New $\beta$-delayed proton precursors in the rare-earth region near the proton drip line

The $\beta$-delayed proton precursors ${}^{125}\mathrm{Nd}{,}^{128}\mathrm{Pm},$${}^{129}\mathrm{Sm}{,}^{137}\mathrm{Gd}$, and ${}^{139}\mathrm{Dy}$ near the proton drip line were produced by the irradiation of ${}^{92}\mathrm{Mo}{,}^{96}\mathrm{Ru}$, and ${}^{106}\mathrm{Cd}$ with an ${}^{36}\mathrm{Ar}$ beam, and definitely identified for the first time using proton-gamma coincidence in combination with a He-jet tape transport system. Their half-lives were determined to be 0.60(15) s, 1.0(3) s, 0.55(10) s, 2.2(2) s, and 0.6(2) s, respectively. The measured energy spectra of $\beta$-delayed protons and estimated proton branching ratios to the final states in “daughter” nuclei were fitted by a statistical model calculation, and then the spins and parities of ${}^{125}\mathrm{Nd},$${}^{129}\mathrm{Sm},$${}^{137}\mathrm{Gd}$, $\mathrm{and}{}^{139}\mathrm{Dy}$ were preliminarily assigned as ${5/2}^{\pm },{1/2}^{+}(or\hspace{0.5em}{3/2}^{+}),{7/2}^{\pm }$, and ${7/2}^{+}$, respectively. The agreement between the spin-parity assignments and the predicted Nilsson diagrams indirectly indicates that the ground states of ${}^{125}\mathrm{Nd},$${}^{129}\mathrm{Sm},$${}^{137}\mathrm{Gd}$, ${\mathrm{and}}^{139}\mathrm{Dy}$ are highly deformed with ${\beta }_2\sim 0.3$.