Several resonances were detected and the existing literature discrepancy was resolved. Although none of the resonances identified are readily experimentally useable, an interesting non-Feshbach scattering length variation with magnetic field was observed in heteronuclear collisions, at field strengths that are experimentally accessible.
Four light-mass nuclei are considered by an effective two-body clusterisation method; $^6$Li as $^2$H$+^4$He, $^7$Li as $^3$H$+^4$He, $^7$Be as $^3$He$+^4$He, and $^8$Be as $^4$He$+^4$He. The low-energy spectrum of each is determined from single-channel Lippmann-Schwinger equations, as are low-energy elastic scattering cross sections for the $^2$H$+^4$He system. These are presented at many angles and energies for which there are data. While some of these systems may be more fully described by many-body theories, this work establishes that a large amount of data may be explained by these two-body clusterisations.
Mixed $^3$He-$^4$He droplets created by hydrodynamic instability of a cryogenic fluid-jet may acquire angular momentum during their passage through the nozzle of the experimental apparatus. These free-standing droplets cool down to very low temperatures undergoing isotopic segregation, developing a nearly pure $^3$He crust surrounding a very $^4$He-rich superfluid core. Here, the stability and appearance of rotating mixed helium droplets are investigated using Density Functional Theory for an isotopic composition that highlights, with some marked exceptions related to the existence of the superfluid inner core, the analogies with viscous rotating droplets.
We calculate microscopically the properties of the dilute He-3 component in a He-3/--He-4 mixture. These depend on both, the dominant interaction between the impurity atom and the background, and the Fermi liquid contribution due to the interaction between the constituents of the He-3 component. We first calculate the dynamic structure function of a He-3 impurity atom moving in He-3. From that we obtain the excitation spectrum and the momentum dependent effective mass. The pole strength of this excitation mode is strongly reduced from the free particle value in agreement with experiments; part of the strength is distributed over high frequency excitations. Above k > 1.7$AA$^{-1}$ the motion of the impurity is damped due to the decay into a roton and a low energy impurity mode. Next we determine the Fermi--Liquid interaction between He-4 atoms and calculate the pressure-- and concentration dependence of the effective mass, magnetic susceptibility, and the He-3--He-3 scattering phase shifts. The calculations are based on a dynamic theory that uses, as input, effective interactions provided by the Fermi hypernetted--chain theory. The relationship between both theories is discussed. Our theoretical effective masses agree well with recent measurements by Yorozu et al. (Phys. Rev. B 48, 9660 (1993)) as well as those by R. Simons and R. M. Mueller (Czekoslowak Journal of Physics Suppl. 46, 201 (1996)), but our analysis suggests a new extrapolation to the zero-concentration limit. With that effective mass we also find a good agreement with the measured Landau parameter F_0^a.
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