Quantum Optics and Heavy Ion Physics

I shall try to say a few words about two particular ways in which my own work has a certain relation to your work with heavy ions. My title is therefore quantum optics and heavy ion physics. Some of this work deals with a form of nuclear scattering theory. The approach I shall talk about is really a nuclear diffraction theory [1]. It grows directly out of the ancient Fraunhofer form of optical diffraction theory, which in effect is a theory of small momentum transfer collisions. The “collisions” take place between a plane-wave and a screen of some sort with an aperture in it, or with a partially absorbing obstacle. These waves in effect describe small momentum transfer collisions because the deflections of the wave are usually small. Most of the scattered intensity is thereby cast near the forward direction. There is of course always a requirement that the wave-length be small compared to the dimensions, whatever they may be, of the aperture or the obstacle. Now how does one apply this approach in nuclear physics? The most elementary and passive model of the nucleus is as a transparent sphere of some sort, perhaps a cloudy or partially absorbing one. That is the so-called optical model. The wave travelling through that sphere suffers changes both of amplitude and phase. Here in Fig. 1a we have such a phase-shift χ(b) at the impact parameter b. Now since deflections of the wave within the interaction region are negligible, all of the scattered intensity is thrust near the forward direction, and that happens to be where the approximation is a good one. In fact it is for that reason a unitary approximation, and it therefore possesses a certain self-consistency. In the case of elastic scattering, for example, you can calculate the same total cross-sections either by integrating the approximate intensity over angles, or by using the “optical theorem.”