Upon the accidental death of a member before retirement; provided, that evidence is submitted to the retirement board proving that the death of the member was the natural and proximate result of an accident while in the performance of duty at some definite time and place, and that the death was not the result of willful negligence on the member’s part, the member’s accumulated contributions shall be paid to the member’s estate, or to the person having an insurable interest in the member’s life that the member has nominated by written designation, duly executed and filed with the retirement board, and, upon application by or on behalf of the dependents of the deceased member, the retirement board shall grant a benefit equal to one-half (½) the rate of compensation of the member in effect at the date of death:

(1)  To his or her widow or widower or domestic partner, to continue for life unless he or she remarries or enters into a domestic partnership; or

(2)  If there is no widow or widower or domestic partner, or if the widow or widower or domestic partner dies or remarries or enters into a domestic partnership before any child of the deceased member has attained the age of eighteen (18) years, then to his or her child or children under that age, divided in any manner that the retirement board in its discretion determines, to continue as a joint and survivor annuity of one-half (½) of that compensation until every child dies or attains that age; or

(3)  If there is no widow, widower, or domestic partner or child under the age of eighteen (18) years surviving the deceased member, then to his or her dependent father or mother, as the deceased member has nominated by written designation, duly acknowledged and filed with the retirement board; or if there is no nomination, then to his or her dependent father or to his or her dependent mother, as the retirement board in its discretion directs, to continue for life.