A new model is presented herein to calculate optimal value for ultra-cold neutron (UCN) production rate of a UCN source. The cold neutron (CN) converter is the main component of UCN source. In this paper, we study the UCN source which contains the D2O neutron moderator, the sD2 converter, 590 Mev proton beam, and the spallation target (a mixture of Pb, D2O and Zr). In order to determine the qua...