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Physical Review B

Calcium atoms attached to mixed helium droplets: A probe for the H3e-H4e interface

Oliver Bünermann, Matthieu Dvořák, Frank Stienkemeier, Alberto Hernando, R. Mayol, Martí Pi, M. Barranco, Francesco Ancilotto

Published Jun 10, 2009• 32 citations

Abstract

Experimental and theoretical results for mixed helium droplets doped with one calcium atom are reported. The absorption spectrum around the $4s4p\ensuremath{\leftarrow}4{s}^{2}$ transition is calculated as a function of the composition of the droplet and compared to the experiment. Our study reveals the distinct feature that for specific $^{3}\text{H}\text{e}$ concentrations, Ca atoms sit at the $^{3}\text{H}\text{e-}^{4}\text{H}\text{e}$ interface. This particular property of Ca, likely not shared with any other atomic or molecular species but the heavier alkaline-earth atoms, might offer the possibility of using it to probe the $^{3}\text{H}\text{e-}^{4}\text{H}\text{e}$ interface of the droplet.

DOI: 10.1103/physrevb.79.214511

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Experimental and theoretical results for mixed helium droplets doped with one calcium atom are reported. The absorption spectrum around the

4s4p\ensuremath{\leftarrow}4{s}^{2}

transition is calculated as a function of the composition of the droplet and compared to the experiment. Our study reveals the distinct feature that for specific

^{3}\text{H}\text{e}

concentrations, Ca atoms sit at the

^{3}\text{H}\text{e-}^{4}\text{H}\text{e}

interface. This particular property of Ca, likely not shared with any other atomic or molecular species but the heavier alkaline-earth atoms, might offer the possibility of using it to probe the

^{3}\text{H}\text{e-}^{4}\text{H}\text{e}

interface of the droplet.

The momentum and energy transferred to large, cold (0.38 K) superfluid

{}^{4}\mathrm{He}

droplets ( $\overline{N}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.5\ifmmode\times\else\texttimes\fi{}{10}^{9}\phantom{\rule{0ex}{0ex}}\mathrm{atoms}$) in low energy (5--10 K) collisions with

{}^{3}\mathrm{He}

and

{}^{4}\mathrm{He}

atoms were determined from time-of-flight and mass spectrometer measurements. At the lowest total collision energies,

{}^{3}\mathrm{He}

atoms transfer only

45%

of their momentum and

60%

of their energy, whereas

{}^{4}\mathrm{He}

atoms transfer

65%

of their momentum and

100%

of their energy. These results are consistent with

{}^{3}\mathrm{He}

atoms being transmitted through the superfluid droplets, while in the case of

{}^{4}\mathrm{He}

atoms some of the momentum is transmitted via phonon mechanisms.

Using density functional theory, we investigate the structure of mixed ${}^{3}{\mathrm{He}}_{{N}_{3}}{\ensuremath{-}}^{4}{\mathrm{He}}_{{N}_{4}}$ droplets with an embedded impurity (Xe atom or HCN molecule) which pins a quantized vortex line. We find that the

\mathrm{dopant}+\mathrm{vortex}{+}^{4}{\mathrm{He}}_{{N}_{4}}

complex, which in a previous work [F. Dalfovo et al., Phys. Rev. Lett. 85, 1028 (2000)] was found to be energetically stable below a critical size

{N}_{\mathrm{cr}}

, is robust against the addition of

{}^{3}\mathrm{He}

. While

{}^{3}\mathrm{He}

atoms are distributed along the vortex line and on the surface of the

{}^{4}\mathrm{He}

drop, the impurity is mostly coated by

{}^{4}\mathrm{He}

atoms. Results for

{N}_{4}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}500

and a number of

{}^{4}\mathrm{He}

atoms ranging from 0 to 100 are presented, and the binding energy of the dopant to the vortex line is determined.

The existence of small helium clusters containing a variable number of

^{\mathrm{4}}\mathrm{H}\mathrm{e}

and

^{\mathrm{3}}\mathrm{H}\mathrm{e}

atoms is studied within a variational Monte Carlo calculation employing the Aziz HFD-B(HE) pair interaction. The clusters

{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{2}

support one and two

^{\mathrm{3}}\mathrm{H}\mathrm{e}

atoms; however, the system with three

^{\mathrm{4}}\mathrm{H}\mathrm{e}

atoms is metastable, and the next bound system requires at least 18 fermions. All clusters obtained by adding

^{\mathrm{3}}\mathrm{H}\mathrm{e}

atoms to the trimer

{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{2}

and the tetramer

^{\mathrm{3}}\mathrm{H}\mathrm{e}

are bound, but the clusters

{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3}

-

{^{\mathrm{3}}\mathrm{H}\mathrm{e}}_{3,4,5}

and

{^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3,4}

-

{^{\mathrm{3}}\mathrm{H}\mathrm{e}}_{9}

are metastable. All remaining clusters with three or more bosons and any number of fermions are stable.