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In BCS theory, the superconducting gap is given by solving at different temperatures the integral $$\frac{1}{N(0)V}=\int_0^{\hbar\omega_c}\frac{\tanh\frac{1}{2}\beta(\xi^2+\Delta^2)^{1/2}}{(\xi^2+\Delta^2)^{1/2}}$$ In textbooks like Tinkham (2nd edition, page 63) and Phillips (Advanced Solid State Physics, page 246) you can find approximate formulas for certain temperature ranges (typically $T\approx T_C$).

In some other references, such as here and here (for the latter, I couldn't find the arxiv version, sorry), it is mentioned an interpolation formula valid in the whole temperature range, that is $$ \Delta(T)=\Delta_0\tanh (k\sqrt{\frac{T_{C}-T}{T}})$$ with $k=1.74$ or $k=2.2$.

Is there someone who can link a reference to this formula, and how it is obtained?

In BCS theory, the superconducting gap is given by solving at different temperatures the integral $$\frac{1}{N(0)V}=\int_0^{\hbar\omega_c}\frac{\tanh\frac{1}{2}\beta(\xi^2+\Delta^2)^{1/2}}{(\xi^2+\Delta^2)^{1/2}} \text{d}\xi$$ In textbooks like Tinkham (2nd edition, page 63) and Phillips (Advanced Solid State Physics, page 246) you can find approximate formulas for certain temperature ranges (typically $T\approx T_C$).

In some other references, such as here and here (for the latter, I couldn't find the arxiv version, sorry), it is mentioned an interpolation formula valid in the whole temperature range, that is $$ \Delta(T)=\Delta_0\tanh (k\sqrt{\frac{T_{C}-T}{T}})$$ with $k=1.74$ or $k=2.2$.

Is there someone who can link a reference to this formula, and how it is obtained?

In BCS theory, the superconducting gap is given by solving at different temperatures the integral $$\frac{1}{N(0)V}=\int_0^{\hbar\omega_c}\frac{\tanh\frac{1}{2}\beta(\xi^2+\Delta^2)^{1/2}}{(\xi^2+\Delta^2)^{1/2}}$$ In textbooks like Tinkham (2nd edition, page 63) and Phillips (Advanced Solid State Physics, page 246) you can find approximate formulas for certain temperature ranges (typically $T\approx T_C$).

In some other references, such as here and here (for the latter, I couldn't find the arxiv version, sorry), it is mentioned an interpolation formula valid in the whole temperature range, that is $$ \Delta(T)=\Delta_0\tanh (k\sqrt{\frac{T_{C}-T}{T}})$$ with $k=1.74$ or $k=2.2$.

Is there someone who can link a reference to this formula, and how it is obtained?

In BCS theory, the superconducting gap is given by solving at different temperatures the integral $$\frac{1}{N(0)V}=\int_0^{\hbar\omega_c}\frac{\tanh\frac{1}{2}\beta(\xi^2+\Delta^2)^{1/2}}{(\xi^2+\Delta^2)^{1/2}}$$ In textbooks like Tinkham (2nd edition, page 63) and Phillips (Advanced Solid State Physics, page 246) you can find approximate formulas for certain temperature ranges (typically $T\approx T_C$).

In some other references, such as here and here (for the latter, I couldn't find the arxiv version, sorry), it is mentioned an interpolation formula valid in the whole temperature range, that is $$ \Delta(T)=\Delta_0\tanh (k\sqrt{\frac{T_{C}-T}{T}})$$ with $k=1.74$ or $k=2.2$.

Is there someone who can link a reference to this formula, and how it is obtained?

In BCS theory, the superconducting gap is given by solving at different temperatures the integral $$\frac{1}{N(0)V}=\int_0^{\hbar\omega_c}\frac{\tanh\frac{1}{2}\beta(\xi^2+\Delta^2)^{1/2}}{(\xi^2+\Delta^2)^{1/2}}$$ In textbooks like Tinkham (2nd edition, page 63) and Phillips (Advanced Solid State Physics, page 246) you can find approximate formulas for certain temperature ranges (typically $T\approx T_C$).

In some other references, such as here and here (for the latter, I couldn't find the arxiv version, sorry), it is mentioned an interpolation formula valid in the whole temperature range, that is $$ \Delta(T)=\Delta_0\tanh (k\sqrt{\frac{T_{C}-T}{T}})$$ with $k=1.74$ or $k=2.2$.

Is there someone who can link a reference to this formula, and how it is obtained

In BCS theory, the superconducting gap is given by solving at different temperatures the integral $$\frac{1}{N(0)V}=\int_0^{\hbar\omega_c}\frac{\tanh\frac{1}{2}\beta(\xi^2+\Delta^2)^{1/2}}{(\xi^2+\Delta^2)^{1/2}}$$ In textbooks like Tinkham (2nd edition, page 63) and Phillips (Advanced Solid State Physics, page 246) you can find approximate formulas for certain temperature ranges (typically $T\approx T_C$).

In some other references, such as here and here (for the latter, I couldn't find the arxiv version, sorry), it is mentioned an interpolation formula valid in the whole temperature range, that is $$ \Delta(T)=\Delta_0\tanh (k\sqrt{\frac{T_{C}-T}{T}})$$ with $k=1.74$ or $k=2.2$.

Is there someone who can link a reference to this formula, and how it is obtained?