The Deuteron as a Canonically Quantized Biskyrmion

Abstract

The ground state configurations of the solution to Skyrme’s topological soliton model for systems with baryon number larger than 1 are well approximated with rational map ansatz, without individual baryon coordinates. Here the canonical quantization of the baryon number 2 system, which represents the deuteron, is carried out in the rational map approximation. The solution, which is described by the six parameters of the chiral group SU(2) × SU(2), is stabilized by the quantum corrections. The matter density of the variational quantized solution has the required exponential large distance falloff and the quantum numbers of the deuteron. Similarly to the axially symmetric semiclassical solution, the radius and quadrupole moment are, however, only about half as large as the corresponding empirical values. The quantized deuteron solution is constructed for representations of arbitrary dimension of the chiral group.