The Nucleus and the Strong Interaction 235
hence there will be a peak in the cross section. The peaks of the cross
section correspond to the energy levels of the excited compound nucleus.
The widths of the peak represent the uncertainty in measuring the energy
of the excited state of the nucleus.
According to the uncertainty principle, the uncertainty in the energy
times the uncertainty in the time of a system is equal to h. The
uncertainty in time of the compound nucleus just corresponds to its
lifetime. We therefore expect on the basis of the uncertainty principle
that the lifetime of the compound nucleus is approximately h/∆E. The
widths of the experimentally measured peaks of the cross section,
therefore, determine the lifetimes of the compound states. Knowing the
energy and lifetime of the excited states of the nucleus helps physicists
determine the structure of the nucleus.
One of the factors determining the final states of a nuclear reaction is
the conservation of energy. There are two types of nuclear reactions,
depending on whether the masses of the final state nuclei are heavier or
lighter than the initial state nuclei. When the final state is heavier, the
reaction takes place by converting a certain amount of the initial kinetic
energy of the incident particle into rest mass energy. An example is the
reaction p(1.0078) + C^13 (13.0034) → H^2 (2.0141) + C^12 (12.00), where the
numbers in parentheses are the mass of the nuclei in atomic mass units
(amu). The total mass of the initial nuclei is 14.0112 whereas the final
state masses sum to 14.014 and hence are 0.0029 amu heavier than
the initial state masses. This reaction has a threshold energy because
unless the proton has a certain amount of kinetic energy, which can be
converted into rest mass energy, the reaction will not proceed.
In the other type of reaction the final masses are lighter than the initial
masses and hence rest mass energy is converted into kinetic energy.
These reactions have no threshold since there is enough energy for the
reaction to proceed in the rest masses of the initial state. There are two
types of reactions which release nuclear energy. The first type is the
fission reaction in which a heavy nucleus divides into two or more parts
as a result of absorbing a neutron. The second type is the fusion reaction
in which two light nuclei combine together to form a heavier nucleus.
Whether fission or fusion is possible depends on the binding energy per
nucleon, which increases with A until a maximum is reached at A = 60.
If two nuclei in the region A < 60 combine to form a third nucleus, the
total binding energy will increase and hence the heavier nucleus will
have less mass than the two nuclei which combined to form it and fusion