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There are many different types of excites states in a nucleus. Since the nucleus is actually comprised of many protons and neutrons, some excited states can be described as single particle states. In this mode one or more protons and/or neutrons are not in their lowest orbits. Another mode of excitation occurs when the nucleons appear to act collectively. Much as a school of individual fish can turn and move as one entity, so can the nucleus. As we learn more about the nucleus, we simplify our understanding of it by considering it to be described by two very different models. In one model, the nucleus is a bag of individual protons and neutrons interacting with each other. In this model, we need to understand and be able to describe all of those interactions. For large nuclei, one nucleon "interacts" with the other 200 and vice-versa. This quickly becomes a "many-body problem" which is very difficult to solve. Therefore we usually describe nuclei as consisting of an "inert core" and a few "valence nucleons" which are involved in the excitation. This simplfied approach is surprisingly good at describing experiments and we call this model, the shell model. Another view of the nucleus is to treat it as a single entity or "liquid-drop". Think of a drop of cold honey. In this case, the individual nucleons have little influence on the whole and the entire system can be described more simply. These models are called "mean-field" models and are very good at describing the nucleus in its collective modes of excitation.

Several modes of excitation are described below.

### Single particle excitation

In single-particle states, individual nucleons are promoted to high lying orbitals within the various shells of the nucleus. Many particles may be raised to these orbitals. Usually, these types of excitations are described as a spherical inert core (nucleons which are in their normal orbitals) surrounded by valence nucleons which take part in the excitation.

In the figure above, a neutron (in the green orbital) is not in its lowest configuration when it is in the largest green shell. This arrangement is unstable and the nuceon will change to a lower energy orbit and emit a gamma-ray. This gamma-ray has a given energy and if we measure this energy, we know the energy of this orbital. Nuclei which are excited in this manor tend to have chaotic energy level spacings which can vary from a few keV to several thousands of keV.

### Collective excitation

There are many collective modes of excitation: rotation, vibration, and giant resonances are three common modes. Even though the nucleus is comprised of individual nucleons, their relationship to each other is governed by many rules. We can take advantage of these rules and consider the nucleus to be a single entity. As such, this entity can take many shapes: spherical (see above), prolate (American football), oblate (planets), octupole (pear-shaped), etc. The non-spherical shapes can rotate about a point or axis and the excited states organize themselves into regular patterns. In addition, to shape, the nucleus can also vibrate like jello (gelatin) and breathing. The vibrational states also are organized into distinctive patterns. In these collective pictures, the protons and neutrons do not interact with each other even though they occupy the same space. However, at large excitation energies, protons and neutrons can move as two separate groups. These excitations are called giant dipole resonances because they emit large energy gamma-rays with all the charged particles shifting to "one-side" of the nucleus or the other. The three modes of excitation are illustrated below.

### In nature

Of course, in reality any nucleus with enough energy can have all these various modes of excitation. And the simplified descriptions above, are approximations. The ultimate goal will be to describe all possible interactions every nucleon can have with every other nucleon. Then we should be able to describe all 3000 known isotopes and the other 7000 yet to be observed.

As an example, look at the excited states (horizontal lines) of 152Dy in the image below. The states are connected by arrows which represents the levels to which the state decays. The length of the arrow represents the energy between the states and the width indicates the intensity observed during the experiment. Dotted horizontal lines helps show the complicated decay pattern when a state has many decays feeding in to it. Predicted shapes of the nucleus are indicated as are the axes of rotation.

The first thing to notice is how the states are grouped into collective states labeled triaxial band and superdeformed bands and non-collective states in the yellow shading. Notice the regular decay pattern of the collective states: they decay to only one state and "cascade down" in energy with the each step getting smaller as one moves downward. This is the typical pattern of a rotating nucleus.

The non collective states tend to have many branches and the energy steps vary widely. No clearly distinguishing pattern exists although there are groupings of many states and transitions in energy which are separated by a few larger energy transitions. This is the typical pattern observed when nucleons lie in high energy shells and there are many orbits the nucleons can occupy.

One interesting thing to note is that the states labeled "superdeformed" are not connected to the other states. Experiments have assigned these decays to 152Dy but the combination of energy, intensity, and decays to many states have not allowed the experiments to determine where these groups feed into the noncollective states. Subsequent experiments have determined these connections.