Fission was the third of the modes of nuclear decay to be discovered. Alpha and beta decay had been studied since their discovery in 1895. Nuclear fission was not discovered until 1938, when O. Hahn and F. Strassmann (1938, 1939) bombarded uranium with neutrons and definitely identified barium atoms in the products in the reaction resulting from neutron capture in uranium. This reaction had been studied extensively (see Amaldi, 1984, for a review of these years of physics) since shortly after the discovery of the neutron in 1932. However, as the reaction was expected to yield transuranium elements it was not until the work by Hahn and Strassmann that it was realised that a new and entirely unexpected nuclear phenomenon was being observed.

Hahn's coworker Lise Meitner and her nephew O. Frisch (Meitner and Frisch, 1939) coined the word fission for the new phenomenon discovered by Hahn and Strassmann. The word is a loan from biology. In close cooperation with Niels Bohr the former authors also correctly interpreted the reaction as a break-up of the nucleus into two smaller fragments and offered the first qualitative explanation of the phenomenon in terms of competition between the disrupting trend of Coulomb repulsion and the shape-stabilising effect of surface tension. The effect should have been anticipated from the liquid-drop model. Thus, for heavy nuclei the large number of positively charged protons repel each other so strongly that the small amount of energy added to the nucleus by the impinging neutron (adding its binding energy) is sufficient to make it break apart.

A general frame for the description of rotational states in nuclei was set in the beginning of the fifties by Bohr (1952) and by Bohr and Mottelson (1953). Rotation is a typical example of a collective degree of freedom in nuclei. A collective excitation is characterised by the coherent movement of a large number of nucleons. Thus, an elementary understanding of collective excitations is often achieved from macroscopic models. One example is nuclear fission, which could be considered as some kind of very large amplitude shape vibration. It is then also straightforward to introduce shape vibrations in general as a collective degree of freedom as illustrated in an elementary way in problem 10.2. In a more general context, shape vibrations can be described for example by the variation around the equilibrium value of the αλµ parameters introduced in chapter 4. The most important and first non-trivial mode corresponds to λ = 2, quadrupole vibrations.

When describing nuclear quadrupole vibrations in the laboratory system, one has to introduce all the fiveα2µ shape parameters. These can, however, be transformed to a body-fixed system where two parameters describe deformations, namely in the ε2 (or β2) and the γ degrees of freedom (the γ parameter was introduced in chapter 8). The three additional parameters then describe the orientation of the body-fixed system, e.g. by the three Euler angles. These three parameters thus describe the rotational motion, which is treated in the present chapter and continued in chapter 12. Vibrations, on the other hand, will not be treated here but instead we refer to the literature, e.g. Rowe (1970) and Eisenberg and Greiner (1987).

We have already discussed the nucleon one-body potential as the coherent external field exerted on one nucleon due to the presence of all the others. We shall now go on to analyse the basic characteristics of the underlying two-body interaction (the strong interaction).

Knowledge of this interaction rests, in part, on the observation of the properties of very simple nuclear systems. Historically, interest centred very much on the deuteron (consisting of a bound state of a neutron and a proton). Also, simple systems such as the trinucleon systems lend themselves to a direct test of the internucleon interaction.

In part the knowledge – and this is now the overwhelmingly important source – derives from a study of the properties of the scattering of protons against protons and protons against neutrons.

To reproduce the remarkably constant quantity of 8 MeV binding per nucleon encountered all over the periodic table, one has to postulate that nuclear forces have a very short range. We thus conclude as a general gross feature, a nucleon–nucleon interaction (or two-body potential) of the character exhibited in fig. 13.1 in terms of the inter-nucleon distance r.

The range, as roughly defined by fig. 13.1, we associate with the distance b marked in the figure. It is found empirically to be of order b = 1.4 fm. This is exactly the Compton wave length of the pi-meson (pion) or b = ħ/mπc. This in turn is indicative of the fact that at this relatively long range (i.e. in the outer regions of the interaction potential) the important agent, transmitting the interaction between the nucleons, is the pi-meson.

Historical remarks

The theory of quantized fields has its origin in the early days of quantum mechanics. For accounts on the early history of quantum field theory see [1.1, 1.2, 1.3, 1.4, 1.5]. After the seminal work of Heisenberg [1.6] the subsequent article of Born and Jordan [1.7] already contains a section in which the quantization of the electromagnetic field is sketched. In the following ‘Drei-Mäanner-Arbeit’ [1.8] the quantization of an arbitrary number of degrees of freedom is worked out in more detail and is applied to a calculation of the thermal and quantal fluctuations of the electromagnetic field. These parts were entirely due to P. Jordan.

In the following years the idea of quantizing classical fields was pursued further by him. But he did not only think of the quantization of the electromagnetic field, which was, apart from the gravitational field, the only known fundamental classical field at that time. He also aimed at a representation of matter by quantized fields. In this case the Schrödinger waves were considered as classical fields. Therefore he called this procedure ‘second quantization’. In this way he attempted a unified description of matter and radiation, in which both were treated on equal footing. Such a formulation should form the framework for a mathematical realization of the duality between waves and particles. Despite the criticisms of many colleagues progress was made along these lines.

The electroweak interactions in the Standard Model are described by a chiral SU(2)L ⊗ U(1)Y symmetric gauge theory. The chiral symmetry is spontaneously broken by the vacuum expectation value of the scalar Higgs boson field. The consequence of the spontaneous symmetry breaking is that most of the elementary particles (weak vector bosons, quarks and leptons) become massive through their coupling to the Higgs boson field [A3,A4]. The study of non-perturbative spontaneous symmetry breaking is one of the main motivations for the lattice investigations of the Higgs sector in the Standard Model.

Another important aspect is the mathematically rigorous definition of the chiral SU(2)L ⊗ U(1)Y symmetric quantum field theory by means of the continuum limit of a suitably discretized lattice theory. In QCD the coupling is asymptotically free, therefore the continuum limit is defined near the ultraviolet stable Gaussian fixed point at zero coupling (see, for instance, in fig. 5.7). The couplings in the electroweak sector, with the exception of the SU(2)L gauge coupling, are not asymptotically free, therefore the Gaussian fixed point at zero couplings is ultraviolet unstable. This means that the lines of constant physics do not converge to the Gaussian fixed point, as in fig. 5.7. The simplest assumption which makes the definition of a continuum limit possible is that there is another, non-trivial (non-Gaussian) fixed point, somewhere else in the bare parameter space, where the lines of constant physics converge.