PHYSICAL REVIEW C 89, 034614 (2014) Importance of nonlinearity in the NN potential B. B. Sahu, 1 , * S. K. Singh, 2 M. Bhuyan, 2 S. K. Biswal, 2 and S. K. Patra 2 1 Department of Physics, School of Applied Sciences, Kalinga Institute of Industrial Technology (KIIT) University, Bhubaneswar 751024, India 2 Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India (Received 18 November 2013; revised manuscript received 10 February 2014; published 17 March 2014) A simple form of nonlinear self-coupling of the scalar meson field is introduced and suggests a new nucleon- nucleon (NN ) potential in relativistic mean field theory (RMFT) analogous to the M3Y interaction. We investigate the ability of RMFT to reproduce nuclear ground state properties and the surface phenomena like proton radioac- tivity simultaneously with the proposed NN interaction. The results obtained agree reasonably well with the widely used M3Y NN interactions and the experimental data in this first application of nucleon-nucleon potential. DOI: 10.1103/PhysRevC.89.034614 PACS number(s): 21.30.Fe, 13.75.Cs, 21.10.−k, 21.65.−f I. INTRODUCTION In the nucleonic regime nuclei behave as sets of interacting nucleons. In order to go beyond some basic nuclear models which provide a global description of the system one has to include in the picture the elementary interaction between nucleons. One can then explore how the average potential well, in which nucleons evolve, can be built up from this elementary stone and thus gain a more microscopic picture of nuclei as constructed from nucleons. Early field theoretical ap- proaches [1] in the 1950s were generally unsuccessful. These eventually gave way to more phenomenological treatments [2] which provided a pragmatic way to describe the abundant NN scattering and bound state (deuteron) data. In the beginning of the 1970s many theoretical models emerged which were more successful than the earlier attempts. These were based on one-pion exchange (OPE), heavy meson exchange, and multimeson exchange plus short-range phenomenology [3–6]. A key idea on which much theoretical machinery is founded is the concept of the nuclear mean field, which basically relies on the fact that nucleons move quasi-independently from one another inside a nucleus. Although the mean field underlies many of our discussions, one should not forget the elementary nucleon-nucleon interaction from which it is built. But it is not our aim to discuss here all the works which have been devoted to the NN interaction. We thus only recall the shape of the interaction with a few gross properties. We content ourselves with noting that the dominant part of the interaction is central and is strongly repulsive at short range (0.4 fm, hard core) and attractive at intermediate range (∼1–1.2 fm). This dominant repulsive and attractive shape of the interaction is the typical widely used well known M3Y NN interaction [7]. The NN interaction cannot yet be derived from first principle (QCD). So the existing potentials are thus, at least partly, phenomenological and contain a possible large number of parameters and are fitted to deuteron properties and available phase shifts. This fitting procedure does not necessarily ensure a proper reproduction of many-body properties, so for the first time we try to give an NN interaction analogous to the M3Y form derived from the relativistic-mean-field (RMF) theory * bbsnou@gmail.com which leads to an overall agreement with the ground state bulk properties, compressibility, and some radioactive properties of proton drip-line nuclei and a superheavy region. A. Importance of nonlinearity It is to be noted that in our recently published paper [8] an attempt has been made to simulate the M3Y NN interaction from a simple Lagrangian [9,10]. However, the value of compressibility obtained is quite large, about 550 MeV (though it is difficult to determine empirically, in fact it is about 210 ± 30 MeV [11]). Later on its application to finite nuclei [12] shows that the results also deviate far from the experiment. To overcome the above mentioned difficulties we take the Lagrangian of Boguta and Bodmer [13] who have for the first time included the cubic and quartic terms in the scalar field. Actually they [13] studied the empirical properties of nuclear matter and finite nuclei without abnormal solution involving the nonlinear terms in the original linear σ -ω model of Miller and Green [9] in 1977. It is well understood that the binding energy (BE), charge radius, and deformation parameter (β 2 ) of finite nuclei from 20 Ne to 238 U is studied thoroughly and some of them are presented in Fig. 1. It is clearly seen from the the figure that the linear model, where nonlinear self-couplings of the mesons are switched off, gives a modest fit. The experimental data can be reproduced with an average error of above 20% for the energies, 0.7% for the radii, and above 50% for the β 2 parameter. The full parametrization, including the nonlinearities, allows an excellent fit. It reproduces the experimental data with an average error of below 0.3% for energies, 0.3% for the radii, and comparatively less error in the β 2 parameter. This proves that a relativistic treatment of the nucleus with an explicit nonlinear mesonic degree of freedom is fully capable of repro- ducing the bulk properties of finite nuclei. The simultaneous explanation of surface phenomena like proton radioactivity is quite impressive over the linear one, which will be discussed later. Also the properties of infinite nuclear matter such as radius and mass of the neutron star cannot be produced within the experimental range with the linear Walecka model. Again this nonlinearity generates an analogous effect of the three body interaction due to its off-shell meson couplings, which is essential for the saturation properties [14,15]. We present 0556-2813/2014/89(3)/034614(8) 034614-1 ©2014 American Physical Society