Structure and Stability of3HeDroplets

Abstract

We have studied the structure of 3 He droplets at zero temperature using a density functional approach plus a configuration interaction calculation in an harmonic oscillator major shell. The most salient feature of open shell drops is that the valence atoms couple their spins to the maximum value compatible with Pauli's principle, building a large magnetic moment. We have determined that 29 atoms constitute the smallest self-bound droplet. [S0031-9007 (97)03450-9] PACS numbers: 36.40.-cThe structure and dynamical properties of liquid helium drops have been the subject of many experimental and theoretical studies during the past 15 years (for recent reviews, see [1,2]). During this time, a severe experimental limitation has been the impossibility of selecting or detecting and identifying quantitatively small van der Waals clusters [3]. The situation has recently changed, and new scattering deflection methods seem able to determine and select the size of large helium clusters [4]. A new method based on diffracting a molecular beam from a transmission grating looks very promising in doing the same for small-size van der Waals clusters [5]. This might shed light onto the ground state structure of 3 He droplets. Prompted by this experimental possibility, we present here a realistic calculation of the structure of these systems using a reliable density functional and powerful techniques borrowed from the shell model description of the atomic nucleus (see, e.g., [6]).The first systematic calculation of the ground state properties of 4 He and 3 He drops was carried out by Pandharipande and co-workers using a variational Monte Carlo (VMC) technique [7] and by Stringari and Treiner within a local, zero range energy density functional (LDF) approximation [8]. At present, diffusion Monte Carlo calculations are also available for 4 He drops [9,10]. For 3 He, there are also two recent systematic calculations which make use of nonlocal, finite-range density functionals (NLDF) built so as to reproduce a large number of properties of the homogeneous and inhomogeneous liquid [11,12]. Within LDF, a random-phase approximation calculation of the collective spectrum of closed shell 3 He drops is also available [13].One of the more interesting issues of these studies is the existence of a minimum number N min of atoms below which 3 He droplets are unbound. That number was estimated to be between 20 and 40 [7], since for N 20 the system was unbound and weakly bound for N 40. Calculations carried out employing local or nonlocal functionals have reproduced this microscopic feature [8,11,12]. These two numbers belong to the ͑p 1 1͒ ͑p 1 2͒ ͑p 1 3͒͞3 sequence with p 0, 1, 2, ... characteristic of the harmonic oscillator (HO) well, each of them defining a major shell closure.NLDF calculations of large drops show departures from that sequence above N 168 [11,12]. These functionals are fitted to reproduce many properties of the homogeneous liquid and of its free surface, as well as Landau parameters and dynamical properties of the liquid [14],...

Spectroscopy and dynamics in helium nanodroplets

“…The lower chemical potential results in higher rates of desorbing atoms; thus the terminal temperature of 3 He nanodroplets in the evaporative cooling process amounts 150 mK [68] which is considerably lower compared to 380 mK for 4 He droplets. Since small 3 He droplets appear not to be stable for sizes N 30 [69,70,71], aggregation is hindered because droplets cannot be grown from small clusters adding one by one to an atom. In contrast, cluster formation requires highly multiple collisions.…”

Structure and energetics of mixed4He-3He drops

“…18 FRDF results for open-shell 3 He droplets has also been reported. 19 As we have indicated, the theoretical effort have been hampered so far by the lack of experimental results on 3 He drops on one hand, and of a full microscopic theory, in contradistinction with the 4 He case, on the other hand.…”

Experimental and theoretical study of the radial density distributions of large3Hedroplets

“…[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] The most recent calculations predict that whereas 4 He clusters from the dimer upwards are all stable, 3 He clusters with less than 29 atoms are all unstable. 26 This is attributed to the large zero-point energy of the 3 He atoms resulting from their smaller mass and because of their Fermion nature. Previously the density distributions of 3 He clusters with several tens of atoms up to droplets with N ϭ1360 atoms 23 have been calculated using a variety of different approximations.…”