of $^{12}$C seeds from earlier stellar generations. This occurs on a slower timescale during the red giant phase in low and intermediate-mass stars or novae (@1994LectureNFhys...439..72, @Meyer1994; @Wilson1994). Thus the $^{12}$C/$^{13}$C ratio is expected to decrease with time and a $^{12}$C/$^{13}$C gradient should exist with Galactocentric distance, assuming an inside-out formation scenario of the Milky way (@Pilkington).

Under certain conditions, isotope abundance ratios can be effectively determined from the strengths of corresponding molecular lines (e.g., H$_2$CO, CO and CN). Measurements of absorption lines of H$_2$CO and H$_2$$^{13}$CO toward strong continuum sources are believed to be one of the best ways to determine the isotope ratio between $^{12}$C and $^{13}$C. Previous observations support the existence of a gradient of $^{12}$C/$^{13}$C, i.e., the ratio increases as a function of Galactocentric distance (Wilson et al. ; Gardner & Whiteoak [-@1979MNRAS...188..331]; Henkel et al. ,,,). A $^{12}$C/$^{13}$C ratio cannot be directly deduced from $^{12}$CO (hereafter CO) and $^{13}$CO, since CO (and sometimes $^{13}$CO) is optically thick. Therefore, their isotopologues C$^{18}$O and $^{13}$C$^{18}$O, exhibiting optically thin lines, are sometimes used to determine $^{12}$C/$^{13}$C (@1990ApJ...357..477). However, this is time-consuming, since thermally excited emission lines with low optical depths can have extremely low intensities (@Wilson1994). CN is 