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35°

106°

vCM

ve

vR

Solid Angle Transformation Jacobian

typical (d,p) reaction

velab

Defining: g = vCM / ve

Note that qlab changes much

more rapidly (at back angles)

than does qCM

This means that a small

solid angle in the CM, dWCM

is spread over a rather large

solid angle dWlab in the lab

This means that although

ds/ dWCM

is largest at small qCM or

near 180° in the lab, the

effect of the Jacobian is that

ds/ dWlab

near 180° is reduced relative

to less backward angles

ds

dWlab

ds

dWCM

=

(1 + g2 + 2g cos q)1/2

? 1+ g cos q ?

e.g. L.I. Schiff, Quantum Mechanics, 3rd Ed., p.113

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