Cyanoalkynes and Cyanopolyynes: From Crossed Beam Experiments to Astrochemistry - Polyynes: Synthesis, Properties, and Applications - page 286

FIGURE 14.2 Velocity vector or Newton diagram showing the relation between the
center-of-mass product scattering angle, , and velocity, u RCN , and the laboratory
equivalent, Y and v RCN . The reactant velocities and the maximum angular range
within which the products can be scattered in the laboratory reference frame,
Y min Y max , are also shown.

u RCN are shown). By taking into account the reactant and product masses
and the laws of conservation of the linear momentum and total energy, it is
possible to calculate the maximum CM speed that the products can reach
and therefore to draw the limiting circles in the Newton diagram which
define the maximum LAB angular ranges (from

Y min to Y max ) within

which the products can be scattered.
It can be easily demonstrated that the relation between LAB and CM
product flux is given by [57,59]

v 2

I CM ð ,u Þ

I LAB ð ,v Þ¼ , ð 14 : 5 Þ

u 2

where

and u are the corresponding CM quantities. Since the electron impact-mass
spectrometric detector measures the number density of products, N(

Y and are the LAB scattering angle and speed, respectively, while

),
rather than the flux, the actual relation between the LAB density and the
CM flux is given by [59]

Y

I CM ð ,u Þ v

N LAB ð ,v Þ¼ : ð 14 : 6 Þ

u 2

Nevertheless, because of the finite resolution of experimental conditions
(angular and velocity spread of the reactant beams and angular resolution of
the detector), the LAB to CM transformation is not single valued and,