Abstract In this study, we present findings on the detection of neutral atomic hydrogen (HI) 21cm absorption in the spectrum of PKS1413+135 at redshift $z=0.24670041$. The observations were conducted by FAST, with a spectral resolution of 10 Hz, using 10 minutes of observing time.The global spectral profile is examined by modeling the absorption line using a single Gaussian function with a resolution of 10kHz within a 2MHz bandwidth. The goal is to determine the rate of the latest cosmic acceleration by directly measuring the evolution of the redshift of HI 21cm absorption line with Hubble flow towards a common background Quasar over a decade or longer time span. This will serve as a detectable signal generated by the accelerated expansion of the Universe at redshift $z < 1$, specifically redshift drift $\dot{z}$ or the SL effect.The measured HI gas column density in this DLA system is approximately equivalent to the initial observation value, considering uncertainties in the spin temperature of a spiral host galaxy. The high signal-to-noise ratio of 57, obtained at a 10kHz resolution, strongly supports the feasibility of using the HI 21cm absorption line in DLA systems to accurately measure the redshift rate at a precision level of around $10^{-10}$ per decade.

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