(2) Amount of Allowance. — Upon receipt by the board of proof of the death of any member as set forth in subdivision (1) of this section, the amount of any accumulated total deductions credited to his account in the annuity savings fund or the amount of any cash refund or pro rata payment of allowance due under the provisions of subdivision (2) of section eleven, as the case may be, shall be paid in one sum in accordance with the provisions of such subdivision to his surviving beneficiary or beneficiaries entitled thereto. In addition to any such payment, there shall be paid to such member's dependent beneficiary or beneficiaries, as hereinafter designated in this subdivision, an accidental death benefit allowance to consist of a yearly amount of pension equal to seventy-two per cent of the annual rate of regular compensation of such member on the date such injury was sustained or such hazard was undergone, or equal to seventy-two per cent of the average annual rate of his regular compensation for the twelve-month period for which he last received regular compensation immediately preceding the date of his death, whichever is greater; provided, that in the event an allowance is paid under this section as the result of the death of a member who had previously been retired for accidental disability, the amount of such allowance shall not be less than the annual amount of the pension portion of the allowance payable to such retired employee as of the date of his death. Such pension shall become effective as of the date of the death of such member and payments thereunder shall be made as provided for in section 13; provided, however, that if a beneficiary is eligible for benefits under this section and under option (c) of section 12, the beneficiary shall elect to receive either a benefit under option (c) or a benefit pursuant to this section but shall not be eligible for both benefits; and provided further, that a full benefit provided under this section and a full benefit provided under option (c) shall not be paid concurrently to 2 different beneficiaries on account of 1 member. Such pension shall be subject to the provisions of paragraph (2) (b) of section seven and to the provisions of sections fourteen and fifteen and shall be paid—

1. (a) To the surviving spouse of such member so long as such spouse survives; provided, that they had been living together at the time of such member's death or the board finds that they had been living apart at such time for justifiable cause or because of the desertion of such spouse by such member; and provided further, that if an ex-spouse is named as an option (c) beneficiary pursuant to a qualified domestic relations order on file with the retirement board, the option (c) benefit shall be paid and any amount so paid shall be deducted from the benefit calculated pursuant to this subdivision.
2. (b) If at any time there is no spouse eligible to receive such pension under the provisions of paragraph (a) of this subdivision, then it shall be paid to a legal guardian for the benefit of any surviving unmarried children of such member who are under age 18, or are over that age and under age 22 and full-time students at accredited educational institutions, or who were over said age and physically or mentally incapacitated from earning on the date of such member's death. Such pension shall be divided for the benefit of such children in such manner as the board shall from time to time determine, and shall be paid so long as any such child survives, remains unmarried and is under age 18, or is over that age and under age 22 and is a full-time student at an accredited educational institution, or if over said age remains physically or mentally incapacitated from earning.
3. (c) If on the date of the death of such member there is no person eligible to receive such pension under the provisions of either paragraph (a) or (b) of this subdivision, then it shall be paid to the surviving totally dependent father or mother of such member or to both and to the survivor of them or if none such, then to any totally dependent unmarried or widowed sister of such member with whom he was living at the time of his death, so long as such beneficiary or beneficiaries survive, do not marry or remarry, and are unable to support themselves. The words ''full-time student'' shall mean a child who is in full-time attendance in an accredited educational institution offering full-time courses of study equivalent to or higher than secondary school study. The words ''accredited educational institution'' shall mean a school, college or university that is licensed, approved or accredited, as the case may be, in the state in which it is located.
4. (d) If there are any surviving unmarried children of such member who are under age eighteen or who are over said age and physically or mentally incapacitated from earning on the date of his death, or who are over said age and under age 22 and full-time students at an accredited educational institution, an additional pension at the rate of three hundred and twelve dollars yearly shall be paid for each such child to the child's natural or legal guardian so long as such child survives, remains unmarried, and is under age eighteen or if over said age remains physically or mentally incapacitated from earning or, if over said age and under age 22 remains a full-time student. The words ''full-time student'' shall mean a child who is in full-time attendance in an accredited educational institution offering full-time courses of study equivalent to or higher than secondary school study. The words ''accredited educational institution'' shall mean any school, college, or university that is licensed, approved or accredited, as the case may be, in the state in which it is located.
5. (i) In the state employees' and teachers' retirement systems, the additional pension shall be fixed at a rate equal to the additional pension determined by the actuary under clause (iii) of paragraph (a) of subdivision (2) of section 7 and shall be increased by an amount equal to the percentage increase of the cost-of-living increase determination made by the general court for each year under section 102.
6. (ii) Any system which has adopted the supplemental dependent allowance under clause (iii) of paragraph (a) of subdivision (2) of section 7, may accept the provisions of this clause by an affirmative vote of the retirement board, ratified by the chief executive officer and legislative body as defined in paragraph (c) of subdivision (8) of section 22, but, in a regional retirement system, the ''chief executive officer and legislative body'' shall mean the regional retirement board advisory council, and the additional pension shall be fixed at a rate equal to the additional pension determined by the actuary under said clause (iii) of said paragraph (a) of said subdivision (2) of said section 7 and shall be increased by an amount equal to the percentage increase of the cost-of-living increase determination made by the general court for each year under section 102. Any increased benefits provided by the acceptance of this clause shall be paid from the date of acceptance and shall not be paid retroactively. Acceptance of this clause may not be revoked. Acceptance of this clause shall be considered to have occurred upon the filing of certification of this vote with the commission.
7. (e) In no event shall the total yearly amount of all pensions provided for under this section on account of any member exceed the greater of the annual rate of his regular compensation on the date such injury was sustained or such hazard was undergone and the average annual rate of his regular compensation for the twelve-month period for which he last received regular compensation immediately preceding the date of his death. If at any time the calculated total amount of such pensions shall exceed such greater annual rate, the amounts of pensions provided for under paragraph (d) of this subdivision shall be prorated among those entitled to receive them so that such total amount shall thereby be reduced to equal such greater annual rate.