Quenched post-starburst galaxies ( QPSBs ) are a rare but important class of galaxies that show signs of rapid cessation or recent rejuvenation of star formation .
A recent observation shows that about half of QPSBs have large amounts of cold gas .
This molecular CO sample is , however , too small and is not without limitations .
Our work aims to verify previous results by applying a new method to study a uniformly selected sample , more than 10 times larger .
In particular , we present detailed analysis of H \alpha /H \beta ratios of face-on QPSBs at z = 0.02 - 0.15 and with M _ { \star } = 10 ^ { 10 } -10 ^ { 11 } M _ { \odot } .
We interpret the H \alpha /H \beta ratios by applying our recent gas mass calibration , which is based on non-PSB galaxies but predicts gas masses that are consistent with CO observations of \sim 100 PSBs .
We estimate the molecular gas by either using PSBs with well-measured H \alpha /H \beta ratios or by measuring them from stacked spectra .
Our analysis reveals that QPSBs have a wide range of H \alpha /H \beta ratios and molecular gas fractions that overlap with the typical gas fractions of star-forming or quiescent galaxies : H \alpha /H \beta \approx 3 - 8 and f _ { \mathrm { H _ { 2 } } } \approx 1 \% - 20 \% with median f _ { \mathrm { H _ { 2 } } } \approx 4 \% - 6 \% , which correspond to M _ { \mathrm { H _ { 2 } } } \approx ( 1 - 3 ) \times 10 ^ { 9 } M _ { \odot } .
Our results indicate that large reservoirs of cold gas are still present in significant numbers of QPSBs , and that they arguably were not removed or destroyed by feedback from active galactic nuclei .