[MUSIC] Hello, welcome to the second module of our introductory course on Subatomic Physics. During this module, we'll deal with nuclear physics and its applications. At the end of the module, we will visit the Tokamak of the Swiss Institute of Technology in Lausanne. And the Beznau Nuclear Power Plant which is the oldest one still in operation. This is pretty much a self-contained module, if your main interest is nuclear physics, you will be well-served. You will also notice that it is somewhat longer than other modules, so just take your time to digest the contents without pressure. In this first video, we will review what is known about the mass of nuclei. The goals for you are the following. To know the nomenclature of atomic nuclei and their periodic system. And to be able to qualitatively describe the mass and binding energy of nuclei. Experiments of the Rutherford type demonstrate the existence of a positively charged nucleus, which is four orders of magnitude smaller than the size of the atom. These experiments only require to understand electromagnetic interactions between the project and the target. Scattering experiments can also yield information about nuclear properties. And thus establish a catalog of the properties of the nuclear interaction that holds together protons and neutrons inside the nucleus. One must not confuse this nuclear force with the strong force introduced in the first module and more extensively discussed in module number five. The strong force binds together quarks inside hadrons by gluon exchange. It does not permit quarks to leave the hadrons. So hadrons in general and nucleons in particular, do not carry a net color charge. Thus gluons cannot bind protons and neutrons to form a nucleus. The nuclear force is more like a long distance residue of the strong force in that it resembles the well-known Van der Waals force, which is a residue of the electromagnetic interaction which acts between electrically neutral molecules. Let us compare some basic properties of atoms, and the electromagnetic force on one side, to nuclei, and the nuclear force on the other side. The electromagnetic force is responsible for holding atoms together. Its properties are well known, classically, and rather easy to extrapolate to quantum distances. The study of atomic spectra indeed gave rise to quantum mechanics, which qualitatively and quantitatively explains many phenomena of condensed matter physics. The fine structure constant, the electromagnetic coupling constant, is a small number. Alpha is about 1/137, which makes perturbative calculations feasible. The nuclear force, on the other hand, must be much stronger, since it wins over the Coulomb repulsion between tightly-packed protons. It must be of short range, since it doesn't make itself felt outside the nuclear volume. It has no classical analog. Only experimental results can help to understand its properties. One thus uses experiments as a guide towards empirical models of the nucleus and of the nuclear force. We will come back to the relation between experiments and models as we go along. Let us first summarize how we identify and denote nuclei. We denote by Z, the nuclear charge, which is equal to the atomic number in the periodic table. Itis given by the number of protons in the nucleus. A is the number of nucleons, the sum of protons and neutrons, it is also called the mass number. Nuclei are thus completely identified by their electric charge and the number of nucleons. The name we give them identifies Z and usually is supplemented by A. When we say carbon 14, that means a nucleus with Z=6 and A=14. Evidently, the number of neutrons is then the difference between the mass number and the atomic number, and is denoted by N. The chemical properties of the elements are determined by the electron cloud surrounding the nucleus. The periodic table is thus organized according to Z. Nuclei with the same number of protons, but with a different number of neutrons, are called isotopes. They have very similar chemical properties but not necessarily similar nuclear properties. Examples are uranium 235 and uranium 238, which have both 92 protons, but a different number of neutrons and thus different stability properties. Another example is hydrogen, deuterium, and tritium which all have one proton and zero, one, or two neutrons. Nuclei can also be excited to higher states, keeping the number of protons and neutrons constant. These are called resonances or isomers. Nuclei with the same number of nucleons but the different number of protons are called isobars. They have roughly the same nuclear mass. Examples are carbon 12 and boron 12, with both have 12 nucleons. Naively one might assume that the mass of nuclei is simply given by the sum of the masses of protons and neutrons they contain. But in reality, this mass is, of course, diminished by the binding energy between the nucleons. The mass deficit ∆M must always be negative so that the nucleus is in a bound state. We call it the binding energy. It has been measured for practically all nuclei. The absolute value of the binding energy is the energy required to decompose the nucleus into separate nucleons. The binding energy per nucleon, ∆M/A, is the energy required to separate the average nucleon from its nucleus. It is much smaller than the mass of a nucleon p and n. The mass of the nucleus is thus indeed dominated by the mass of its constituents. For the nucleons themselves the situation is very different. The total mass of the quarks inside the nucleon is only around 1% of the nucleon mass. It is their binding energy which dominates the nucleon mass. When one analyzes the dependance of the binding energy, ∆M per nucleon A, on the mass number A one notices the following. For A less than 20 on the left side of this graph, ∆M/A oscillates but rises rapidly with increasing A. For A between 20 and 60, ∆M/A saturates. For A about 60, it has a broad maximum. That is, the iron group formed by nickel, iron, and cobalt with about 9 MeV per nucleon of binding energy. And then for A larger than 60, the binding energy per nucleon decreases slowly. The general mean is about 8 MeV per nucleon. The kinetic energy of nucleons inside the nucleus must thus be relatively small. Otherwise, they would not stay bound. The velocities of bound nucleons are thus non-relativistic. The binding energy corresponds indeed to a wavelength of nucleons inside the nucleus. This wavelength is less than two Fermi of the order of the nucleus' size itself. It is thus plausible that the nucleus can contain nucleons with the maximum kinetic energy of about 8 MeV. Or a maximum momentum of about 120 Me. If, on the other hand, the nucleus would contain electrons, they would be relativistic and their wavelength would be 2.5 x 10^-12 centimeters, much bigger than the nucleus size. The nucleus can thus not contain bound electrons. They need a much larger volume to be contained. This is obviously in agreement with the findings of Geiger and Marsden, that we have discussed in the previous module. In the next video, we will talk about the size and the spin of nuclei. [MUSIC]
