This mod (lite esp) increases the radiation duration timer for the Fat Man mini nuke explosion, nuka grenade, and car explosion to 7 days, up from 30 seconds.
The hardcore esp increases the timer instead to 1 year of game time and the persistent rad effect to 250 magnitude. (Sure, it's not technically forever, but I've never played a F4 character that was around for a whole in game year anyway.)
The hardercore esp requires hardcore, and further adjusts fat man explosion radius to the MaxiNuke "smaller" file (Much, much larger than vanilla) and applies a similar set of values, only divided by 6, to the mirv explosion.
Secondary changes include upping the standard fat man explosion to very high stagger, the MIRV explosions to high, and removing LOS checks, and adding a rad burst of 550 rads at the mini nuke explosion.

I made this because I wanted a more tangible representation of the caustic nature of atomic warfare in the player's control. I was inspired by thinking I saw a mod that did this already and not finding one. I feel this makes the fat man more unique than just a mega rocket launcher with less thrust. This will make you more apprehensive of using nuclear arms near your settlement, which I also feel fits the theme nicely.

Compatibility:
This was built on Fat Man Radiation Hazard by fadingsignal, so it supersedes that mod's functions. Head on over there to grab a download and drop an endorsement, cause they were very generous to let me build on their esp instead of mimicking it myself.
This will conflict with mods that edit the nuka grenade or fat man or mirv's explosion damage, I.e., fat man overhauls. I want to make this mod compatible with your favorite nuclear weapons and explosions! (At least the best I can. I can confidently add the fatman effect to other explosions, but creating a new custom effect for a mod that doesn't already have one will still be new to me.)
I'm currently waiting on a new custom pc that'll be in in a few weeks to actually dive into my new fallout builds and see the mod in effect in person, so if there's other explosions already in the game that you think fit this profile, I'll do my best to add patches for them, along with other nuclear themed mods. I want to make this feel like a system level standard for radiation.

Patches:
Fatman (Fat Man) Weapon Rework - Mav's Marvelous Mods - Patch available. Doesn't actually require the rework, just applies these changes on top of MMM's adjusted explosion values. Load after Fat Man Rework. This is unnecessary if you're using another patch, all it does is edit the base explosion entries to match MMM and will be overwritten in complete by another patch.
Fat Man Artillery Piece - No conflicts, but I don't know if it will be affected by FR. That mod appears to function by script, rather than simple fo4edit values, so it's beyond me.
Power of Atom - Patch available. See Load Order guide below. V3 radburst addition does not affect this mod
XXL Nukes - Patch available. See Load Order guide below. V3 radburst is less noticeable with this patch than with a standard version, since pretty much anything that would recieve the rads gets fried by the damage effects, but it should still be working as intended.

Delta Patch
This file requires Wasteland Ballistics vanilla lasers version and XXL Nukes. This is intended to be used alongside MMM (no MMM patch), Hardcore, EvenHarderCore, and XXL HC and EHC patches for a cohesive experience. This is the one that I personally use, and I feel that it has the best of all worlds. This particular one will not be supported for use with any other configuration of files than the ones described above.


Installation:
Lite version - Use only the light esp (and any "L" patches)
For Hardcore - Use only the hardcore esp (and any "HC" patches)
For Even Hardercore - Use Hardcore esp AND even hardercore esp (and both "HC" and "EHC" patches)
Loading this after another mod that edits the same explosion entries without a patch will overwrite it's changes to default damage values, but with the long timer.

Load Order: 
Base version.esp (Lite or Hardcore)
(Optional) Even Hardercore.esp
Power of Atom or XXL Nukes
Patches
OR:
Base version.esp (Lite or Hardcore)
(Optional) Even Hardercore.esp
MMM Patch

Credits:
fadingsignal for the oh-so-important for continuity Fat Man Radiation Hazard mod, which fixed a stereotypical oversight by Bethesda.
My work was much easier for their permission to release a modified version of their esp.