Elements of Modern Physics
346
the reaction (endothermic) and if Q is negative , energy is absorbed in the reaction
(endothermic). A reaction cannot proceed unless the energy of the bombarding
particle is greater than a minimum value known as the threshold energy, equal
to | Q | for negative Q reactions and zero for positive Q reactions.
Two specific examples of historic importance are
14
N + α →
17
O + p,
14
N (α , p)
17
O
(9.92)
7
Li + p → α + α,
7
Li (p, α )
4
He
(9.93)
The first reaction was observed by Rutherford (1919), using α particles of
7.68 MeV energy. from a natural, radioactive source. It is an endothermic reaction
with Q ≈ – 1.2 MeV, with a threshold energy of about 1.2 MeV. The process in
Eq. (9.93) was the first nuclear reaction produced by artificially accelerated
particles. Cockcroft and Walton (1932) obserbed the reaction using protons
accelerated through a potential difference of about 0.5 MeV. This is an
exothermic reaction with Q ≈ 17.3 MeV and illustrates the possibility of
extracting energy from a nuclear reaction.
Cross-Section
The probability for a nuclear reaction to take place is expressed in terms of the
effective cross-section σ.
Consider a beam of projectiles incident on a collection of targets in the
form of a thin plate (sufficiently thin so that the nuclei do not overlap). An
effective cross-sectional area σ [Fig. 9.8 (a)] is associated with each target such
that every projectile incident within that area produces a reaction. If there are n
targets per unit volume and t is the thickness of the plate, the probability of a
single projectile producing a reaction is
P = σnt
(9.94)
(it is the fraction of the effective target area). Therefore, the fraction of projectiles
∆N/N producing reactions, is
N
N
∆ = σnt
(9.95)
which leads to
σ =
N
Nnt
∆
(9.96)
This relation allows us to determine the effective cross-section for a nuclear
reaction. It is usually expressed in terms of barns, 1 barn = 10
–28
m
2
.
Nuclear reaction cross-sections vary over large ranges. Of particular interest
are the cross-sections for neutron projectiles. In this case, the neutrons, being
neutral, can enter a nucleus with ease even at low energies. In fact, since the
346
the reaction (endothermic) and if Q is negative , energy is absorbed in the reaction
(endothermic). A reaction cannot proceed unless the energy of the bombarding
particle is greater than a minimum value known as the threshold energy, equal
to | Q | for negative Q reactions and zero for positive Q reactions.
Two specific examples of historic importance are
14
N + α →
17
O + p,
14
N (α , p)
17
O
(9.92)
7
Li + p → α + α,
7
Li (p, α )
4
He
(9.93)
The first reaction was observed by Rutherford (1919), using α particles of
7.68 MeV energy. from a natural, radioactive source. It is an endothermic reaction
with Q ≈ – 1.2 MeV, with a threshold energy of about 1.2 MeV. The process in
Eq. (9.93) was the first nuclear reaction produced by artificially accelerated
particles. Cockcroft and Walton (1932) obserbed the reaction using protons
accelerated through a potential difference of about 0.5 MeV. This is an
exothermic reaction with Q ≈ 17.3 MeV and illustrates the possibility of
extracting energy from a nuclear reaction.
Cross-Section
The probability for a nuclear reaction to take place is expressed in terms of the
effective cross-section σ.
Consider a beam of projectiles incident on a collection of targets in the
form of a thin plate (sufficiently thin so that the nuclei do not overlap). An
effective cross-sectional area σ [Fig. 9.8 (a)] is associated with each target such
that every projectile incident within that area produces a reaction. If there are n
targets per unit volume and t is the thickness of the plate, the probability of a
single projectile producing a reaction is
P = σnt
(9.94)
(it is the fraction of the effective target area). Therefore, the fraction of projectiles
∆N/N producing reactions, is
N
N
∆ = σnt
(9.95)
which leads to
σ =
N
Nnt
∆
(9.96)
This relation allows us to determine the effective cross-section for a nuclear
reaction. It is usually expressed in terms of barns, 1 barn = 10
–28
m
2
.
Nuclear reaction cross-sections vary over large ranges. Of particular interest
are the cross-sections for neutron projectiles. In this case, the neutrons, being
neutral, can enter a nucleus with ease even at low energies. In fact, since the