Nucleus of a (lead) isotope:Lead-lead (PbPb) collisions at the LHC with electromagnetic fields (note Lorentz-contraction):Indicating the impact parameter:

Main idea

At first I tried randomly assigning an angle and radius (sampling sqrt((rand+1)/2) for uniform distribution along the radius):This did not fill up so evenly as I wanted, so I tried to generate the nucleons uniformly on ring layers using polar coordinates:Adding a bit of random offsets to the angle and radius in the polar coordinate:Randomly shuffling the nucleons along the rings so the overlap of consecutive balls is not regular, and the even/odd coloring looks more random:The rings have constant distance between them because each ring's radius is set with a simple linear equation of the form r=R*i/N. To make the nucleus look more like a 3D sphere, we can gradually pull the outers rings closer together by reducing the ring radius quadratically: r'=r-C*r^2 for some tunable parameter C ~ 0.2:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
% Author: Izaak Neutelings (March 2024)
% Description: Lead-lead collisions
\documentclass[border=3pt,tikz]{standalone}
\usepackage{amsmath}
\usepackage{listofitems} % to create arrays with \readlist
\usepackage{ifthen} % for \whiledo
%\usetikzlibrary{arrows.meta} % for arrow size
% COLORS
\colorlet{myred}{red!75!black}
\colorlet{myblue}{blue!70!black}
% STYLES
\tikzset{
  >=latex, % for LaTeX arrow head
  ball/.style={ultra thin,draw=black,fill=\getcol{#1},
               circle,inner sep=1pt,minimum size=15pt,scale=0.8},
  ball/.default=1,
}
\def\getcol#1{\ifodd#1 blue!20 \else red!20 \fi}
\def\drawgrid#1{
  \pgfmathsetmacro\xmax{ceil(#1)+0.6}
  \pgfmathsetmacro\xmin{0.3-\xmax}
  \draw[black!20] (\xmin,\xmin) grid (\xmax,\xmax);
  \draw[thick,->] (\xmin,0) -- (\xmax,0);
  \draw[thick,->] (0,\xmin) -- (0,\xmax);
  \draw[black!20] (0,0) circle(#1);
}
\begin{document}
% NUCLEUS - random radius & angle
\def\R{2.0}
\def\Nlay{5} % number of rings/layers
\def\N{100}
\begin{tikzpicture}
  \drawgrid{\R}
  
  % NUCLEUS
  \foreach \i [evaluate={
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Run LaTeX here

Full code

Edit and compile if you like:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
% Author: Izaak Neutelings (March 2024)
% Description: Lead-lead collisions
% Inspiration: https://arxiv.org/abs/2010.07855
\documentclass[border=3pt,tikz]{standalone}
\usepackage{listofitems} % to create arrays with \readlist
\usepackage{ifthen} % for \whiledo
\usepackage{siunitx} % for \SI
\usetikzlibrary{decorations.pathmorphing} % for snake, coil, zigzag
% COLORS
\colorlet{protoncol}{red!68!black!80}
\colorlet{neutroncol}{green!68!black!80}
\colorlet{photoncol}{yellow!85!orange!95!black}
% STYLES
\tikzset{
  >=latex, % for LaTeX arrow head
  vector/.style={->,thick,green!60!black},
  photon/.style={->,line width=0.7,line cap=round,photoncol,decorate,decoration={
    snake,amplitude=.4mm,segment length=2.2mm,post length=1.5mm}
  },
  ball/.style={
    circle,draw=none,ball color=#1,postaction={
    fill=#1,fill opacity=0.8,draw=#1!40!black,line width=0.04}
  },
  ball/.default=protroncol,
  pics/nucleus/.style={%
    code={%
      \fill[protoncol] (0,0) circle(0.86*\R); % background to fill any holes
      \pgfmathsetmacro\Rball{0.18*\R} % ball radius
      \pgfmathsetmacro\Rcorr{\R-\Rball} % subtract ball radius
      \pgfmathsetmacro\C{min(1/(4*\Rcorr),0.24)} % put balls at edges closer in to create 3D ball effect
      \pgfmathsetmacro\D{1-4*\C*\Rcorr} % discriminant
      \pgfmathsetmacro\Rs{2*(\Rcorr)/(1+sqrt(\D)} % scaled total radius
      \message{^^J R=\R, R=\Rcorr, Rs=\Rs, C=\C, D=1-4cR=\D (must be >0)}
      \foreach \lay [evaluate={
        \r=\Rs*(\lay-0.05)/\Nlay; % ring radius
        \rC=\r-\C*\r*\r; % reduce outer radii to create 3D effect
        \aR=3*rand; % random angular offset
        \Nring=int(round(2*\rC*\N/(\Rs*(\Nlay+1)*(1-\C*\Rs*(2*\Nlay+1)/(3*\Nlay))))) % number of balls on this ring
      }] in {\Nlay,...,1}{
 
 
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Run LaTeX here
Click to download: PbPb_collisions.tex • PbPb_collisions.pdf
Open in Overleaf: PbPb_collisions.tex