Nuclear weapons were invented with one clear purpose in mind- wiping out the enemy. Since their creation, nukes have been used primarily in clandestine tests, and as a way for nations with nukes to flex their militaristic muscle.
Before (and perhaps a bit after) the nuke holding nations of the world realized the damaging long term effects of radiation exposure they had all kinds of wacky ideas in mind about what to do with their destructive new toys.
Nuking Canada for oil, detonating a nuke on the moon, and creating a massive lake in Egypt by detonating 200 hydrogen bombs in the Qattara Depression were all kicked around by madmen scientists who really should have known better than to use nuclear technology as a development tool!
Read on to discover The Ten Most Bizarre Ideas For Using Nuclear Weapons
I mean . . . using H-bombs to build a new lake or harbor?
I can't comment on the tree biology, but one potential problem with trees is that light elements, especially hydrogen, are really effective at slowing down neutrons. So things like water and organic compounds, meaning thicker trees or stuff in the soil might not get much neutron radiation (still plenty of gamma around) depending on its distance from the bomb. On the other end you'll get neutron activation of elements in the area, leading to weeks or longer of radioactivity in the area depending on what is around and what type of bomb was used. Insects also tend to handle 10 times or more as much radiation as vertebrates, and might survive up until close enough to be killed by the blast or fire.
In other words, it is one of those things that probably needs a lot of simple but monotonous calculations and a good materials reference book... and could go either way. Or digging through badly scanned reports from the Cold War when way too many calculations on radiation damage was done, probably including effects on trees and insects.
Leukemia is sometimes treated by removing bone marrow from the patient and then using drugs to kill the leukemic cells, leaving normal blood stem cells alive. The patient's body is then irradiated to kill the rest of their bone marrow, and the extracted stem cells are injected into the bone to re-populate it. (or a bone marrow transplant is performed). The idea is that the largely non-living structure of the bone will be retained, and will provide a scaffold on which the healthy cells will establish themselves.
One day, I was looking at a tree that was riddled with the holes left by some kind of beetle. The beetle larvae killed the tree, but the dead wood retained the overall shape of the tree when it was alive. Trees are made largely of non-living material, with a thin layer of living cells called the cambium layer (not to be confused with the cambrian layer, which is a geologic stratum formed half a billion years ago). If the living cells of the cambium could be extracted and grown in cell culture, an infected tree could then be irradiated to kill off invading beetles. The cells could then be re-introduced into the cambium layer to re-populate the structure of the tree and restore it to its healthy, living condition.
Unlike humans, though, a tree cannot be moved into a nuclear medicine facility for radiation treatments. Some means would be needed to bring the irradiation to the tree. Happily, our military already developed the notorious neutron bomb. Remember, this bomb is able to kill all living things, but leave buildings intact. Bark beetle (or fungal disease) infections of trees never occur in isolation, but are area-wide effects, which are just the right scale for the neutron bomb. A forest that is suffering from an infestation could be sterilized by neutron bomb, and then the trees could be revitalized by infiltration with new cells.
By extension, whole neighborhoods could be rid of pests, such as roaches, termites, fire ants, bedbugs or rodents by evacuating the people and their pets, followed by a neutron bomb blast. Minor structural damage could be repaired, and then people could return. They would have to re-seed their lawns and gardens, but would start from a clean slate, pest-wise.