Needs["MaTeX`"]
SetOptions[MaTeX,"Preamble"->{"\\usepackage{amssymb,amsmath,latexsym,amsfonts,amsthm,xcolor,bm,mhchem}","\\definecolor{darkgreen}{RGB}{0, 180, 0}"}];

HUMP[λ_,t_,U_]=(({{-((2 (t^2) λ)/U), 0, 0, ((2 (t^2) λ)/U)}, {0, U-((2 (t^2) λ)/U), ((2 (t^2) λ)/U), ((2 t (Sqrt[-4 (t^2)+(U^2)]) λ)/U)}, {0, ((2 (t^2) λ)/U), U-((2 (t^2) λ)/U), -((2 t (Sqrt[-4 (t^2)+(U^2)]) λ)/U)}, {((2 (t^2) λ)/U), ((2 t (Sqrt[-4 (t^2)+(U^2)]) λ)/U), -((2 t (Sqrt[-4 (t^2)+(U^2)]) λ)/U), -2 U (-1+λ)+((6 (t^2) λ)/U)}}));
ϵUMP[λ_,t_,U_]=Eigenvalues[HUMP[λ,t,U]];

RadConv[t_,U_]:=
Sort[
Abs[λ]/.NSolve[
{
Det[HUMP[λ,t,U]-Ε IdentityMatrix[Length[HUMP[λ,t,U]]]],(∂_Ε)Det[HUMP[λ,t,U]-Ε IdentityMatrix[Length[HUMP[λ,t,U]]]]
},{Ε,λ}]
]//DeleteDuplicates

TabRadConv=With[{ΔU=(1/100)},Table[{U,RadConv[1,U]},{U,ΔU,8,ΔU}]];

ListPlot[{
Table[{TabRadConv[[k,1]],TabRadConv[[k,2,2]]},{k,Length[TabRadConv]}],
Table[{TabRadConv[[k,1]],TabRadConv[[k,2,3]]},{k,Length[TabRadConv]}]
},Joined->True,InterpolationOrder->2,PlotTheme->"Scientific",
PlotRange->{All,{0,2.1}},PlotStyle->Thickness[0.005],
BaseStyle->20,ImageSize->Large,GridLines->Automatic,FrameLabel->{MaTeX["U/t",FontSize->20],MaTeX["r_c",FontSize->20]}]