I don't know enough about neutron physics to comment usefully on your mean free path logic, but I do know that solar eruptive activity can launch relativistic neutrons at Earth which can be detected even at sea level using scintillators, and that mountaintop detection has been around since the early 1980s. Shibata 1994, Propagation of Solar Neutrons <https://sci-hub.se/https://doi.org/10.1029/93JA03175>, ยง4.2.1 (Fig 3) higher energy neutrons get further into the atmosphere, so I don't think the atmosphere is much of a barrier for the comparable (MeV-GeV) teleported neutron-star neutrons.
We seem to agree that free neutrons don't stay free neutrons when they slam into the solid earth.
I too wanted to think about neutrons as a non-self-interacting gas, but that just doesn't work: Meyer 1994, https://ned.ipac.caltech.edu/level5/Sept01/Meyer/Meyer3.html (Paragraph beginning with, "Only the strong gravity of the neutron star keeps such matter from exploding apart." Cold in this context is partly explained in the preceding paragraph; in inner regions the matter is a degenerate gas meaning the particle kinetic energy becomes dependent on the density or equivalently pressure becomes independent of temperature; even at enormous pressures, degenerate gases don't hold much thermal energy -- that was practically all radiated away when the NS was young. Our teleporting (of inner region matter) therefore engages a very low-entropy r-process.
Outer regions are just too complicated and varied for a HN comment. The crust is thin -- a few to a few hundred metres or so compared to an NS radius of ~ 10km. It's also much less dense, so is a small fraction of the NS mass, and thus maybe not a target for our teleportation. Here's a 180-page open access review: https://link.springer.com/article/10.12942/lrr-2008-10 Pesky electrons and protons complicating things.
If I'm reading that figure right, at sea level the attenuation is at least a factor of 2000 for all energies they're graphing. That sounds about right to me.
I realise now that I may have been unclear in intent previously: if you look at figure 2, and then consider a typical solid or liquid's cross sectional mass density, hopefully that explains why I was speaking of neutron mean free path of centimetres โ 100g/cm^2 is 1m of water.
However this is just the initial condition, and I don't think this scenario is one where the atmospheric density can be accurately approximated as constant over time.
I wouldn't sweat it, and I don't know enough about the nuclear physics to keep up (and we haven't even been talking about the neutrino energy in beta- decays, the gamma spectrum, or what becomes of the electrons; resonances go way over my head). This isn't really a gravitational problem (but...footnote [1]), so I'm not so useful here.
So, more for the original questioner than for us:
What's inside a neutron star stays inside a neutron star. Unless of course the NS is destroyed via e.g. collision, tidal disruption, or infall pushing it over a mass limit like Tolman-Oppenheimer-Volkoff.
Sci-Fi teleporters don't exist, and there's no basis to think they ever will.
The closest neutron stars are between hundreds and a thousand light-years away and IIRC all the close ones are isolated (in the sense of no stellar multiplicity; they have no binary partner(s)).
Consequently what ben_w and I have been yakking about is inaccessible to experiment (we can't generate the relevant pressures, and artificial neutron sources are not very bright yet (pardon the BrightnESS pun, <https://europeanspallationsource.se/about>)).
It's not accessible to astronomical observation either. The closest physical phenomenon I can think of is an NS mass ejection (for which there is an ample and active academic literature), and that's far from a close match. At least in some parts of the spectrum we can see a large NS mass ejection -- large meaning somewhere around 10% of the mass of the sun -- but there's practically no hope to see just a spoonful, and not hurled into a close-by planet's atmosphere or even that of a noncompact companion star.
So the answer to the question ultimately is -- if we imagined the magical arrival of a small ball of NS matter on Earth at rest on the Earth's surface -- "complex nuclear physics" is in the details of the practically-instantaneous kaboom, and a lot of that complexity is because the Earth is not the practical vacuum around a neutron-star/neutron-star collision that ejects a lot more than a spoonful of material.
- --
footnote [1]: I mean, one can think of it in terms of Raychaudhuri's equation (and that's where I started, in fact): the initial radial divergence of the acceleration vector from the sudden release of pressure dominates, causing the bits to tend to fly away beyond the hope of recollapse. But the solid earth (and as the thread involved, considerations of nuclear interactions even in the atmosphere) generates enormous shear via contact forces, so some of the energy-density of the NS matter will stick around, and in due course what wasn't ejected "to infinity" settles back to a basically round Earth (hydrostatic equilibirium returns). From this perspective comparing the NS matter with an asteroid impact makes sense to me, but probably undersells the nuclear fallout.
We seem to agree that free neutrons don't stay free neutrons when they slam into the solid earth.
I too wanted to think about neutrons as a non-self-interacting gas, but that just doesn't work: Meyer 1994, https://ned.ipac.caltech.edu/level5/Sept01/Meyer/Meyer3.html (Paragraph beginning with, "Only the strong gravity of the neutron star keeps such matter from exploding apart." Cold in this context is partly explained in the preceding paragraph; in inner regions the matter is a degenerate gas meaning the particle kinetic energy becomes dependent on the density or equivalently pressure becomes independent of temperature; even at enormous pressures, degenerate gases don't hold much thermal energy -- that was practically all radiated away when the NS was young. Our teleporting (of inner region matter) therefore engages a very low-entropy r-process.
Outer regions are just too complicated and varied for a HN comment. The crust is thin -- a few to a few hundred metres or so compared to an NS radius of ~ 10km. It's also much less dense, so is a small fraction of the NS mass, and thus maybe not a target for our teleportation. Here's a 180-page open access review: https://link.springer.com/article/10.12942/lrr-2008-10 Pesky electrons and protons complicating things.