An electrochemical storage cell or battery with at least one anode filled with a molten alkali metal as the anolyte and at least one cathode chamber filled with a sulfur-containing catholyte substance with the anode chamber and the cathode chamber separated from each other by an alkali-ion-conducting solid electrolyte. To the catholyte substance is added an additive which converts the sulfur chains into an electrically charged state for obtaining electromigration of the sulfur phase. This induces mobilization of the sulfur phase in the cathode chamber and prevents major accumulation of liquid sulfur as an insulator. As a result the cell can be repeatedly recharged with large currents to a greater capacity. Additives are a dienophilic compound or a reaction product of a dienophilic compound and sulfur.