We have used the Herschel-HIFI instrument to observe both nuclear spin symmetries of amidogen (NH2) towards the high-mass star-forming regions W31C (G10.6-0.4), W49N (G43.2-0.1), W51 (G49.5-0.4) and G34.3+0.1. The aim is to investigate the ratio of nuclear spin types, the ortho-to-para ratio (OPR), of NH2. The excited NH2 transitions are used to construct radiative transfer models of the hot cores and surrounding envelopes in order to investigate the excitation and possible emission of the ground state rotational transitions of ortho-NH2 N_(K_a,K_c} J=1_(1,1) 3/2 - 0_(0,0) 1/2 and para-NH2 2_(1,2) 5/2 - 1_(0,1) 3/2$ used in the OPR calculations. Our best estimate of the average OPR in the envelopes lie above the high temperature limit of three for W49N, specifically 3.5 with formal errors of pm0.1, but for W31C, W51, and G34.3+0.1 we find lower values of 2.5pm0.1, 2.7pm0.1, and 2.3pm0.1, respectively. Such low values are strictly forbidden in thermodynamical equilibrium since the OPR is expected to increase above three at low temperatures. In the translucent interstellar gas towards W31C, where the excitation effects are low, we find similar values between 2.2pm0.2 and 2.9pm0.2. In contrast, we find an OPR of 3.4pm0.1 in the dense and cold filament connected to W51, and also two lower limits of >4.2 and >5.0 in two other translucent gas components towards W31C and W49N. At low temperatures (T lesssim 50 K) the OPR of H2 is <10^-1, far lower than the terrestrial laboratory normal value of three. In such a para-enriched H2 gas, our astrochemical models can reproduce the variations of the observed OPR, both below and above the thermodynamical equilibrium value, by considering nuclear-spin gas-phase chemistry. The models suggest that values below three arise in regions with temperatures >20-25 K, depending on time, and values above three at lower temperatures.
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