Physics and Engineering of Radiation Detection

702 Chapter 12. Radiation Spectroscopy

Ef

kf

ki

Ei

ki

kf

Detector

2θ

Sample

(b)

(a)

Neutron

2θ Q

Figure 12.3.1: (a) A simple

setup to study neutron scatter-

ing. The movable detector can

be positioned to detect diffrac-

tion maxima. (b) Addition of

initial and final wave vectors

to obtain the momentum trans-

ferred to the sample.

Inelastic Scattering: During an inelastic scattering process a neutron can

loose or gain energy, that is

Ef = Ei

and kf = ki.

This implies that

ω = Ei−Ef=0.

The quantity on the left hand side of the above equation represents the energy

transferred to the sample. It can be obtained in terms of wave vector by using

the relationsp=h/λ=
kandE=p^2 / 2 m,thatis

E =

p^2

2 m

=

^2 k^2

2 m

⇒
ω =

^2

2 m

[

ki^2 −kf^2

]

⇒ω =

2 m

[

ki^2 −kf^2

]

. (12.3.10)