Excitation levels and magic numbers of small para-Hydrogen clusters (N le 40 )

📝 Abstract

The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of one molecule from 3 to 40 molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L=13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N=13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies the partition function has been obtained, thus allowing for an estimate of thermal effects. An enhanced production is predicted for cluster sizes N=13, 31 and 36, in agreement with experiment.

💡 Analysis

The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of one molecule from 3 to 40 molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L=13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N=13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies the partition function has been obtained, thus allowing for an estimate of thermal effects. An enhanced production is predicted for cluster sizes N=13, 31 and 36, in agreement with experiment.

📄 Content

arXiv:0802.2000v1 [physics.atm-clus] 14 Feb 2008 Excitation levels and magic numbers of small para-Hydrogen clusters (N≤40) Rafael Guardiola1 and Jes´us Navarro2 1 Departamento de F´ısica At´omica y Nuclear, Facultad de F´ısica, 46100 Burjassot, Spain 2 IFIC (CSIC-Universidad de Valencia), Apdo. 22085, 46071 Valencia, Spain (Dated: October 27, 2018) Abstract The excitation energies of parahydrogen clusters have been systematically calculated by the diffusion Monte Carlo technique in steps of one molecule from 3 to 40 molecules. These clusters possess a very rich spectra, with angular momentum excitations arriving up to L = 13 for the heavier ones. No regular pattern can be guessed in terms of the angular momenta and the size of the cluster. Clusters with N = 13 and 36 are characterized by a peak in the chemical potential and a large energy gap of the first excited level, which indicate the magical character of these clusters. From the calculated excitation energies the partition function has been obtained, thus allowing for an estimate of thermal effects. An enhanced production is predicted for cluster sizes N = 13, 31 and 36, in agreement with experiment. PACS numbers: 67.40.Db, 36.40.-c, 61.46.Bc 1 I. INTRODUCTION Small (pH2)N clusters of parahydrogen have been produced in a cryogenic free jet expan- sion and studied by Raman spectroscopy [1]. The Q(0) Raman line of the H2 monomer is shifted as the number N of molecules in the cluster changes, thus providing a method to identify the cluster mass. The first seven resolved peaks next the monomer line have been assigned to clusters with N = 2, . . . , 8 molecules. Although in that experiment the resolu- tion was not enough to resolve larger sizes, broad maxima were observed at N ≈13 and 33, and perhaps 55, which have been interpreted as a propensity for geometric shell structures. Indeed, classical static [2, 3, 4] and molecular dynamics [4, 5] results, based on a generic Lennard-Jones interaction potential, indicate that the expected structures for such clusters are the so-called Mackay icosahedra [6], exhibiting some magic sizes (13, 33, 55…) related to the packing of molecules in closed icosahedral arrangements. A very complete discussion of classical geometrical patterns and their relation with the interaction features can be found in Ref. [7] and references herein. However, quantum effects play a major role in pH2 clusters, like in their analogous helium droplets. The path integral Monte Carlo (PIMC) simulations of Sindzingre et al. [8] have shown indeed that the superfluid fraction in pH2 clusters with 13 and 18 molecules become large at temperatures below T ≃2 K. This prediction prompted both experimental [9] and theoretical [10, 11, 12, 13] research of small clusters consisting of pH2 molecules surrounding an OCS chromophore, confirming the existence of a superfluid response. Quantum Monte Carlo (QMC) methods have been widely used in recent years as a the- oretical tool to study pH2 clusters. Several QMC techniques have been employed to cal- culate their properties, namely variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) [14, 15, 16, 17, 18], path integral Monte Carlo (PIMC) [8, 19, 20, 21, 22], reptation Monte Carlo (RMC) [23] and path integral ground state (PIGS) Monte Carlo [24]. Only some specific values of the number of constituents N have been considered in the past, re- lated to the expected MacKay icosahedra structures. More recently, systematic calculations as a function of the number of molecules in the cluster have been performed. The ground state energies and the one-body densities of pHN clusters have been calculated by the DMC technique in steps of one molecule from N=3 to 50 [17], by the PIGS technique from N=2 to 20 [24] and by the PIMC from N=5 to 40 [21, 22]. The calculations show that (pH2)N 2 clusters exhibit a clear geometrical order, with the molecules occupying concentric spherical shells, which could be related to some polyhedric arrangement. The apparent incompati- bility between the large superfluid fractions and the structured radial distribution densities has been recently clarified [21, 22] by PIMC calculations which show that superfluidity is localized at the surface of the clusters. Whereas up to N ≃22 these calculations are substantially in agreement, for heavier clusters there are noticeable differences between DMC and PIMC results, particularly for N ≥26. PIMC chemical potentials show very prominent peaks at N=26, 29, 34 and 39, in contrast with a smoother behavior obtained with DMC. These differences subsist even after an improved DMC calculation [18], and seem to be related to thermal effects. According to Mezzacapo and Boninsegni [21] they should be associated to a coexistence of solid-like and liquid-like phases, with a dominance of the latter at low T, as a result of both the zero-point motion and quantum permutation exchanges. However, thermal effects could manifest in enhanced stability thresholds at finite tem

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