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Register a new userThe structure and energetics of $^3$He and $^4$He nanodroplets doped with alkaline earth atoms
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We present systematic results, based on density functional calculations, for the structure and energetics of $^3$He and $^4$He nanodroplets doped with alkaline earth atoms. We predict that alkaline earth atoms from Mg to Ba go to the center of $^3$He drops, whereas Ca, Sr, and Ba reside in a deep dimple at the surface of $^4$He drops, and Mg is at their center. For Ca and Sr, the structure of the dimples is shown to be very sensitive to the He-alkaline earth pair potentials used in the calculations. The $5s5pleftarrow5s^2$ transition of strontium atoms attached to helium nanodroplets of either isotope has been probed in absorption experiments. The spectra show that strontium is solvated inside $^3$He nanodroplets, supporting the calculations. In the light of our findings, we emphasize the relevance of the heavier alkaline earth atoms for analyzing mixed $^3$He-$^4$He nanodroplets, and in particular, we suggest their use to experimentally probe the $^3$He-$^4$He interface.
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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.
Within density functional theory, we have obtained the structure of $^4$He droplets doped with neutral calcium atoms. These results have been used, in conjunction with newly determined {it ab-initio} $^1Sigma$ and $^1Pi$ Ca-He pair potentials, to address the $4s4p$ $^1$P$_1 leftarrow 4s^2$ $^1$S$_0$ transition of the attached Ca atom, finding a fairly good agreement with absorption experimental data. We have studied the drop structure as a function of the position of the Ca atom with respect of the center of mass of the helium moiety. The interplay between the density oscillations arising from the helium intrinsic structure and the density oscillations produced by the impurity in its neighborhood plays a role in the determination of the equilibrium state, and hence in the solvation properties of alkaline earth atoms. In a case of study, the thermal motion of the impurity within the drop surface region has been analyzed in a semi-quantitative way. We have found that, although the atomic shift shows a sizeable dependence on the impurity location, the thermal effect is statistically small, contributing by about a 10% to the line broadening. The structure of vortices attached to the calcium atom has been also addressed, and its effect on the calcium absorption spectrum discussed. At variance with previous theoretical predictions, we conclude that spectroscopic experiments on Ca atoms attached to $^4$He drops will be likely unable to detect the presence of quantized vortices in helium nanodrops.
We develop a first principles, microscopic theory of impurity atom scattering from inhomogeneous quantum liquids such as adsorbed films, slabs, or clusters of He-4. The theory is built upon a quantitative, microscopic description of the ground state of both the host liquid as well as the impurity atom. Dynamic effects are treated by allowing all ground-state correlation functions to be time-dependent. Our description includes both the elastic and inelastic coupling of impurity motion to the excitations of the host liquid. As a specific example, we study the scattering of He-3 atoms from adsorbed He-4 films. We examine the dependence of ``quantum reflection on the substrate, and the consequences of impurity bound states, resonances, and background excitations for scattering properties. A thorough analysis of the theoretical approach and the physical circumstances point towards the essential role played by inelastic processes which determine almost exclusively the reflection probabilities. The coupling to impurity resonances within the film leads to a visible dependence of the reflection coefficient on the direction of the impinging particle.
We have experimentally studied the electronic $3pleftarrow 3s$ excitation of Na atoms attached to $^3$He droplets by means of laser-induced fluorescence as well as beam depletion spectroscopy. From the similarities of the spectra (width/shift of absorption lines) with these of Na on $^4$He droplets, we conclude that sodium atoms reside in a ``dimple on the droplet surface. The experimental results are supported by Density Functional calculations at zero temperature, which confirm the surface location of sodium on $^3$He droplets, and provide a microscopic description of the ``dimple structure.
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.
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