Biomedical Engineering Reference
In-Depth Information
Tab l e 9 . 4
Maximum Fraction of Energy Lost,
Q
max
/
E
n
from
Eq. (9.3), by Neutron in Single Elastic Collision with Various
Nuclei
Nucleus
Q
max
/
E
n
1
H
1.000
2
1
H
0.889
2
He
0.640
4
Be
0.360
1
6
C
0.284
1
8
O
0.221
5
26
Fe
0.069
118
50
Sn
0.033
238
92
U
0.017
The maximum energy that a neutron of mass
M
and kinetic energy
E
n
can trans-
fer to a nucleus of mass
m
in a single (head-on) elastic collision is given by Eq. (5.4):
4
mME
n
(
M
+
m
)
2
.
Q
max
=
(9.3)
Setting
M
1
, we can calculate the maximum fraction of a neutron's energy that
can be lost in a collision with nuclei of different atomic-mass numbers
m
.Some
results are shown in Table 9.4 for nuclei that span the periodic system. For ordinary
hydrogen, because the proton and neutron masses are equal, the neutron can lose
all of its kinetic energy in a head-on, billiard-ball-like collision. As the nuclear mass
increases, one can see how the efficiency of a material per collision for moderating
neutrons grows progressively worse. As a rule of thumb, the average energy lost
per collision is approximately one-half the maximum.
An interesting consequence of the equality of the masses in neutron-proton scat-
tering is that the particles separate at right angles after collision, when the collision
is nonrelativistic. Figure 9.5(a) represents a neutron of mass
M
and momentum
M
V
approaching a stationary nucleus of mass
m
. After collision, in Figure 9.5(b),
the nucleus and neutron, respectively, have momenta
m
v
and
M
V
. The conserva-
tion of momentum requires that the sum of the vectors,
m
v
+
M
V
, be equal to the
initial momentum vector
M
V
, as shown in Figure 9.5(c). Since kinetic energy is
conserved, we have
1
2
MV
2
=
1
2
mv
2
+
1
2
MV
2
.
(9.4)
=
v
2
+
V
2
, which implies the Pythagorean theorem for the trian-
gle in (c). Therefore,
v
and
V
are at right angles.
The elastic scattering of neutrons plays an important role in neutron energy mea-
surements. As discussed in the next chapter, under suitable conditions the recoil
m
,then
V
2
If
M
=
=
