A study of the fragmentation of molecular clouds and the form of initial mass-function for low-mass protostellar fragments

Opacity limited fragmentation is considered for a spherically-collapsing isothermal molecular cloud in a low temperature range where molecular hydrogen and grains are the only cooling and opacity sources. The minimum Jeans mass of a fragment is calculated for different values of the parameters. The form of the initial mass function (IMF) is derived for low-mass protostellar fragments for different values of the parameters. They are discussed and compared with observations. A rough estimate of the cloud mass contained in the brown-dwarf regime is given.