shift_factor_closed

Function shift_factor_closed 

Source
pub fn shift_factor_closed(l: u32, kappa: f64) -> f64
Expand description

Shift factor at imaginary channel argument S_l(iκ) for a closed channel.

For a channel with energy E_c < 0 (below threshold), the wave number is imaginary: k_c = iκ with κ = sqrt(2μ|E_c|) / ħ. The penetrability is zero by definition, but the shift factor S_l(iκ) is real and finite and must be included in the level matrix diagonal L_c = (S_c − B_c) + i·P_c.

S_l(iκ) is obtained by analytic continuation of S_l(ρ) to imaginary argument, i.e. substituting ρ² → −κ² in the Blatt-Weisskopf formula. For l ≤ 4 the result is a closed-form rational function of κ². For l > 4 a complex Bessel recursion is used.

Note: at κ = 1 for l = 1 the denominator vanishes (virtual-state pole). This is a genuine physical singularity; the caller receives ±∞ from floating-point arithmetic and should handle it via the normal |L_c| guard in the Y-matrix construction.

Reference: Lane & Thomas, Rev. Mod. Phys. 30 (1958); SAMMY rml/mrml07.f Pgh — PH = 1/(S−B+iP).