Nuclear Energy Levels

Analogies with the atom energy levels ...

A gamma spectrum
A consequence of the nuclear energy levels is the emission of gamma photons with characteristic energies. These rays play the part of digital fingerprints, frequently used to identify radioactive nuclei in a given sample. The image above shows the photons coming out of such a sample, and the precisely measured energies associated with each. We can quickly see a series of characteristic lines, indicating the existence of certain elements. The continuous background measurements, which exceed the 100 kiloelectronvolts that is the maximum energy X rays can have, are caused by the presence of poorly detected gamma rays.

At first glance, nuclei seem to be very different from atoms. More than a hundred thousand times smaller, they are also vastly more complex; atoms are primarily made up of empty space whereas the inside of the nucleus is extremely dense. Despite these differences, however, atoms and nuclei have a lot in common.

The behaviour of a nucleus is governed by the laws of quantum mechanics; laws which supersede those of classical mechanics at the microscopic scale. These quantum laws force the nucleus to exist in any one of a finite number of ‘states’, primarily defined in terms of the energy it possesses. This energy is at a minimum when the nucleus is in isolation – a state usually referred to as the ‘ground state’.

Energy levels of Nickel 60:
This diagram represents the energy ladder of a nickel 60 nucleus (product of the decay of the cobalt-60), whose rungs indicate the energy levels the nucleus can reach. The lowest called the ground state, represents the energy of a nucleus at rest. If raised to any of the higher levels, the nucleus immediately emits one or more characteristic gamma rays, lowering its energy sufficiently to allow it to regain the ground state. These energies are calculated by taking the difference between the (very accurately measured) departure and arrival energies. The transitions numbered 4 and 5, by far the more common, have been represented with thicker arrows.
When the nucleus is at a different level, it finds itself with a surplus of energy. This extra energy is released in the form of a _ or gamma photon, thereby allowing the nucleus to reach its ground state once more. These gamma photons are of the same kind as the X rays emitted by atoms, but have far greater energies – which can be of the order of a million electronvolts (MeV).

The energy states of the community of nucleons coexisting in any given nucleus can vary, primarily due to a kind ‘layer’ structure not dissimilar to that which exists in the atom. The binding energy holding the nucleons together can take any of a selection of values that correspond to the number of ‘layers’ that exist.

Nuclei with 2, 8, 20, 28, 50, 82 or 126 nucleons are observed to be particularly stable; an interesting analogy with the stability of atoms of the noble gases whose outermost electron layers are said to be complete.

Cobalt 60 gamma spectrum:
The excited states of nickel 60 are reached when cobalt 60, an isotope widely used in medicine, undergoes beta decay. On the nucleus’s path to the ground state, it emits a number of gamma rays to expend the extra energy it possesses. The diagram above shows the energy and the frequency of these gamma. It shows also that two of these gamma rays are emitted virtually 100% of the time. These two gamma rays emitted in cascade have an energy of around 1 MeV. The presence of these two characteristic gamma ray energies (1.17324 and 1.33250 MeV) serves as an extraordinarily sensitive indicator of the cobalt 60 decay.
In addition to this layered structure, the nucleons can undergo collective movements which correspond to new nuclear energy states. If the entire cluster starts vibrating, for instance, the vibrational energies can only take certain specific values, precisely determined by the laws of quantum mechanics.

Finally, it is important to remember that these nuclei are not necessarily spherical in shape, and can undergo deformation or start rotating. The energies associated with these rotations can also only take well-defined values – they are said to be ‘quantified’.

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