Module penetrability 

Hard-sphere penetrability, shift, and phase shift functions.

These are the standard neutron penetrability factors for a hard-sphere potential, needed for the R-matrix cross-section calculation.

SAMMY Reference

• rml/mrml07.f: Sinsix (phase shifts), Pgh (penetrability + shift), Pf (penetrability only)
• SAMMY manual Section 2 (R-matrix theory)

Definitions

For channel radius a and neutron wave number k: ρ = k·a

The penetrability P_l(ρ), shift factor S_l(ρ), and hard-sphere phase shift φ_l(ρ) depend on orbital angular momentum l.

Functions

penetrability

Penetrability factor P_l(ρ) for orbital angular momentum l.

phase_shift

Hard-sphere phase shift φ_l(ρ).

shift_factor

Shift factor S_l(ρ).

shift_factor_closed

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