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Collider experiments put all their energy into $ \sqrt{s} = 2E $ while target experiments only provide $ \sqrt{s} = \sqrt{2Em+m^²} $.

Yet, there are fixed target experiments. Why?

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    $\begingroup$ Well, they are a lot easier to arrange for random mixes of incident particle and target. Not quite sure how Geiger and Marsden would have arranged a collider experiment. $\endgroup$ – Jon Custer Aug 19 at 21:28
  • $\begingroup$ :D I doubt that the Rutherford experiment (didn't hear it as Geiger and Marsden before) is a "particle accelerator", seen in a current technical manner ;) But yet, it is true $\endgroup$ – Ben Aug 19 at 21:35
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    $\begingroup$ Luminosity, cost, the option of continuous operation (no fill-n-spill), ... If your exposure to particle physics had been mostly through the popular press then you probably have a very warped impression of what particle physics consists of. $\endgroup$ – dmckee Aug 19 at 21:35
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    $\begingroup$ The experimental paper was authored by Geiger and Marsden, who worked in Rutherford's lab. en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment $\endgroup$ – Jon Custer Aug 19 at 21:38
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    $\begingroup$ As an aside, the limitations of using natural alpha sources were the motivation for Cockroft and Walton, as well as Van de Graaff, to develop high voltage electrostatic accelerators. Ditto for Wideroe (linac) and Lawrence (cyclotron). Note that none of those were originally colliders yet lots of useful nuclear and particle physics were done with them. $\endgroup$ – Jon Custer Aug 19 at 21:56
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The target density is much greater, i.e you don't have a bullet trying to hit another bullet but rather a single bullet trying to hits lots of (more) densely packed targets. As a result, the luminosity (i.e. the reaction rate) is greater.

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  • $\begingroup$ Is there really such a difference? I thought the emittance(?) would be good enough in colliding experiments respectively quite similar? $\endgroup$ – Ben Aug 19 at 21:38
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    $\begingroup$ there is a huge difference.... several orders of magnitude depending on the targets. $\endgroup$ – ZeroTheHero Aug 19 at 21:38
  • $\begingroup$ Plus, colliders may be hard to arrange. It is easy to accelerate protons at a gold target. Much harder to arrange a collider with proton and gold beams. And then do protons on to silver next hour, then alphas on to gold, then silver... $\endgroup$ – Jon Custer Aug 19 at 21:58
  • $\begingroup$ @Jon One of my grad school buddies ended up at RHIC for about a decade. That's what their life was like, but with added gold-on-gold, lead-on-lead, ... $\endgroup$ – dmckee Aug 19 at 22:01
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    $\begingroup$ Maybe you can develop an intuition for the difference in density by considering that an accelerator is not filled with drops of, say, liquid hydrogen. If I have the numbers correct the LHC contains 10^14 protons at any given time. 1g (~ 15mL) of liquid hydrogen contains 10^23 protons -- 10^9 times more. One reason for the difference is of course the same reason why I differentiated between hydrogen and the protons which are what actually circulates around the LHC: in a fixed target you have electrically neutral substances which can be packed much more tightly -- but which can't be accelerated. $\endgroup$ – tobi_s Aug 20 at 9:19

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