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Short version: I think this story is almost certainly "Aspic's Mystery" a short story by Arsen Darnay. Originally published in Analog in 1976, it was later anthologised in "Space Mail, Volume II" which is probably where you read it. The text is available online at the Luminist Archives where you can find the September 1976 issue of Analog.

Long version: As I remarked in a comment, the "atomic priesthood" reminded me strongly of a novella by Arsen Darnay entitled "Plutonium" published in Galaxy 1976. This deals with a future history in which the long-term storage of nuclear waste is done by a "priesthood" specifically set up for this purpose - the point being that only institutions like the Roman Catholic church have demonstrated the kind of longevity comparable to the half-life of plutonium (24000 years). The monks are conditioned to seek out and hoard radioactive waste, and in particular they have a holy ritual in which they rub the waste against their skins (their equivalent of communion). To ensure that the order does not die out, some mad-science was employed so that the priests are reincarnated. So the cycle endlessly repeats: they work with radioactive material, the material kills them, they are reborn and return to their lethal work.

This does not fit the other details provided by the OP, but Darnay wrote a number of works set in this universe. In particular "Aspic's Mystery" seems an excellent fit to the question. This deals with the reminiscences of Hamsters Dugout, one of the Plutonium Priests. He is investigating the origin of the order, and has managed to extract some ancient documents from a rusted safe. Deep within the monastery are tanks and vats of "godbod" (the radioactive waste), which gives the monk a type of holy ecstasy when he feels its radiation on his skin.

As the OP recalls, the monastery contains a Mystery (which has been destroyed/gone missing):

The stories had it that the Mystery consisted of three rooms. Each room was named as follows: Power, Signal Acquisition, and Conditioning... Only the Abbot could enter Power (or so the brothers speculated), and that explained why the abbots had so brief a life. Godbod's love called them to an early bliss.

The monastery is in decay, and a new faction has arisen, which wants to cover the sacred godbod with the heretical metal, lead, which blocks its radiation. The monk is furious about this, but does not throw himself in the waste as the question mentions. He is clearly in the last stages of radiation sickness, and just hopes to die before the desecration occurs.

Short version: I think this story is almost certainly "Aspic's Mystery" a short story by Arsen Darnay. Originally published in Analog in 1976, it was later anthologised in "Space Mail, Volume II" which is probably where you read it. The text is available online at the Luminist Archives where you can find the September 1976 issue of Analog.

Long version: As I remarked in a comment, the "atomic priesthood" reminded me strongly of a novella by Arsen Darnay entitled "Plutonium" published in Galaxy 1976. This deals with a future history in which the long-term storage of nuclear waste is done by a "priesthood" specifically set up for this purpose - the point being that only institutions like the Roman Catholic church have demonstrated the kind of longevity comparable to the half-life of plutonium (24000 years). The monks are conditioned to seek out and hoard radioactive waste, and in particular they have a holy ritual in which they rub the waste against their skins (their equivalent of communion). To ensure that the order does not die out, some mad-science was employed so that the priests are reincarnated. So the cycle endlessly repeats: they work with radioactive material, the material kills them, they are reborn and return to their lethal work.

This does not fit the other details provided by the OP, but Darnay wrote a number of works set in this universe. In particular "Aspic's Mystery" seems an excellent fit to the question. This deals with the reminiscences of Hamsters Dugout, one of the Plutonium Priests. He is investigating the origin of the order, and has managed to extract some ancient documents from a rusted safe. Deep within the monastery are tanks and vats of "godbod" (the radioactive waste), which gives the monk a type of holy ecstasy when he feels its radiation on his skin.

As the OP recalls, the monastery contains a Mystery (which has been destroyed/gone missing):

The stories had it that the Mystery consisted of three rooms. Each room was named as follows: Power, Signal Acquisition, and Conditioning... Only the Abbot could enter Power (or so the brothers speculated), and that explained why the abbots had so brief a life. Godbod's love called them to an early bliss.

The monastery is in decay, and a new faction has arisen, which wants to cover the sacred godbod with the heretical metal, lead, which blocks its radiation. The monk is furious about this, but does not throw himself in the waste as the question mentions. He is clearly in the last stages of radiation sickness, and just hopes to die before the desecration occurs.

