Impact parameter

<h2 id="scattering-from-a-hard-sphere">Scattering from a hard sphere</h2>
<p>The simplest example illustrating the use of the impact parameter is in the case of scattering from a  sphere. Here, the object that the projectile is approaching is a hard sphere with radius 
  
    
      
        R
      
    
    {\displaystyle R}
  
. In the case of a hard sphere, 
  
    
      
        U
        (
        r
        )
        =
        0
      
    
    {\displaystyle U(r)=0}
  
 when 
  
    
      
        r
        >
        R
      
    
    {\displaystyle r>R}
  
, and 
  
    
      
        U
        (
        r
        )
        =
        ∞
      
    
    {\displaystyle U(r)=\infty }
  
  for 
  
    
      
        r
        ≤
        R
      
    
    {\displaystyle r\leq R}
  
. When 
  
    
      
        b
        >
        R
      
    
    {\displaystyle b>R}
  
, the projectile misses the hard sphere. We immediately see that 
  
    
      
        θ
        =
        0
      
    
    {\displaystyle \theta =0}
  
. When 
  
    
      
        b
        ≤
        R
      
    
    {\displaystyle b\leq R}
  
, we find that 
  
    
      
        b
        =
        R
        cos
        ⁡
        
          
            
              θ
              2
            
          
        
        .
      
    
    {\displaystyle b=R\cos {\tfrac {\theta }{2}}.}
  
<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>
</p>
<h2 id="collision-centrality">Collision centrality</h2>
<p>In <a href="/facts/Particle_physics/YgIuyj2t">high-energy nuclear physics</a> — specifically, in <a href="/facts/Collider/j6wTDohV">colliding-beam experiments</a> — collisions may be classified according to their impact parameter. Central collisions have 
  
    
      
        b
        ≈
        0
      
    
    {\displaystyle b\approx 0}
  
, peripheral collisions have 
  
    
      
        0
        <
        b
        <
        2
        R
      
    
    {\displaystyle 0<b<2R}
  
, and ultraperipheral collisions (UPCs)<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> have 
  
    
      
        b
        >
        2
        R
      
    
    {\displaystyle b>2R}
  
, where the colliding <a href="/facts/Atomic_nucleus/orpIm5Xl">nuclei</a> are viewed as <a href="/facts/Hard_spheres/91Gfe05N">hard spheres</a> with radius 
  
    
      
        R
      
    
    {\displaystyle R}
  
.
</p><p>Because the <a href="/facts/Strong_interaction/JjRsKcLg">color force</a> has an extremely short range, it cannot couple quarks that are separated by much more than one <a href="/facts/Nucleon/6fguU9Xk">nucleon</a>'s radius; hence, strong interactions are suppressed in peripheral and ultraperipheral collisions. This means that final-state particle multiplicity (the total number of particles resulting from the collision), is typically greatest in the most central collisions, due to the <a href="/facts/Parton_(particle_physics)/XDuqEaqN">partons</a> involved having the greatest probability of interacting in some way. This has led to <a href="/facts/Charged_particle/2zqBJGse">charged particle</a> multiplicity being used as a common measure of collision centrality, as charged particles are much easier to detect than uncharged particles.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a>
</p><p>Because strong interactions are effectively impossible in ultraperipheral collisions, they may be used to study electromagnetic interactions — i.e. <a href="/facts/Two-photon_physics/1wRvmRsY">photon–photon</a>, photon–nucleon, or photon–nucleus interactions — with low background contamination. Because UPCs typically produce only two to four final-state particles, they are also relatively "clean" when compared to central collisions, which may produce hundreds of particles per <a href="/facts/Event_(particle_physics)/8ma0SlWf">event</a>.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Distance_of_closest_approach/FEYnrckM">Distance of closest approach</a></li>
<li><a href="/facts/Hyperbolic_trajectory/4wEAXaez">Hyperbolic trajectory § Impact parameter</a></li>
<li><a href="/facts/Schwarzschild_geodesics/n6Sl69xV">Schwarzschild geodesics § Bending of light by gravity</a></li>
<li><a href="/facts/Tests_of_general_relativity/yDgwtNrw">Tests of general relativity</a></li></ul>

<ul><li><a href="http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/rutsca2.html">http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/rutsca2.html</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Landau L. D. and Lifshitz E. M. (1976) Mechanics, 3rd. ed., Pergamon Press. ISBN 0-08-021022-8 (hardcover) and ISBN 0-08-029141-4 (softcover). <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>mitopercourseware, MIT (3 September 2021). "Notes" (PDF). <a href="https://ocw.mit.edu/courses/nuclear-engineering/22-105-electromagnetic-interactions-fall-2005/readings/chap6.pdf" target="_blank">https://ocw.mit.edu/courses/nuclear-engineering/22-105-electromagnetic-interactions-fall-2005/readings/chap6.pdf</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>"Impact Parameter for Nuclear Scattering". hyperphysics.phy-astr.gsu.edu. Retrieved 2021-09-03. <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/impar.html" target="_blank">http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/impar.html</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
<li id="fn:4"><p>* Relativistic Heavy Ion Physics without Nuclear Contact, C.A. Bertulani and G. Baur, Physics Today, March 1994, pg. 22. <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li>
<li id="fn:5"><p>Drozhzhova, Tatiana (January 2017). "Centrality and collision event-plane determination in ALICE at the LHC". Journal of Physics: Conference Series. 798 (1): 012061. Bibcode:2017JPhCS.798a2061D. doi:10.1088/1742-6596/798/1/012061. <a href="https://doi.org/10.1088%2F1742-6596%2F798%2F1%2F012061" target="_blank">https://doi.org/10.1088%2F1742-6596%2F798%2F1%2F012061</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li>
</ol>

Impact parameter open-in-new

Impact parameter