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Structure of $^{10}_Λ$Be and $^{10}_Λ$B hypernuclei studied with the four-body cluster model

The structure of the isodoublet hypernuclei, $^{10}_Λ$B and $^{10}_Λ$Be within the framework of an $α+α+Λ+N$ four-body cluster model is studied. Interactions between the constituent subunits are determined so as to reproduce reasonably well the observed low-energy properties of the $αα$, $αN$, $αΛ$, $ααΛ$ and $ααN$ subsystems. Furthermore, the two-body $ΛN$ interaction is adjusted so as to reproduce the $0^+$-$1^+$ splitting of $^4_Λ$H. The $Λ$ binding energies of $^{10}_Λ$B and $^{10}_Λ$Be are 8.76 MeV and 8.94 MeV, respectively. The energy splitting of the $1^-$-$2^-$ levels in $^{10}_Λ$B is 0.08 MeV, which does not contradict the experimental report in BNL-E930. An even-state $ΛN$ charge symmetry breaking (CSB) interaction determined from the A=4 systems works repulsively by +0.1 MeV (attractively by -0.1 MeV) in $^{10}_Λ$Be ($^{10}_Λ$B). We discuss a possibility that an odd-state CSB interaction improves the fitting to the experimental data of A=10 double $Λ$ hypernuclei.