Short version: I think this story is almost certainly "Aspic's Mystery" a short story by Arsen Darnay. Originally published in Analog in 1976, it was later anthologised in "Space Mail, Volume II" which is probably where you read it. The text is available online at the Luminist Archives where you can find the September 1976 issue of Analog.

As I remarked in a comment, the "atomic priesthood" reminded me strongly of a novelette by Arsen Darnay entitled "Plutonium" published in Galaxy 1976. This deals with a future history in which the long-term storage of nuclear waste is done by a "priesthood" specifically set up for this purpose - the point being that only institutions like the Roman Catholic church have demonstrated the kind of longevity comparable to the half-life of plutonium (24000 years). The monks are conditioned to seek out and hoard radioactive waste, and in particular they have a holy ritual in which they rub the waste against their skins (their equivalent of communion). To ensure that the order does not die out, some mad-science was employed so that the priests are reincarnated. So the cycle endlessly repeats: they work with radioactive material, the material kills them, they are reborn and return to their lethal work.

This does not fit the other details provided by the OP, but Darnay wrote a number of works set in this universe. In particular "Aspic's Mystery" seems an excellent fit to the question. This deals with the reminiscences of Hamsters Dugout, one of the Plutonium Priests. He is investigating the origin of the order, and has managed to extract some ancient documents from a rusted safe. Deep within the monastery are tanks and vats of "godbod" (the radioactive waste), which gives the monk a type of holy ecstasy when he feels its radiation on his skin.

As the OP recalls, the monastery contains a Mystery (which has been destroyed/gone missing):

The stories had it that the Mystery consisted of three rooms. Each room was named as follows: Power, Signal Acquisition, and Conditioning... Only the Abbot could enter Power (or so the brothers speculated), and that explained why the abbots had so brief a life. Godbod's love called them to an early bliss.

The monastery is in decay, and a new faction has arisen, which wants to cover the sacred godbod with the heretical metal, lead, which blocks its radiation. The monk is furious about this, but does not throw himself in the waste as the question mentions. He is clearly in the last stages of radiation sickness, and just hopes to die before the desecration occurs.

Short version: I think this story is almost certainly "Aspic's Mystery" a short story by Arsen Darnay. Originally published in Analog in 1976, it was later anthologised in "Space Mail, Volume II" which is probably where you read it. The text is available online at the Luminist Archives where you can find the September 1976 issue of Analog.

Long version: As I remarked in a comment, the "atomic priesthood" reminded me strongly of a novella by Arsen Darnay entitled "Plutonium" published in Galaxy 1976. This deals with a future history in which the long-term storage of nuclear waste is done by a "priesthood" specifically set up for this purpose - the point being that only institutions like the Roman Catholic church have demonstrated the kind of longevity comparable to the half-life of plutonium (24000 years). The monks are conditioned to seek out and hoard radioactive waste, and in particular they have a holy ritual in which they rub the waste against their skins (their equivalent of communion). To ensure that the order does not die out, some mad-science was employed so that the priests are reincarnated. So the cycle endlessly repeats: they work with radioactive material, the material kills them, they are reborn and return to their lethal work.

This does not fit the other details provided by the OP, but Darnay wrote a number of works set in this universe. In particular "Aspic's Mystery" seems an excellent fit to the question. This deals with the reminiscences of Hamsters Dugout, one of the Plutonium Priests. He is investigating the origin of the order, and has managed to extract some ancient documents from a rusted safe. Deep within the monastery are tanks and vats of "godbod" (the radioactive waste), which gives the monk a type of holy ecstasy when he feels its radiation on his skin.

As the OP recalls, the monastery contains a Mystery (which has been destroyed/gone missing):

The stories had it that the Mystery consisted of three rooms. Each room was named as follows: Power, Signal Acquisition, and Conditioning... Only the Abbot could enter Power (or so the brothers speculated), and that explained why the abbots had so brief a life. Godbod's love called them to an early bliss.

