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Method: Measuring excitation functions for $^{6}$He+$\alpha$ scattering,populating states in the excitation energy range from 4.5 MeV to 8 MeV in$^{10}$Be using a $^6$He rare-isotope beam and a thick helium gas target.Results: No new excited states in $^{10}$Be have been observed. Stringentlimitation on the possible degree of $\alpha$-clustering of the hypotheticalyrast 6$^+$ state has been obtained. Conclusions: The high-spin members of the$\alpha$:2n:$\alpha$ molecular-like rotational band configuration, that isconsidered to have a 0$^+$ bandhead at 6.18 MeV, either do not exist or havesmall overlap with the $^{6}$He(g.s.)+$\alpha$ channel.

Search for the high-spin members of the $\alpha$:2n:$\alpha$ band in $^{10}$Be