  The atomic masses of the isotopes $^{206,207}$Ra have been measured via
decay-correlated mass spectroscopy using a multi-reflection time-of-flight mass
spectrograph equipped with an $\alpha$-TOF detector. The Ra isotopes were
produced as fusion-evaporation products in the $^{51}$V+$^{159}$Tb reaction
system and delivered by the gas-filled recoil ion separator GARIS-II at RIKEN.
The $\alpha$-TOF detector provides for high-accuracy mass measurements by
correlating time-of-flight signals with subsequent $\alpha$-decay events. The
masses of $^{206}$Ra and $^{207g,m}$Ra were directly measured using a
multi-reflection time-of-flight mass spectrograph equipped with an $\alpha$-TOF
detector. A mass excess of ME = 3538(15) keV/c$^2$ and an excitation energy of
E$_{\rm ex}$ = 552(42) keV were determined. The $\alpha$-decay branching ratio
of $^{207m}$Ra, b$\alpha$ = 0.26(20), was directly determined from
decay-correlated time-of-flight signals, and the reduced alpha width of
$^{207m}$Ra was calculated to be $\delta^2$ = 50+62-41 keV from the branching
ratio. The spin-parity of $^{207m}$Ra was confirmed to be $J^\pi$ = 13/2$^-$
from decay correlated mass measurement results.
