To approximate the expected number of multi-way collisions, I used a simple physical model where nuclei are spheres with density 2.5e17 kg/m^3 and they interact if the centre of one goes within another.   Then in the code below I work out a "volume fraction" of the focal ellipsoid that is filled and an "area fraction" that is filled in 2D projection seen from the side with largest area.   2-way collisions are expected to occur N*Afrac times and this matches the traditional luminosity formula if you expand it out.   True 3-way collisions require an additional factor of Vfrac to get the 3rd nucleus exactly where you want it at that instant, whereas chained 3-way collisons (two consecutive collisions within the focal point) require only a factor of Afrac, which is larger.   This gave the graphs in my previous post.   The numbers behave similarly with a small shift for different nuclei although I used calcium as a mid-Z choice.   Things like the D-T resonance are not included!
<br />#accelerators #physics <p><a href='posts/202603/post-20260306-165442-a.png'><img src='posts/202603/post-20260306-165442-a.png' loading='lazy' /></a></p>