Waves in the Nucleus

lead and mercury

The early models of the nucleus assumed that the protons were distributed uniformly over a sphere of radius R. The picture shows the actual density profiles for mercury (with 80 protons) and lead (with 82 protons). The density on the y-axis is plotted against distance on the x-axis with the center of the nucleus in the middle. Distances in nuclei are measured in fermis - a unit that is 15 orders of magnitude smaller than a meter. The total diameter of these nuclei is about 10 fermis. The circles are the experimental densities obtained from the scattering of electrons from nuclei. The experimental points are compared with a Hartree-Fock calculation  - the solid line. 

One observes two features that differ from the early model.

(1) The nuclear density falls off at the surface over a distance scale of about two fermis.

(2) There are waves in the nuclear interior. These waves are frozen in shape.

Both of these effects are related to the quantum structure in the nuclear shell model. The density oscillations reflect the different orbits that are filled as a function of increasing proton number, and it is particularly interesting in this figure how much the oscillations change by the addition of only two protons.

The work for this webpage was done in collaboration with Prof. Werner Richter from the University of the Western Cape in South Africa. 
  
charge densities The picture on the left shows the charge densities densities for a wider variety of nuclei from silicon (with 14 protons) to lead (with 82 protons) as a function of the radial distance from the center. The number above the element symbol is the total number of nucleons (protons plus neutrons). The density on the y-axis is measured in units of protons per cubic fermi. The densities for the nuclei beyond silicon are shifted so they do not overlap in the plot. The data points are compared with two different Hartree-Fock  calculations (the solid and dashed lines).

For more details about the data and theory for nuclear waves see Physical Review C67, page 034317 (2003).