A Nuclear Model with Explicit Mesons
- PDF / 311,317 Bytes
- 8 Pages / 595.276 x 790.866 pts Page_size
- 92 Downloads / 186 Views
D. V. Fedorov
A Nuclear Model with Explicit Mesons
Received: 10 June 2020 / Accepted: 1 October 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract A nuclear model is proposed where the nucleons interact by emitting and absorbing mesons, and where the mesons are treated explicitly. A nucleus in this model finds itself in a quantum superposition of states with different number of mesons. Transitions between these states hold the nucleus together. The model—in its simplest incarnation—is applied to the deuteron, where the latter becomes a superposition of a neutron-proton state and a neutron-proton-meson state. Coupling between these states leads to an effective attraction between the nucleons and results in a bound state with negative energy, the deuteron. The model is able to reproduce the accepted values for the binding energy and the charge radius of the deuteron. The model, should it work in practice, has several potential advantages over the existing non-relativistic few-body nuclear models: the reduced number of model parameters, natural inclusion of few-body forces, and natural inclusion of mesonic physics. 1 Introduction In the low-energy regime the nucleons are believed to interact by exchanging mesons [1–3]. However the accepted contemporary non-relativistic few-body nuclear models customarily eliminate mesons from the picture and introduce instead phenomenological meson-exchange-inspired nucleon-nucleon potentials tuned to reproduce available experimental data [3–6]. In this contribution the meson-exchange paradigm is going to be applied literally by allowing nucleons to explicitly emit and absorb mesons which will be treated on the same footing as the nucleons. A nucleus in this model will be a superposition of states with different number of emitted mesons. Since it takes energy to generate a meson, in the low-energy regime the states with mesons will find themselves under a potential barrier equal to the total mass of the mesons. One might expect that in the first approximation only the state with one meson will contribute significantly. In one-meson approximation a nucleus becomes a superposition of two subsystems: a subsystem with zero mesons, and a subsystem with one meson. The corresponding Hamiltonian is then given as a matrix, KN W H= , (1) W † K N + Kσ + mσ where K N is the kinetic energy of nucleons, K σ is the kinetic energy of the meson, m σ is the mass of the meson, and W is the operator that couples these two subsystems by generating/annihilating the meson. The corresponding Schrodinger equation for the nucleus is then given as KN W ψN ψN =E , (2) ψσ N ψσ N W † K N + Kσ + mσ D. V. Fedorov (B) Aarhus University, Aarhus, Denmark E-mail: [email protected]
0123456789().: V,-vol
40
Page 2 of 8
D. V. Fedorov
where ψ N is the wave-function of the subsystem with nucleons only; ψσ N is the wave-function of the subsystem with nucleons and a meson; and E is the energy. If E < m σ the meson is under barrier and cannot leave the nucleus. In the literature
Data Loading...
