A general shell model formalism for the nonmesonic weak decay of the hypernuclei has been developed. It involves a partial wave expansion of the emitted nucleon waves, preserves naturally the antisymmetrization between the escaping particles and the residual core, and contains as a particular case the weak lambda-core coupling formalism. The hypernuclei are grouped having in view their A - 1 cores, that is in those with even-even, even-odd and odd-oddcores. It is shown that in all three cases the nuclear structure manifests itself basically through Pauli Principle, and very simple expressions are derived for the neutron and proton induced decays rates, gamman and gammap, which does not involve the spectroscopic factors. For the strangeness-changing weak lambda N ->N N transition potential we use the One-Meson-Exchange Model (OMEM), which comprises the exchange of the complete pseudoscalar and vector meson octets (pi, <FONT FACE=Symbol>h,</FONT>K<FONT FACE=Symbol>, r</FONT>, omega, K*).We evaluate ³H, 4H, 4lambdaHe, 5lambdaHe, 11B, 12lambdaC, 16lambdaO, 17lambdaO, and 28Si hypernuclei, with commonly used parametrization for the OMEM, and compare the results with the available experimental information. The calculated rates gammaNM = gamman + gammap are consistent with the data, but the measurements of gamman/p = gamman/gammap are not well accounted for by the theory. It is suggested that, unless additional degrees of freedom are incorporated, the OMEM parameters should be radically modified.
