Hamada—Johnston potential

To most of us, Tom Kuo is best known for this seminal work on the effective interaction of two valence nucleons in nuclei ( Kuo-Brown matrix elements ) published in 1966 [1]. One of the most fundamental goals of theoretical nuclear physics is to understand atomic nuclei in terms of the basic nucleon-nucleon (NN) interaction. Tom and Gerry s work of 1966 was the first successful step towards this goal. Microscopic nuclear structure has essentially two ingredients many-body theory and the nuclear potential. During the past 25 years, there has been progress in both of these fields. Tom Kuo has worked consistently on the improvement of the many-body approaches appropriate for nuclear structure problems [2,3]. On the other hand, there have also been substantial advances in our understanding of the NN interaction since 1966, when the Hamada-Johnston potential [4] was the only available quantitative NN potential. 

In the 1960s, the rapidly growing experimental data made it possible to construct phenomenological potentials that could describe various effects of NN interaction. Such are the Hamada-Johnston potential with hard core (Hamada and Johnston 1962), the Yale potential with hard core (Lassila et al. 1962), the nonlocal Tabakin potential (Tabakin 1964), and the Reid potential with soft core (Reid 1968). 

In the hard-core potentials, infinitely strong repulsions are used at distances <0.5 fin. The Reid potential is also very repulsive in the core region, but it is gradually growing as the distance between the nucleons decreases. The explicit form of the Hamada—Johnston potential is as follows ... 

The potential contains 28 fitted (nonzero) parameters. The Hamada-Johnston potential predicts the following data for the deuteron (S = 1,1 even) ... 

The one-pion exchange potential shows a reasonable agreement with the Hamada-Johnston potential far from the hard core (r > 2 fin). At small distances there are deviations. A detailed comparison of different nucleon—nucleon potentials can be foimd, e.g., in Fenyes (2002). 

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