During a severe accident of a pressurized water nuclear reactor, a large mass of corium could pour into the vessel bottom as a compact jet. When the corium mass reaches the water at the bottom of the vessel, an intense fragmentation may occur. This could lead to a significant mixing of corium and water, likely to cause a steam explosion which could damage the structures. An analytical study has been established in order to quantify the corium jet fragmentation. This study consists mainly in modeling the vapor flow surrounding the jet as well as the instability which occurs at its interface. In comparison with previous studies, this model pays particular attention to the jet-produced particles which interact with the vapor flow. A complete model has been set up in order to calculate the jet breakup length and the generated particles' diameter under each specific situation characterized by initial conditions. This model mainly relies upon results from boundary layer theory and linear instability calculations. The full model's results are compared to existing experiences in this field and a final correlation of the results is established. A good agreement is obtained on the jet breakup length, however the predicted particle diameter tends to be too large. This last result could be explained by a secondary breakup of the particles in water and by a large uncertainty in the vapor flow.