The discussion centers on deriving an approximation formula for the differential cross section of hard sphere scattering at high energy, referencing "Methods of Theoretical Physics" by PM Morse and H. Feshbach. Key insights include that the total cross section approximates 2πa², and for large ka, the scattered intensity is expressed as S = a²/4r² + (a²/4r²)cot²(θ/2) J₁₂(ka sin θ). The conversation highlights the importance of understanding Green's functions and steepest descent methods for deriving the formula, as well as the need for clarity in communication regarding the specific mathematical results sought.
PREREQUISITESPhysics students, particularly undergraduates and graduates involved in theoretical physics projects, as well as researchers focusing on scattering theory and mathematical methods in physics.
Please try to make it clear from the outset what it is you have and what it is you want. You said it involved "three special functions in a summation." There is nothing on p 1484 like that. The formula I quoted is derived much later in the chapter, using Green's functions and steepest descent, but I see no point in pursuing it only to be told you have it already.aim1732 said:Thank you but you know I already have the result.I do not know how to get there however.Yes it is exactly what I am looking for but I think I would require a bit more.
Bill_K said:[Taking my copy of Morse and Feshbach from beneath its helium-filled bell jar...]
Please try to make it clear from the outset what it is you have and what it is you want. You said it involved "three special functions in a summation." There is nothing on p 1484 like that. The formula I quoted is derived much later in the chapter, using Green's functions and steepest descent, but I see no point in pursuing it only to be told you have it already.