The beta-delayed proton precursors Nd-125, Pm-128, Sm-129, Gd-137 and Dy-13
9 near the proton drip line were produced by the irradiation of Mo-92, Ru-9
6 and Cd-106 with an Ar-36 beam, and conclusively identified for the first
time by using proton-gamma coincidence in combination with a He-jet tape tr
ansport 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 sta
tes in "daughter" nuclei for the precursors Nd-125, Sm-129, Gd-137 and Dy-1
39, as well as the previously reported ones for the precursors Gd-135 and C
e-121, were fitted by a statistical model calculation. The ground-state spi
ns and parities of Ce-121, 125Nd, Sm-129, Gd-135, Gd-137 and Dy-139 were th
en assigned as 5/2 (+/-),5/2 (+/-), 1/2 (+/-) (or 3/2 (+)),5/2 (+),7/2 (+/-
) and 7/2, respectively. The consistency between the experimental spin-pari
ty assignment and the predicted Nilsson diagrams indirectly indicates that
the ground states of Ce-121, Nd-125, Sm-129, Gd-135, Gd-137 and Dy-139 and
highly deformed with beta(2) similar to 0.3.