234 The Poetry of Physics and The Physics of Poetry
discover the energy levels of the nucleus just as one studies the energy
levels of the atom through atomic spectroscopy.
Nuclear reactions in which the incoming projectile and target nucleus
completely change their character also provide an opportunity to study
the energy levels of the nucleus among other things. The first nuclear
reaction was observed in 1919 by Rutherford when he bombarded
nitrogen nuclei with alpha particles obtained from a radioactive source.
He found that the helium and nitrogen nuclei were transformed into a
proton and the oxygen-17 nucleus: He^4 + N^14 → O^17 + p.
By initiating this reaction Rutherford had realized the alchemist’s
dream of artificially transmuting a basic element. He had transformed
nitrogen into oxygen using a radioactive source. In 1932 Cockcroft and
Walton were the first to induce the transmutation of an element by
bombarding a nucleus with an artificially accelerated particle. They
directed a beam of protons at Lithium-7 nuclei. They found that the Li-7
absorbed the proton to form Beryllium-8 and quickly broke up into two
alpha particles: p + Li^7 → He^4 + He^4.
In 1936 Niels Bohr explained the mechanism of low energy nuclear
reactions as a two-step process. The first step involved the formation of a
compound nucleus composed of all the nucleons in the reaction. The
compound nucleus lives a very short time, approximately 10-18 sec, and
then decays into the final state. The relative probability of the states into
which the compound nucleus decays is independent of how it is formed.
Let us consider, for example, the production of the excited state of
nitrogen-14 (N14). This state can be formed by bombarding carbon-13
nuclei with protons. The compound nucleus N 14 can decay into a
number of final states:
p + C^13 → N14* → B^10 + He^4 or C^12 + H^2 or N^13 + n or N^14 + γ.The relative probabilities of these final states would be the same if we
had created N14* by bombarding boron-10 nuclei with alpha particles or
nitrogen-13 nuclei with neutrons.
The energy levels of a nucleus are determined by measuring the cross
section for a nuclear reaction as a function of the energy. The cross
section for a reaction is the probability that the reaction will take place. If
the energy of the incident particle plus the rest mass energy of the
nucleus correspond to the energy of an excited state of the compound
nucleus, the probability of the reaction taking place will be large, and