n = 100;
core[ [Epsilon]_, [Sigma]_,
F_] := ( [Epsilon] Exp[- [Beta] [Epsilon]])/(
2 Sqrt[R[ [Epsilon], [Sigma], F]] Cos[ [Theta]]) /. para;
core1[ [Epsilon]_, [Sigma]_] :=
NIntegrate[
core[ [Epsilon], [Sigma], F], {F, Fm,
Fc[ [Epsilon], [Sigma]]}] /. para;
core1data =
Flatten[Table[{{ [Epsilon], [Sigma]},
core1[ [Epsilon], [Sigma]]}, { [Epsilon], [Epsilon]m,
[Epsilon]M, ( [Epsilon]M - [Epsilon]m)/
n}, { [Sigma], [Sigma]m, [Sigma]M, ( [Sigma]M - [Sigma]m)/
n}], 1];
corefunc = Interpolation@core1data;
NIntegrate[
corefunc[ [Epsilon], [Sigma]], { [Epsilon], [Epsilon]m,
[Epsilon]M}, { [Sigma], [Sigma]m, [Sigma]M}]