In this paper we extend our studies to the micro-structure of the Matthew effect for countries (MEC). The MEC allows the ranking of countries by their Matthew Index. The rank distribution of countries, observable only at a macro-level, has its roots in re-distribution processes of citations in every journal of the database. These re-distributed citations we call Matthew citations. Data for 44 countries and 2712 journals (based on the Science Citation Index) are analyzed. The strength of the contribution of the individual journals to the MEC (their number of Matthew citations) is skewly distributed. Due to this high concentration of the MEC we are able to define a new type of journal: the Matthew core journal: 145 Matthew core journals account for 50% of the MEC. These journals carry a high potential of gaining a surplus of citations over what is expected and the risk of losing a high number of citations as well.