Introduction to Nuclear Physics

Nuclear Physics is physics at lengths scales around $1~{\rm fm}$, and its study started around the turn of the century with several important experimental discoveries. As you all know, it was the inadequacy of J.J. Thompson's "Plum-Pudding Model" of the atom to describe the back-angle scattering of $\alpha$-particles from atoms that lead Ernest Rutherford (a New Zealander) to propose the "Solar System" (if you like) model of the atom. In Rutherford's model, most of the mass of the atom, of radius $r_{\rm atom}~\sim~10^{-8}~{\rm cm}$. is concentrated in a much smaller volume of radius, $r_{\rm nucleus}~\sim~10^{-13}~{\rm cm}$, leaving most of the atom void from mass except that carried by the atomic electrons. This is in contrast to Thompson's model where the mass is uniformly distributed over the atomic volume, with the electrons stuck in like the plums in a plum-pudding. Rutherford's model, one with a compact hard scattering core, could explain a large cross section for back-angle $\alpha$-scattering, or as we know it know, "Rutherford Scattering". He was looking at electromagnetic scattering (Nuclear Interactions were not known about at the time) and hence was guided by what he knew about electromagnetic interactions. Previous models had the charge distribution smeared out over a large volume, whereas he found that the charge was required to be highly localized, point-like, on the scale of his probe. This type of investigation continued for the rest of this century. Large angle scattering which is physics of today, becomes the small-angle backgrounds of the physics of tomorrow. Rutherford scattering is a prime demonstration of this. As one fires in smaller and smaller wavelength objects to probe the response of a given system, at some energy the wavelength becomes short enough to see the finite extent of the scattering center and hence things start looking like the Thompson model again! On should also recall that at Rutherford's time, and for many years after, the neutron was not known about, the only "fundamental" particles were the electron and the proton. It was only in 1932, that Chadwick discovered the neutron. This really was the start of nuclear physics as we know it (in my opinion of course).

The phenomenology of nuclear physics is vast, by which I mean that there are many very interesting effects, observations and descriptions that exist. The theory at a descriptive level (e.g. the shell model) is well developed, and describes the features of nuclei and their excitations at an acceptable level. Understanding nuclear physics at a fundamental level (i.e. from QCD) is still in its infancy. The hope is that the global symmetries of QCD (e.g. chiral symmetry) will constrain hadronic interactions sufficiently to give rise to calculable nuclear observables. Such ideas are not new, but they are difficult to implement. It is only over the last few years that such a program has become feasible and that nuclear physicists have become interested. Significant progress has been made in the one-, two- and three-body sectors by employing effective field theory techniques. I hope that we will be able to discuss these developments during the next quarter. If you have had a course in field theory you might be interested in looking at the recent work (e.g. [1] and references therein).

It seems logical that the approach to take is to understand the one-nucleon, two-nucleon and other few nucleon systems at all relevant momentum transfer and then go ahead and compute nuclear observables, such as binding energies, magnetic moments, quadrupole moments and anything else you might think of doing. Certainly, in my mind this is the only approach that ultimately allows us to understand what is going on. However, the real world is not so nice, but just as pretty! Collective effects play a central role in much of nuclear physics. For example, nuclei in the $A=20$ region are highly "deformed", which can be seen by the relative size of electric quadrupole radiation emitted in transitions between excited states. Such collective effects are difficult to see when we are only looking at the microscopic interactions. Hence, it is sometimes much easier to go to a much more phenomenological approach. The shell-model is a good example of this where the nucleons are (to first approx) non-interacting objects moving in independent single particle orbits of a central potential, whose radial dependence is determined empirically. Such models works OK. We will look at this in much more detail later.