Nuclear+Structure

What is nuclear structure?
The study of the structure of nuclei, or the pattern of nuclear excited states, attempts to understand the interactions of protons and neutrons in the confined nuclear space. It is well known that each element has a "fingerprint" series of electronic excited states, or atomic structure. The same is true of nuclei; each isotope can be characterized by a unique set of nuclear excited states that describes the interactions between nucleons as a function of the available energy. There are many comparisons that can be drawn between atomic and nuclear studies; However, an important distinction between these particles arises when considering forces. Electrons interact via the Coulomb force (attracted to the nucleus, repulsed from other electrons), while protons and neutrons are subject to the strong force (protons are also subject to Coulomb forces). Due to the strong force, protons and neutrons will pair with a nucleon of the same type if possible. The shells are therefore filled differently than they are for electrons (see above). The strong force is not well understood, and the many interactions that are possible in the extremely dense nuclear environment make it very difficult to calculate the expected excited states. These states must be observed experimentally, and the nuclear models continuously modified. A wide range of phenomena has been observed, making nuclear structure an exciting and ever-changing field of study. Shown below is the Chart of Nuclides, where isotopes are shown as a function of proton and neutron number. This is the nuclear scientist's adaptation of the Periodic Chart, where elements are shown as a function of electron number. While the Periodic Chart allows scientists to quickly see features of the atomic activity for a given element, the Chart of Nuclides allows scientists to quickly see features of nuclear activity for a given isotope. Different regions of the Chart of Nuclides are characterized by different properties. ==Nuclear shapes== In a shell model, individual nucleons are depicted as moving freely within a potential well that represents the average interaction of each nucleon with all others. When the Schrödinger equation is solved for a nucleon within this potential field, the solution will give a series of quantized energy levels. The energy level configuration is sensitive to the potential function used. In it's simplest form, the potential well is assumed to be spherically symmetric. The resulting energy diagram will have wide energy gaps at the magic numbers, (single particle values of 2, 8, 20, 28, 50, 82, and 126), where the levels between each gap constitute a shell. Use of a spherically symmetric potential adequately represents nuclei with protons and/or neutrons near magic numbers. As the number of nucleons deviates from magic values, nuclei become deformed and the symmetric assumption fails. Non-spherical nuclei are better approximated by a deformed shell model. In the Nilsson model, each spherically symmetric energy level is split into doubly degenerate states holding only two nucleons and forming the ground state of a rotational band. The arrangement of energy levels is contingent on the extent of deformation, as the nucleus will assume a shape by which the potential energy will be minimized. To a first approximation, only oblate (cigar-shaped) and prolate (football-shaped) deformations are considered. Nuclear energy levels are then calculated as a function of a deformation parameter. As in the spherical model, wide energy gaps are found, but at different (non-magic) single particle levels. The presence of these deformed shell gaps is thought to help drive deformation. The influence of spherical shell gaps is well known; nuclei with one or both particles magic often approximate a spherical shape. Deformed shell gaps may function in a similar manner, only becoming influential when both proton and neutron single-particle energies are minimized at similar deformation values. In this circumstance, occupied proton and neutron orbitals may reinforce each other's drive toward that deformation. N = Z nuclei, with protons and neutrons occupying identical orbitals, will then produce some of the largest deformations as has been seen experimentally. With energy, particles may be excited to higher-lying states. Pairs of nuclei may also be broken, and one or both particles excited. Understanding the energy difference and the ability to populate various states is an important component of nuclear structure. As stated earlier, the shape of the potential (or more colloquially the nuclear shape) is understood by examining the pattern of excited states and decays between them. The shape is often a macroscopic component upon which (microscopic) particle excitations may be built.
 * atomic structure: study of atomic states created by electronic excitations
 * nuclear structure: study of nuclear states created by proton and/or neutron excitations

How are the excited energy levels measured?
The energies of the nuclear excited states are measured by monitoring the de-population of these states by the emission of charged particles (p,a ß-, ß+) and/or electromagnetic photons (gamma-rays). The most common is the observation of gamma-rays, since most nuclear states exist for less than 10-9 s. To detect the gamma-rays, multiple Ge semiconductor detectors are used. Many arrays exist; here are some well-known examples: > [|Gammaphere] > [|CLARION] > [|YRAST-Ball] > [|Euroball] > [|GASP]

How are the excited states populated?
In order to measure the de-population of the excited states we will have to populate them first! This is commonly done using heavy ion reactions. There are many different types of reactions; all involve an accelerated beam of ions impinging on a stationary target.

> > > > Decay spectroscopy involves the production of the parent nuclide via one of the above reactions, and then monitors the gamma-transitions in the daughter after the parent radioactively decays.
 * Fusion evaporation
 * Deep inelastic
 * Transfer
 * Incomplete fusion

TRIUMF-related nuclear structure studies
Due to the large amount of equipment and personnel needed to do these studies, nuclear structure experments typically take place at a large facility. Near Simon Fraser University is the Canadian national laboratory, TRIUMF. Much of our research is accomplished with TRIUMF, although we sometimes travel abroad to other institutions. Some of the TRIUMF-related research is described [|here]. > Last modified 08 June 2004 > This document was originally posted at [|www.sfu.ca/chemistry/faculty/jressler/struc.htmlSend] comments/questions to J. J. Ressler.I have included it here for use in this course.