# 6805: 1094 Activities 2

Write your name and answers on this sheet and hand it in when requested.

Work with others nearby on these activities. Argue about the answers but work efficiently!

## Discussion questions on nuclear structure

Goal: Think about some of the key points motivating present and future nuclear structure experiments. Discuss with your neighbor(s) and ask questions!

1. Give an explanation (based on your current understanding) for the "periodic" part of the table of the elements (e.g., why there are "magic" numbers).

2. What is the "liquid drop" model of the nucleus and its consequences?

3. What do you think is(are) the motivation(s) to study rare isotopes experimentally and theoretically?

## Radius systematics from elastic scattering

Goal: Use elastic proton differential cross sections from a range of nuclei to estimate the A dependence of their radii in the form R = r0 An (i.e., you are to estimate n).

1. Follow the "in class" link to the "proton-nucleus elastic scattering figure" (proton-nucleus.png) and save it somewhere convenient on your computer (e.g., the desktop).
2. We will extract the values of the angular minima from this figure using a plot digitizer. Google "web digitizer" and one of the first links will be to WebPlotDigitizer. If you are not already at the App page, click on "Launch App!". You should see an x-y graph with some menus at the top left.
3. Under the File menu, select "Load Image" and then "Browse ..." and load the scattering figure. For "Choose plot type", choose "2D (X-Y) Plot" and click on "Align Axes".
4. Follow the pop-up instructions to align the axes: you first pick two definite x points (use the zoom on the upper right), like 5 and 30 degrees, and then two definite y points (pick anything, because we won't use them). Click "Complete!" when done, then enter the x points and y points (and y is a log scale), and click "OK".
5. Now we are ready to find points! With "Add Point (A)" selected, successively click on the minima of the solid lines (use the zoom!) for 40Ca, 48Ca, 90Zr, and 208Pb. Use "Delete Point (D)" if you make a mistake. When done, select "View Data". The first column will be the theta values we need. How many digits do you estimate are significant? Record below the angles with this many digits in a table with the value of A, which is the total number of protons plus neutrons.

6. Open the Mathematica notebook fitting_a_nonlinear_function_to_data.nb from the "in class" link. The notebook contains an example of fitting a power law to four data points. Run it first and ask any questions. Then you can simply replace the example numbers with your (A,θ) pairs and run the notebook again! What do you get for n?

7. Now go back to your result for the radius of lead from the last session and use it to find (roughly) r0. What value do you get (show the details)?

8. Is your result consistent with a liquid drop model of the nucleus (for which the volume occupied by the nucleus is A times the volume for a nucleon)? Explain.

## Rutherford scattering

Goal: Think about how determining (or bounding) the size of a nucleus with Rutherford scattering is different from how we did it with elastic scattering. Also, test whether PhET Java simulations will work.

1. From the 6805 home page, go to the simulations page and find the PhET simulation of Rutherford scattering (use original). Start it up. You may get some warning dialogs; agree to everything.
2. Run the simulation for 208Pb. What are the proton and neutron numbers?

3. From the 28/29-Aug-2017 "Unit Q nuclear size excerpt", how is Rutherford scattering used to put a bound on the nuclear size. Why is it only a bound? (Hint: How does the electric field outside a spherical distribution of charge depend on its radius?) What would you adjust in the simulation to get the best bound?

4. Does this application of Rutherford scattering use quantum mechanics or classical physics?

5. List some ways that Rutherford scattering is different from using diffraction to determine the nuclear size?

## Quick questions relating to nuclear and nucleon sizes

Goal: check that basic definitions are understood.

1. What is a "halo nucleus"?

2. What is the "neutron skin" of a nucleus?

3. How can the neutron have an electric charge distribution if it is a neutral particle?