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Physical Review Letters

Interplay between Magic Number Stabilities and Superfluidity of Small Parahydrogen Clusters

Saad A. Khairallah, Mikhail Borisovich Sevryuk, David M. Ceperley, J. P. Toennies

Published May 4, 2007• 86 citations
Publisher

Abstract

The interplay between magic number stabilities and superfluidity of small parahydrogen clusters with sizes N=5 to 40 and temperatures 0.5 K</=T</=4.5 K is explored with classical and quantum path integral Monte Carlo calculations. Clusters with N<26 and T</=1.5 K have large superfluid fractions even at the stable magic numbers 13, 19, and 23. In larger clusters, superfluidity is quenched especially at the magic numbers 26, 29, 32, and 37 while below 1 K, superfluidity is recovered for the pairs (27,28), (30,31), and (35,36). For all clusters superfluidity is localized at the surface and correlates with long exchange cycles involving loosely bound surface molecules.

DOI
10.1103/physrevlett.98.183401

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The interplay between magic number stabilities and superfluidity of small parahydrogen clusters with sizes N=5 to 40 and temperatures 0.5 K</=T</=4.5 K is explored with classical and quantum path integral Monte Carlo calculations. Clusters with N<26 and T</=1.5 K have large superfluid fractions even at the stable magic numbers 13, 19, and 23. In larger clusters, superfluidity is quenched especially at the magic numbers 26, 29, 32, and 37 while below 1 K, superfluidity is recovered for the pairs (27,28), (30,31), and (35,36). For all clusters superfluidity is localized at the surface and correlates with long exchange cycles involving loosely bound surface molecules.
The interplay between magic number stabilities and superfluidity of small para-hydrogen clusters with sizes N=5N = 5N=5 to 40 and temperatures $0.5 K \leq T \leq 4.5 $K is explored with classical and quantum Path Integral Monte Carlo calculations. Clusters with N<26N < 26N<26 and T ≤1.5K\leq 1.5 K≤1.5K have large superfluid fractions even at the stable magic numbers 13, 19, and 23. In larger clusters, superfluidity is quenched especially at the magic numbers 23, 26, 29, 32, and 37 while below 1 K, superfluidity is recovered for the pairs (27,28)(27,28)(27,28), (30,31)(30,31)(30,31), and (35,36)(35,36)(35,36). For all clusters superfluidity is localized at the surface and correlates with long exchange cycles involving loosely bound surface molecules.
We study by quantum Monte Carlo simulations the local superfluid response of small (up to 27 molecules) parahydrogen clusters, down to temperatures as low as 0.05 K. We show that at low temperature superfluidity is not confined at the surface of the clusters, as recently claimed by Khairallah et al. [Phys. Rev. Lett. 98, 183401 (2007)10.1103/PhysRevLett.98.183401]. Rather, even clusters with a pronounced shell structure are essentially uniformly superfluid. Superfluidity occurs as a result of long exchange cycles involving all molecules.
The structure and thermodynamic properties of the 4He/H2{}^{4}{\mathrm{H}\mathrm{e}/\mathrm{H}}_{2}4He/H2​ binary clusters are studied by path-integral Monte Carlo simulations. It has been found that, despite their lower mass, the H2{\mathrm{H}}_{2}H2​ molecules form a subcluster of their own at the center of the system. When the number of helium atoms increases for a fixed number of hydrogen molecules, those inner clusters get compressed but retain their original form. The fraction of H2{\mathrm{H}}_{2}H2​ in the superfluid state decreases with the subcluster compression, but remains finite for small H2{\mathrm{H}}_{2}H2​ concentrations.
A stability chart of mixed 4He{}^{4}\mathrm{He}4He and 3He{}^{3}\mathrm{He}3He clusters has been obtained by means of the diffusion Monte Carlo method, using both the Aziz HFD-B and the Tang-Toennies-Yiu atom-atom interaction. The investigated clusters contain up to eight 4He{}^{4}\mathrm{He}4He atoms and up to 20 3He{}^{3}\mathrm{He}3He atoms. One single 4He{}^{4}\mathrm{He}4He binds 20 3He{}^{3}\mathrm{He}3He atoms, and two 4He{}^{4}\mathrm{He}4He bind 1, 2, 8, and more than 14 3He{}^{3}\mathrm{He}3He atoms. All clusters with three or more 4He{}^{4}\mathrm{He}4He atoms are bound, although the combinations 4He33He9,10,11{}^{4}{\mathrm{He}}_{3}^{3}{\mathrm{He}}_{9,10,11}4He33​He9,10,11​ and 4He43He9{}^{4}{\mathrm{He}}_{4}^{3}{\mathrm{He}}_{9}4He43​He9​ are metastable. Clusters with 2, 8, and 20 3He{}^{3}\mathrm{He}3He atoms are particularly stable and define magic 3He{}^{3}\mathrm{He}3He numbers.
The size distributions of neutral 4He clusters in cryogenic jet beams, analyzed by diffraction from a 100 nm period transmission grating, reveal magic numbers at N=10-11, 14, 22, 26-27, and 44 atoms. Whereas magic numbers in nuclei and clusters are attributed to enhanced stabilities, this is not expected for quantum fluid He clusters on the basis of numerous calculations. These magic numbers occur at threshold sizes for which the quantized excitations calculated with the diffusion Monte Carlo method are stabilized, thereby providing the first experimental confirmation for the energy levels of 4He clusters.
The existence of small helium clusters containing a variable number of 4He^{\mathrm{4}}\mathrm{H}\mathrm{e}4He and 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms is studied within a variational Monte Carlo calculation employing the Aziz HFD-B(HE) pair interaction. The clusters 4He2{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{2}4He2​ support one and two 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms; however, the system with three 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms is metastable, and the next bound system requires at least 18 fermions. All clusters obtained by adding 3He^{\mathrm{3}}\mathrm{H}\mathrm{e}3He atoms to the trimer 4He3{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3}4He3​ and the tetramer 4He4{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{4}4He4​ are bound, but the clusters 4He3{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3}4He3​-3He3,4,5{^{\mathrm{3}}\mathrm{H}\mathrm{e}}_{3,4,5}3He3,4,5​ and 4He3,4{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3,4}4He3,4​-3He9{^{\mathrm{3}}\mathrm{H}\mathrm{e}}_{9}3He9​ are metastable. All remaining clusters with three or more bosons and any number of fermions are stable.