Consequent on the death of a Scheme member or former Scheme member and to whom or in respect of whom a pension or death gratuity, or preserved pension or lump sum payment has been or may be awarded, the Minister may, where the deceased member is survived by one or more dependent children, grant for such children a pension (in this Part referred to as a "children's pension") in respect of the deceased member's service as a pensionable public servant.