We present the results of formaldehyde and methanol deuteration measurements towards the Class I low-mass protostar SVS13-A, in the framework of the IRAM 30-m ASAI (Astrochemical Surveys At IRAM) project. We detected emission lines of formaldehyde, methanol, and their deuterated forms (HDCO, D2CO, CHD2OH, CH3OD) with Eup up to 276 K. The formaldehyde analysis indicates Tkin = 15 - 30 K, n (H2) >= 10^6 cm^-3, and a size of about 1200 AU suggesting an origin in the protostellar envelope. For methanol we find two components: (i) a high temperature (Tkin = 80 K) and very dense (> 10^8 cm^-3}) gas from a hot corino (radius about 35 AU), and (ii) a colder Tkin <= 70 K) and more extended (radius about 350 AU) region. The deuterium fractionation is 9 10^-2 for HDCO, 4 10^-3 for D2CO, and 2 - 7 10^-3 for CH2DOH, up to two orders of magnitude lower than the values measured in Class 0 sources. We derive also formaldehyde deuteration in the outflow: 4 10^-3, in agreement with what found in the L1157-B1 protostellar shock. Finally, we estimate [CH2DOH]/[CH3OD] about 2. The decrease of deuteration in the Class I source SVS13-A with respect to Class 0 sources can be explained by gas-phase processes. Alternatively, a lower deuteration could be the effect of a gradual collapse of less deuterated external shells of the protostellar evelope. The present measurements fill in the gap between prestellar cores and protoplanetary disks in the context of organics deuteration measurements.
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