The details of how the nucleus manifests that extra energy are complicated, but you can imagine it as like, picking up a certain vibrational frequency.
[0] https://en.wikipedia.org/wiki/Photofission [1] https://en.wikipedia.org/wiki/Isotopes_of_tantalum#Tantalum-...
The half life concept seems to be standard over much of physics.
That a Markov assumption could hold might suggest some new physics.
Now in this case they use lasers. I suspect if you choose the right wavelenght (=frequency) of light there is some sort of resonance phenomenom.
> This nucleus has two very closely adjacent energy states – so closely adjacent that a laser should in principle be sufficient to change the state of the atomic nucleus.
> the correct energy of the thorium transition was hit exactly, the thorium nuclei delivered a clear signal for the first time. The laser beam had actually switched their state.
I don't know enough to explain any further.
The laser is used to transition the nucleus from the ground state to the excited isometric state.
> The decay back to ground state happens at a very precise rate that is not influenced by effectively anything
That sounds contradictory to me.
So they hit their thorium with a laser, and then instead of the laser passing through, it gets absorbed, and then they get a flash of radiation back, letting them know the thorium was excited. The delay between the laser pulse and the flash of radiation is a property of the particular thorium nucleus, and is not affected by environmental circumstances like temperature or electric/magnetic fields, so can be relied on as a very precise measurement of time.
https://en.wikipedia.org/wiki/Hafnium_controversy
This would be Iron Man and Star Wars tech if it worked. Unfortunately experiments went dark after 2009, probably because it worked haha, but maybe because Hf is too rare to make a practical battery. So it looks like they tried spalling element 73 Tantalum (Ta), 74 Tungsten (W) and 75 Rhenium (Re) with protons at 90-650 MeV to create 72 Hf with atomic masses 178, 179 and high spin 178m2, 179m2 isomers if I read this right:
https://publications.jinr.ru/record/151982/files/071%28E6-20...
https://apps.dtic.mil/sti/tr/pdf/ADA525435.pdf
There's a lot here though, so I can't really get a clear picture of what the yields are, or simply how many joules it takes to store one joule in an excited isomer. Which is of course all that matters, but papers often leave off the one part we're curious about, forcing us to learn nearly the entirety of the subject matter to derive it ourselves. Although on the bright side, maybe that protects us from nuclear armageddon and stuff.
Maybe someone can fill us in?
Edit: dangit _Microft beat me by 17 minutes, please answer there :-)