Fermion to boson mappings revisited

Abstract

We briefly review various mappings of fermion pairs to bosons, including those based on mapping operators, such as Belyaev-Zelevinskii, and those on mapping states, such as Marumori; in particular we consider the work of Otsuka-Arima-Iachello, aimed at deriving the Interacting Boson Model. We then give a rigorous and unified description of state-mapping procedures which allows one to systematically go beyond Otsuka-Arima-Iachello and related approaches, along with several exact results.

Implications of pseudospin symmetry on relativistic magnetic properties and Gamow-Teller transitions in nuclei

“…Recent investigations suggest that pseudospin symmetry appears to be only slightly broken particularly near the Fermi sea [2][3][4]10,9,5]. The empirical evidence for pseudospin symmetry has been in the small energy splittings between doublets.…”

“…For nucleons moving in a relativistic mean field with scalar V S and vector potentials V V , an SU(2) symmetry exists for the case for which V S = −V V [1]. This symmetry manifests itself in nuclei as a slightly broken symmetry [2][3][4][5]…”

“…A few years ago it was shown that relativistic mean field theories gave approximately the correct spin orbit splitting to produce the pseudospin doublets [19]. Finally the source of pseudospin symmetry as a broken symmetry of the Dirac Hamiltonian related to V S ≈ −V V was pointed out [2][3][4][5]. For spherical nuclei, pseudo-orbital angular momentuml is also conserved and physically is the "orbital angular momentum" of the lower component of the Dirac wavefunction.…”

“…One consequence of this relativistic SU(2) pseudospin symmetry is that the spatial wavefunction for the lower component of the Dirac wavefunctions will be equal in shape and magnitude for the two states in the doublet [3][4][5]. For spherical nuclei, this means that the radial wavefunctions for the lower components in the doublet will have the same number of nodes, so we label these states with pseudo-radial quantum number (i.e.…”

“…However, to date, the effect of pseudospin symmetry on the relativistic wavefunction has not been tested empirically. Since the lower component of the Dirac wavefunction is small [3,5,10] this effect will be difficult to detect except perhaps in certain forbidden transitions. For example, single -nucleon magnetic dipole and Gamow-Teller transitions between pseudospin doublets are forbidden non-relativistically (i.e., "ℓ forbidden" [20,21]) because the orbital angular momenta of the two states differ by two units.…”