Potential scattering with varying projectile flux near metastable levels

In usual scatering experiments, projectiles (electrons, atoms, ions, etc.) scattered from targets (molecules, surfaces, etc.) are closely approximated by plane waves. We propose to modify this traditional scheme by preparing projectiles in a quantum state where every projectile is emitted with a varied probability in time P(t), such that P(t) ∞ exp(−γt). The potential scattering with the new incident wave packet demonstrates significant differences from the usual plane wave experiment: Usual resonance peaks characterized by widths Γ_Γ are significantly narrowed for γ < Γ_γ and transformed to discrete lines for γ ≥ Γ_γ.