Heatmap resolution issues

Question

I am trying to plot a heatmap from the following code. I have a problem where the colour seems to stop before reaching the corners. Please can someone help me to make the colour run all the way to the edge? Also, am I doing something wrong with the axis labels? Why do they not appear as "x" and "y"? Thanks!

n = 100;
a = 1.05;
γ[a_, x_] := Gamma[a] - Gamma[a, x]
ρc[x_, y_, n_] := 
 Sqrt[2/π]*Gamma[n - 1, x^2 + y^2]/Gamma[n - 1]*Abs[y]*Exp[2*y^2]*
  Erfc[Sqrt[2]*Abs[y]]

Show[
  DensityPlot[
    ρc[x, y, n], 
    {x, -a*Sqrt[n], a*Sqrt[n]}, {y, -a*Sqrt[n], a*Sqrt[n]}, 
    ScalingFunctions -> "Log", 
    ColorFunction -> "Rainbow", PlotLegends -> Automatic, 
    AxesLabel -> {x, y}
  ], 
  Graphics[
    {Black, Thick, Circle[{0, 0}, Sqrt[n]]},
    {Red, Thick, Line[{-Sqrt[n], 0}, {Sqrt[n], 0}]}
  ]
]

Answer 1

Increase PlotPoints

FrameLabel instead of Axeslabel

Some bracketing mistakes inside Graphics

I had to omit ScalingFunctions -> "Log" to get a result which is in accordance with Graphics

pl =
 DensityPlot[\[Rho]c[x, y, n], {x, -a*Sqrt[n], 
   a*Sqrt[n]}, {y, -a*Sqrt[n], a*Sqrt[n]},
  ColorFunction -> "Rainbow",
  PlotLegends -> Automatic,
  PlotPoints -> 60,
  FrameLabel -> {x, y}];

gr =
  Graphics[{{Black, Thick, Circle[{0, 0}, Sqrt[n]]}, {Red, Thick, 
     Line[{{-Sqrt[n], 0}, {Sqrt[n], 0}}]}}];


Show[pl, gr]