Advanced General Physics 323/324

Modern Physics Unit NP Nuclear Physics

Overview: This unit gives an introduction to nuclear physics. It begins with some of the basic facts about atomic nuclei and how they can be understood as consequences of the properties of the nucleon-nucleon interaction. It then discusses some more detailed nuclear models and nuclear decays and reactions.

Prerequisite: QM5

Read:

R. Eisberg and R. Resnick Quantum Mechanics of Atoms, Solids, Nuclei and Particles (2nd Ed.) , Chapt. 15 - Nuclear Models, Sec. 1-9; Chapt. 16 - Nuclear Decay and Nuclear Reactions, Sec. 1-3,5,7.

COMMENT: The physics we study can be divided into two classes:

1. The way particles act under the influence of arbitrary forces. This includes classical and quantum mechanics and relativity.
2. The study of what forces particles exert on each other. Four classes of forces are known: gravitational, electromagnetic, weak and strong. We have simple expressions for the first two (although the quantum theory of gravity is still a challenge and an active topic of research). The weak force is now known to be closely related to the electromagnetic force. The strong force is now thought to be described by "quantum chromodynamics" (QCD) but the consequences of this theory for situations such as nuclear physics are still not understood in detail.

A majority of physicists work in just one of the above classes, but study what happens when a certain collection of particles behave as determined by (a) under forces determined by (b). It is a long step from understanding the principles of quantum mechanics and Maxwell's equations to understanding all of solid state physics, even though we believe all of know solid state physics should follow from these two fundamental theories.

If the underlying forces are unknown, or cannot be simply expressed, the problem of how a collection of many particles interact with each other becomes even more difficult. Ideally, on should first try to arrange systems where the effect of the forces on the motion is simple. For example, we would not have discovered Maxwell's equations by trying to discover which of all possible force laws explained the properties of large chunks of, say, iron. They were in fact discovered by measuring the forces between two charged spheres as a function of their separation, and similar simple systems.

Unfortunately we cannot hold a neutron and a proton 10^(-13) cm apart and measure the force between them to determine the propertied of the nuclear forcee. There is an unavoidable mix in nuclear physics between the problem of what the forces are and the problem of how nucleons behave under given forces. Perhaps in the future a way to understand the application of QCD to systems like nuclei will be found. In the meantime nuclear physics consists of somewhat vague understandings and approximate models.

Quesions:

Problems:

1. Suppose nucleons had intrinsic spin 3/2 instead of 1/2, but that spin-orbit and spin-spin coupling could still be ignored. How many different values of the z-component of spin could each nucleon have. How would the Mayer and Jensen shell model scheme be modified?
2. ²²¹Po -> ²⁰⁸Pb + ⁴He is an allowed decay. Calulate the mutual electrostatic potential energy of the lead and the helium nuclei when they are just touching, using the approximate radii for the two nuclei. If classical mechanics were correct the α particle would emerge with this energy. With what kinetic energy does it actually emerge? How is the difference in these two numbers reconciled?
3. Why is the cross section σ called a cross section? You might consider a nucleus which induced a scattering every time an incident particle came within it. Are there any conceptual problems with this interpretation?
4. A certain compound nucleus ²⁰Ne can be formed by bombarding either ¹⁹F with a proton or ¹⁶O with and alpha particle. The cross sections for these reactions are σ(¹⁹F (p,p)¹⁹F) = 50 mb, σ(¹⁹F (p,α)¹⁶O) = 5 mb, and σ(¹⁶O (α,p)¹⁹F) = 20 mb at the energies which correspond to the production of the compound nucleus. What is the cross section for ¹⁶O (α,α)¹⁶O at this energy?