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We investigate low-lying bound states of the neutron-rich nucleus ${}^{15}$Bby assuming it is a three-body system made of an inert core ${}^{13}$B and twovalence neutrons. The three-body wave functions are obtained using the Faddeevformalism. Special attention is paid to the excited state at $3.48(6)$ MeVobserved in the${}^{13}\text{C}({}^{14}\text{C},{}^{12}\text{N}){}^{15}\text{B}$ reaction,whose properties are less clear theoretically. In our three-body model, besidesthe ground state $3/2_1^-$, a second $3/2_2^-$ state is discovered at around$3.61$ MeV, which might be identified with the excited state observed at$3.48(6)$ MeV. We study this $3/2_2^-$ state in detail, which turns out to be atwo-neutron halo state with a large matter radius $r_\text{m}\approx 4.770$ fm.

Two-Neutron Halo State of ${}^{15}$B Around $3.48$ MeV By A Three-Body Model