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A pair of electrodes of discharge (15a and 15b) are laid out face to face in the longitudinal direction of a tube with arc (14) carried out in glass of permeable quartz to the ultraviolet rays and delimiting a space of discharge (13) hermetic to the air, filled up of a mixture of filling containing a sufficient quantity of rare gas to maintain the discharge arc, mercury, a luminescent metal and a halogen constitutes an ultraviolet lamp (100), emitting in the ultra-violet in mode of lighting. This lamp UV is placed in the interior tube (21) of a unit of cooling (200) to double permeable tubes with the ultraviolet rays. A coolant 24 intended to cool lamp UV (100) there circulates between its interior tubes (21) and outsides (22). The distance D [mm] of lamp UV (100) to the interior tube (21) is connected to its power of entry P [W/cm] by the relation D ≤ -0, 2 P + 35, with 120 ≤ P ≤ 170.