Observation of Mixed Fermionic-Bosonic Helium Clusters by Transmission Grating Diffraction

Small weakly bound boson-fermion ${}^4\mathrm{He}_m{}^3\mathrm{He}_n$ clusters formed in a free jet expansion are identified using nondestructive transmission grating diffraction. The observations confirm the existence of more than 11 very tenuous complexes including the three-body halo molecule ${}^4\mathrm{He}_2{}^3\mathrm{He}$ and the pseudo-Borromean complex ${}^4\mathrm{He}_2{}^3\mathrm{He}_2$. Effective cluster formation temperatures, extracted from a sudden freeze model for cluster growth using theoretical binding energies, increase smoothly with cluster size, thereby confirming the calculations with the possible exception of ${}^4\mathrm{He}_2{}^3\mathrm{He}_2$.

Figure 1

Diffraction patterns of clusters in a cryogenic free jet expansion of 9%–10% ${}^4\mathrm{He}$ in ${}^3\mathrm{He}$ gas mixtures measured for different ion fragments: (a) on mass 3 amu (${}^3\mathrm{He}^{+}$), (b) on mass 4 amu (${}^4\mathrm{He}^{+}$), and (c),(d) on mass 7 amu (${}^4\mathrm{He}{}^3\mathrm{He}^{+}$), which are assigned to mixed clusters ${}^4\mathrm{He}_m{}^3\mathrm{He}_n$. The diffraction angles in (d) correspond to the same masses after correcting for the different beam velocity compared to (c). The top and bottom abscissas in (c) and (d) show the assigned cluster masses and compositions, respectively.

Figure 2

Comparison of diffraction patterns measured with 1% ${}^4\mathrm{He}$ in ${}^3\mathrm{He}$ gas mixtures: (a) on mass 8 amu (${}^4\mathrm{He}_2{}^{+}$) and (b)–(d) on mass 7 amu (${}^4\mathrm{He}{}^3\mathrm{He}^{+}$) plotted on a mass scale (top abscissa) and composition scale (bottom abscissa). The smaller $\pm$ standard deviations result from longer measurement times. The crosshatched region corresponds to the ${}^4\mathrm{He}_4{}^3\mathrm{He}_3$ cluster. The small peak in (d) between $(5,1)$ and $(4,3)$ might correspond to the metastable ${}^4\mathrm{He}_3{}^3\mathrm{He}_4$ cluster.

Figure 3

Effective cluster formation sudden freeze temperatures evaluated with Eq. (3) for the measurements in Figs. 1, 2. Major deviations from the otherwise smooth correlation are found only for the $(3,1)$ cluster in (a) and for $(2,2)$ in (b). With these exceptions, standard deviations are generally smaller than the size of the symbols.