Разрешение применить даёт президент США, но такое разрешение может быть дано заранее, с формулировкой, скажем, "если красные прорвут вот этот оборонительный рубеж". А непосредственно решение на применение - со списком целей и т.д. - вырабатывает как раз штаб корпуса ЕМНИП (надо бы поискать, где я это читал).
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FM 100-15 Corps Operations 1996 г.
Political and strategic objectives rather than tactical
effects will likely guide the employment of
nuclear weapons. Not in all circumstances, but in
some, the corps may be involved in planning the use
of nuclear weapons. In such situations, the corps
will nominate nuclear weapons targets to achieve
operational and tactical objectives that support the
campaign plan. The corps could use nuclear
weapons to-
Create a window for future offensive action.
Destroy, slow, or reduce reinforcing forces.
Create the time and space for maneuver against
attacking echelons.
Destroy high-payoff targets.
Force dispersal of enemy units.
The corps’ plan that supports the nuclear planning
of higher headquarters is called a nuclear option. An
option is the basic element for providing nuclear
support. It is a discrete grouping of nuclear targets,
Operational-level and corps commanders formally
recommend nuclear targets as part of an option.
It has specific yields and is planned for a
specific geographic area, during a short time, and
for a specific purpose.
Planning an option begins with mission receipt...
...
Corps planners develop each option in concert
with the campaign plan and transmit it to higher
headquarters for approval. Throughout the process
each option is treated as a single entity.
Only the President, as a member of the National
Command Authorities (NCA), can authorize the use
(release) of US nuclear weapons. The NCA grants
release through the US military chain of command
to the combatant commander.
A corps commander will not be involved in receiving
release messages. He should, however, receive
operational messages alerting him to the
requirements for nuclear nominations. If the corps
commander feels release of nuclear weapons is
feasible, he may ask the CINC to request release.
The corps also receives strike warnings
(STRIKWARN) from higher headquarters. The
corps uses formal STRIKWARN procedures to
warn lower and adjacent units. (Refer to FM 100-30
for details.)