The monastery is in decay, and a new faction has arisen, which wants to cover the sacred godbod with the heretical metal, lead, which blocks its radiation. The monk is furious about this, but does not throw himself in the waste as the question mentions. He is clearly in the last stages of radiation sickness, and just hopes to die before the desecration occurs.

As I remarked in a comment, the "atomic priesthood" reminded me strongly of a novelette by Arsen Darnay entitled "Plutonium" published in Galaxy 1976. This deals with a future history in which the long-term storage of nuclear waste is done by a "priesthood" specifically set up for this purpose - the point being that only institutions like the Roman Catholic church have demonstrated the kind of longevity comparable to the half-life of plutonium (24000 years). The monks are conditioned to seek out and hoard radioactive waste, and in particular they have a holy ritual in which they rub the waste against their skins (their equivalent of communion). To ensure that the order does not die out, some mad-science was employed so that the priests are reincarnated. So the cycle endlessly repeats: they work with radioactive material, the material kills them, they are reborn and return to their lethal work.

This does not fit the other details provided by the OP, but Darnay wrote a number of works set in this universe. In particular "Aspic's Mystery", published in 1976 in Analog seems an excellent fit to the question. This deals with the reminiscences of Hamsters Dugout, one of the plutonium priests. He is investigating the origin of the order, and has managed to extract some ancient documents from a rusted safe. Deep within the monastery are tanks and vats of "godbod" (the radioactive waste), which gives the monk a type of holy ecstasy when he feels its radiation on his skin.

As the OP recalls, the monastery contains a Mystery (which has been destroyed/gone missing):

The stories had it that the Mystery consisted of three rooms. Each room was named as follows: Power, Signal Acquisition, and Conditioning... Only the Abbot could enter Power (or so the brothers speculated), and that explained why the abbots had so brief a life. Godbod's love called them to an early bliss.

The monastery is in decay, and a new faction has arisen, which wants to cover the sacred godbod with the heretical metal, lead, which blocks its radiation. The monk is furious about this, but does not throw himself in the waste as the question mentions. He is clearly in the last stages of radiation sickness, and just hopes to die before the desecration occurs.

Short version: I think this story is almost certainly "Aspic's Mystery" a short story by Arsen Darnay. Originally published in Analog in 1976, it was later anthologised in "Space Mail, Volume II" which is probably where you read it. The text is available online at the Luminist Archives where you can find the September 1976 issue of Analog.

As I remarked in a comment, the "atomic priesthood" reminded me strongly of a novelette by Arsen Darnay entitled "Plutonium" published in Galaxy 1976. This deals with a future history in which the long-term storage of nuclear waste is done by a "priesthood" specifically set up for this purpose - the point being that only institutions like the Roman Catholic church have demonstrated the kind of longevity comparable to the half-life of plutonium (24000 years). The monks are conditioned to seek out and hoard radioactive waste, and in particular they have a holy ritual in which they rub the waste against their skins (their equivalent of communion). To ensure that the order does not die out, some mad-science was employed so that the priests are reincarnated. So the cycle endlessly repeats: they work with radioactive material, the material kills them, they are reborn and return to their lethal work.

This does not fit the other details provided by the OP, but Darnay wrote a number of works set in this universe. In particular "Aspic's Mystery" seems an excellent fit to the question. This deals with the reminiscences of Hamsters Dugout, one of the Plutonium Priests. He is investigating the origin of the order, and has managed to extract some ancient documents from a rusted safe. Deep within the monastery are tanks and vats of "godbod" (the radioactive waste), which gives the monk a type of holy ecstasy when he feels its radiation on his skin.

As the OP recalls, the monastery contains a Mystery (which has been destroyed/gone missing):

The stories had it that the Mystery consisted of three rooms. Each room was named as follows: Power, Signal Acquisition, and Conditioning... Only the Abbot could enter Power (or so the brothers speculated), and that explained why the abbots had so brief a life. Godbod's love called them to an early bliss.

The monastery is in decay, and a new faction has arisen, which wants to cover the sacred godbod with the heretical metal, lead, which blocks its radiation. The monk is furious about this, but does not throw himself in the waste as the question mentions. He is clearly in the last stages of radiation sickness, and just hopes to die before the desecration occurs.