Luneburg-lens-like structural Pauli attractive core of the nuclear force at short distances

Abstract

The nuclear force has been understood to have a repulsive core at short distances, similar to a molecular force, since Jastrow proposed it in 1951. The existence of the repulsion was experimentally confirmed from the proton-proton scattering 1 S0 phase shift, which becomes negative beyond 230 MeV. This repulsion is essential for preventing the nucleon-nucleon system from collapsing by attraction. The origin of the repulsion has been considered to be due to the Pauli principle, similar to the repulsion originally revealed in α-α scattering, in many studies including recent lattice QCD calculations. On the other hand, very recently it was shown that an inter-nuclear potential including α-α interactions has a Luneburg-lens-like attraction at short distances rather than repulsion. We show that the nuclear force with an attractive potential at short distances that reproduces the experimental phase shifts well has a Luneburg-lens-like structural Pauli attractive core (SPAC) at short distances and acts as apparent repulsion. The apparent repulsion is caused by the deeply embedded unobservable Pauli forbidden state similar to nucleus-nucleus potentials. In this paper it is shown the nuclear force with an attractive potential at short distances that reproduces the experimental phase shifts well, has a Luneburglens-like structural Pauli attractive core similar to the nucleus-nucleus potential and acts as apparent repulsion. This study was inspired by the recent discovery of the Luneburg-lens-like structural Pauli attraction in nucleusnucleus potentials [1].The nuclear force is essential for the existence of nuclei [2]. It binds nucleons, which allows the stable existence of atoms and matter, therefore life. The origin of the nuclear force was theoretically revealed by Yukawa [3]. The nuclear force was extensively studied by the Japanese nuclear force group [4][5][6][7] based on the three-stage theory of Taketani [4,5]. Jastrow proposed the existence of short range repulsion at short distances [8], which was supported by the negative 1 S 0 phase shift observed by 310 MeV proton-proton scattering [9]. As shown in Fig. 1, a tremendous number of studies [5,[8][9][10][11][12][13][14][15][16][17] show that the nuclear force has a repulsive core (hard or soft) at short distances in the innermost region III, and is attractive in the intermediate range region II and in the outermost one pion exchange potential (OPEP) region I. Phenomenological potential models proposed in the 1960s include the Hamada-Johnston (HJ) potential with a hard core [10], Reid soft core potential [11] and Tamagaki's Gaussian 3 range soft (G3RS) core potential [12]. The modern high-precision potentials fitting many N N data [17] [16], in which a repulsive core is introduced phenomenologically. The origin of the repulsive core has remained a challenging subject. It has been ascribed to heavy meson exchanges [18] and the Pauli principle due to the substructure of the nucleon [19][20][21][22].After QCD was established, new light was shed on the origin of th...

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“…Notice that the role of the Pauli principle is to dampen the radial wave function at short distances, and both the Pauli repulsion and the Pauli attraction achieve this in a similar way. This has recently been advocated by Ohkubo for a nucleon-nucleon interaction [134]. The Pauli attraction can naturally emerge from the semi-classical theory in such a way that the physical wave function has to be orthogonalized to Pauli forbidden states and thus the potential has to be deep enough to hold the forbidden states [135][136][137][138].…”

Luneburg-lens-like structural Pauli attractive core of the nuclear force at short distances

“…A recent paper [1] finds a nuclear force with an attractive potential at short distances that reproduces the experimental 1 S 0 phase shifts well. Such a potential can be motivated by early quark-model ideas [2], but later work [3] showed that quark model ideas lead to short distance repulsion between nucleons.…”

“…The low-energy nucleon-nucleon wave functions of the potential of Eq. ( 1) have a node [1], which arises from the necessary orthogonality of the bound state with all scattering states. The nodes in the wave function would vastly reduce the mentioned transition amplitudes.…”

“…The corresponding uncertainty principle estimate of the kinetic energy, 2 /(M r 2 0 ), with M as the nucleon mass, is 259 MeV, so that the quickest look at this potential leads to the conclusion that the existence of a deeply bound state is an immediate consequence of using Eq. (1).…”

“…Thus there must be a bound state, and its binding energy must be greater than or equal to 620 MeV. Numerical solution of the Schroedinger equation yields a binding energy of about 640 MeV [1].…”