Case Study: The Development of the Liquid Drop Model

The liquid drop model of the atomic nucleus was developed from the late 1920s onwards, during a time when physicists were trying to extend their understanding of atoms to the structure of the atomic nucleus itself.90 The model was first proposed in 1928-29 by George Gamow, then a Russian doctoral student visiting Western Europe, who suggested that the nucleus “may be treated somewhat as a small drop of water in which the particles are held together by surface tension” (Gamow, in Rutherford et al 1929: 386). In line with common assumptions at the time, he modelled the nucleus as consisting of a collection of α-particles and assumed that the nucleus is in equilibrium between the kinetic energy of the particles and the surface tension. On this basis, Gamow then tried to derive an expression for the mass defects (i.e. the nuclear binding energy) of the different nuclei.

Niels Bohr and Ernest Rutherford were enthusiastic about the model and worked to secure additional support for Gamow to continue working in Western Europe between 1929 and 1931. However, while Gamow made some progress with the model, he quickly ran into problems. Although his theoretically predicted mass defects traced a curve of the same general shape as the experimentally determined ones, it gave reasonably accurate quantitative predictions only for the lighter elements. He suspected this could be remedied by instead assuming that the nucleus also contains free electrons in addition to α-particles, as some physicists at the time suspected. However, when he tried to incorporate these into his model he ran into a major theoretical problem (the so-called Klein paradox) that he

90 _{This section is primarily based on Stuewer’s (1994) historical account of the development of the liquid}

was unable to overcome. Consequently, by the summer of 1930, Gamow began to turn his attention elsewhere (Stuewer 1994: 78-85).

Despite these problems, the model quickly became popular among physicists. This was not because they were confident it accurately represented the nucleus. Rather, they saw it as a speculative but nonetheless promising approach which might help them answer some of the questions about the atomic nucleus which physicists were grappling with. For instance, in 1930 Rutherford wrote that Gamow’s model “while admittedly imperfect and speculative in character is of much interest as the first attempt to give an interpretation of the mass-defect curve of the elements” (Rutherford, Chadwick and Ellis 1930: 534; quoted from Steuwer 1994: 86-7). The model was further developed during the 1930s, along two broad trajectories. First, following the discovery of neutrons in 1932, Werner Heisenberg, and subsequently Carl von Weizsäcker, tried to revise the model on the assumption that the nucleus contains a combination of protons and neutrons. Their aim was essentially the same as Gamow, namely to derive an empirically more accurate mass defect curve. Their efforts resulted around 1935-6 in what is today known as the Semi- Empirical Mass Formula (Stuewer 1994: 87-97).91 Second, from circa 1936 onwards, Bohr and several of his collaborators attempted to adapt the model in order to account for artificially induced radioactivity, i.e. radioactive elements produced by bombarding stable elements with neutrons. Their explanation of this phenomenon was that the impinging neutrons resulted in an excitation of the nucleus and that the resulting vibrations caused the ‘evaporation’ of particles from the drop of ‘nuclear fluid’ (97-107).92 _{Finally, in 1938-}

39, Lise Meitner and Otto Frisch realised that, by combining elements of both research

91 _{The Semi-Empirical Mass Formula is so called because it is not derived from purely theoretical}

principles. Rather, it was constructed by calibrating certain empirical parameters in the revised liquid drop model to best fit the empirically determined mass-defect curve.

92 _{A number of alternative (but related) analogies also influenced this line of physical theorising about}

programmes, the liquid drop model could be adapted to explain nuclear fission, a newly discovered and, at the time, highly puzzling phenomenon (107-116).93

From the latter part of this story, it is clear that the drop analogy not only inspired Gamow’s original model, but played an important role in guiding the revisions and extensions of this model in subsequent work. There are two questions we might ask about this. The first concerns why the drop analogy suggested some revisions rather than others, that is, why these revisions seemed more natural to those who chose to work with the liquid drop model. This use of analogy is what generative accounts aim to analyse. I will say more about this in Section 4.5.

The second, which I will focus on for now, is why physicists chose to pursue the model in the first place, before there was any particular reason to think it even approximately true. We can distinguish a number of such decisions. First, after Gamow had the original idea, he chose to spend some of his limited time in Western Europe developing it into a formal model. Second, after he had presented the initial model in 1929, Bohr and Rutherford were sufficiently impressed to secure financial support to allow Gamow to continue working on the model. Third, after 1930, Rutherford continued to praise the model despite the empirical and theoretical problems it faced. Finally, during the 1930s, the model was pursued within several different research projects.

A more fine-grained analysis would be necessary to account for all the factors involved in the decisions to pursue the model in each of these cases. In this chapter, I will focus on just one question; namely, whether the drop analogy could have played any role in motivating the pursuit of the model. More specifically, I will discuss two extant pursuit worthiness accounts of analogy, arguing that these fail to plausibly account for the liquid

93 _{See also Andersen (1997) on the experimental and theoretical developments which lead to the discovery}

drop case, before proposing an alternative, more satisfactory account of how analogies can justify pursuit in cases like the liquid drop model in Section 4.5.