Abstract In this study, we explore the entanglement and correlation in two-nucleon systems using isospin formalism. With the help of Slater decomposition, we derive analytical expressions for various entanglement measures. Specifically, we analyse the one- and two-mode entropies, mutual informations, and a basis-independent characteristic known as the one-body entanglement entropy. To understand the impact of pairing, we consider interactions involving isovector and isoscalar L = 0 pairing terms. Our findings show that certain pairing interactions can maximize one-body entanglement entropy of ground states when both total angular momentum and total isospin have zero projections. We provide numerical examples for the sd shell and explore the mutual informations in LS coupled and jj coupled single-particle bases. We find that the shell structure and angular momentum coupling significantly impact the measures of entanglement. We outline the implications of conserving angular momentum and isospin on one-mode entropies, irrespective of particle number.
Equations for all the seniority-zero eigenstates of
2N nucleons in an arbitrary charge- and spin-independent potential well and interacting through charge- and spin-independent pairing forces are derived. These equations are solved exactly for a large number of states of this system. The interaction in this Hamiltonian is effective in the
L=0 states of the two-nucleon system, and its strength is independent of the remaining quantum numbers of the two nucleons. We solve our equations exactly for those states whose wave functions are totally symmetric functions of the spin-isospin coordinates of the
N L=0 pairs of nucleons in the state. The wave functions of these states factor into a spin-isospin-dependent part and a spatially dependent part. The spin-isospin-dependent part of one of these wave functions is an eigenvector of three tridiagonal matrices which insure that the state is a spin, isospin, and supermultiplet eigenstate, respectively. Explicit expressions are given for the eigenvalues of these three matrices in terms of the quantum numbers of the state. The spatially-dependent part of one of these wave functions is given explicitly in terms of
N parameters which we call pair energies. These pair energies are shown to satisfy
N coupled algebraic equations which depend parametrically upon the supermultiplet quantum numbers of the state. An expression for the occupation probabilities of the levels of the single-particle well is given. Throughout this work, an arbitrary splitting of the single-particle levels is treated exactly.
Expressions for the ground and excited state energies of a system of nucleons interacting through pairing forces are given as a power series in inverse powers of the number of particles. The expressions are valid for systems with superfluid ground states and either J=0 or L=0 pairing. The first three terms in the expansion are given explicitly, and they exhibit excitations with both vibrational and rotational (in isospin space) character. Analytical and numerical results are given for a model system with a two-level single-particle spectrum.