It can now be seen that 2 n ℏ ℏ k momentum states are populated with a probability of P n = J n 2 ( θ θ ) where n = 0 , ± ± 1 , ± ± 2 , … … and the pulse area (duration and amplitude of the interaction) θ θ = ω ω R 2 2 δ δ τ τ = ω ω R ( 2 ) τ τ . The transverse RMS momentum of the diffracted particles is therefore linearly proportional to the pulse area: p rms = ∑ ∑ n = − − ∞ ∞ ∞ ∞ ( n ℏ ℏ k ) 2 P n = 2 θ θ ℏ ℏ k .