Use of Padé Approximations in the Analytical Evaluation of the J(θ,β) Function and Its Temperature Derivative

For the first time, analytical forms have been obtained for the finite resonance integral J(θ, β;x,₁x₂)defined by ψ( x ,θ)/ [ψ(x, θ) + β] dx through the use of Padé approximations for the complex probability function. The analytical forms are in terms of elementary functions. We have investigated several 2-pole, 3-pole, and 4-pole Padé approximations, and of these, the 4-pole evaluation reproduces J(θ, β) with the best accuracy. We have also indicated how analytical forms for the temperature derivative of J(θ, β) may be obtained and discuss their utility.