Microscopic studies of collective spectra of quantum liquid clusters

Abstract

Theoretical methods are developed for determining the collective vibrational excitation spectra of quantum clusters, and applied to clusters of 4He. A quantum liquid drop model gives excitation energies in terms of two-point ground state density correlations, which are evaluated from microscopic calculations of the ground state wave functions. An alternative approach based on a Bijl–Feynman ansatz for the excited states also yields excitation energies in terms of ground state correlations, without the imposition of a sharp liquid surface. These methods are applied to the calculation of the excitation spectra of 4HeN , N=20, 70, and 240 clusters. The relationship between the collective spectra of these clusters and that of bulk fluid He II, and the significance of an observed roton minimum in the spectrum for N≥70 are discussed.

Spectroscopy of alkali atoms (Li, Na, K) attached to large helium clusters

“…Nonclassical ideas to explain the capture of Cs atoms by large helium clusters were introduced as early as 1986 [3], while recently, Toennies et al [4] have measured the electronic spectrum of glyoxal molecules embedded in He clusters and found it consistent with a theoretical simulation computed using the phonon dispersion curve of superfluid bulk He II. The authors themselves, however, point out that at the average cluster size of 5500 He atoms reported in [4], the phonon dispersion curve is well in the bulk limit (see also [5,6]); it is therefore not surprising that they find results consistent with the bulk case, especially for a molecule readily solvated inside the cluster, for which surface effects play a minor role. Therefore the influence on superfluidity of the He clusters size has not been detected so far.…”

“…These two assumptions allow us to drop the AJSQR (R G ) term in (5) and to separate the radial part of the electronic wave function. Recalling that the angular part of electronic wave function is given by ½J KJ ( , ) for Li and by (3) for Na and K, the expression for the absorption cross section (4) after summing over all excited states and averaging over the light polarization, reads:…”

Excited states of4Hedroplets

“…Depending on the size of the cluster, ␣ lies between 0.27 and 0.30 Å Ϫ1 . An interesting outcome of our J-CI3 ground-state calculations 14 is that the ground-state energies are not very sensitive to the precise value of ␣ in a large interval around that obtained without triplet correlations. Finally, the yet unknown functions f 2 and f 3 can be optimally determined by minimizing the expectation value of the Hamiltonian, as will be shown below.…”

“…7,[11][12][13][14][15] The excitation spectrum of quantum liquids is expected to be experimentally more easily accessible than the ground-state energetics. Moreover, study of the excitation spectrum varying the number of constituents has been used 11 to establish the onset of superfluidity in finite 4 He clusters.…”

Quantum Dynamics of Helium Clusters

“…Comparison with recent experimental measurements of such shifts for SF 6 in HeN is underway. 4 ) Development of quantum theoretical approaches to excited states for the collective modes (papers 2,5). This began with a variational approach to excited compressional states which was based on the Feynman operator approach, and has recently been extended to excited states of overall rotation of the cluster.…”