, at least in part, the present invention generally containing (i) a carboxylic acid group with preparing an aqueous monomer solution containing neutralized, monoethylenically unsaturated monomers ( 1) and at least one cross-linking agent ( 3) ( ) be in the aqueous monomer solution comprising the steps of: selectively adding the fine particles of the absorbent polymer ( ) the step of adding at least one component of the polymerization initiator system comprises a polymerization initiator or two or more components in the aqueous monomer solution (Iv) reducing the oxygen content of the aqueous monomer solution (V) the step of filling the aqueous monomer solution to the polymerization reactor (Vi) the polymerization to obtain a polymer gel by polymerizing a monomer in the aqueous monomer solution in the polymerization reactor ( ) and pulverizing the polymer gel phase and, optionally, to release the polymer gel out of the polymerization reactor, thereby obtaining a polymer gel particles by ( ) drying the polymer gel particles (Ix) ppatah the dried polymer gel particles thereto fine particles can by-step to obtain a water-absorbent polymer particles (X) the number of binary ppatah - arranging the water absorbent polymer particles by size And (xi) be the ppatah are arranged in order of size - and a step of treating the surface of the water absorbent polymer particles Wherein the process steps (i) preparation of the aqueous monomer solution: (ia) by mixing an aqueous solution of acrylic acid and sodium hydroxide to obtain a polymerization, at least, at least in part, an aqueous solution of the neutralized acrylic acid partially neutralized acrylic acid (Ib) includes a heat exchanger (2) for cooling the aqueous solution of the neutralized acrylic acid, at least in part by the cooling liquid in steps, wherein the cooling liquid used in the heat exchanger is at least heat of the heated cooling liquid obtained in the heat exchanger (2) portion can be cooled in the absorption c
