M.G. Vassanji

The symplectic shell-model theory of collective states

Abstract The implications of the microscopic structure of collective Lie algebras and their hydrodynamic (contraction) limits are explored. A decomposition of the nuclear Hubert space into collective subspaces and symplectic shells is proposed. The resultant symplectic shell model is shown to provide a basis for microscopic calculations which are immediately interpretable in collective-model terms.

The shell-model theory of nuclear rotational states

Abstract The symplectic model of two of the authors is presented as a simple unified independent-particle-collective model which simultaneously divides the nuclear shell-model space into horizontal layers (independent-particle shells) and vertical slices (invariant collective subspaces). This segmentation of the single-particle space makes it possible to diagonalize a unified model hamiltonian in shell-model space to obtain a description of rare-earth rotational states in remarkably good agreement with experiment. It is shown that the rotational states so obtained span a shell-model space of some 20 major harmonic oscillator shells and challenge the conventional viewpoint that rotational energies are kinetic.

The coupled-rotor-vibrator model☆

Abstract Some recent advances in the theory of dynamical groups are used to extend and put the CRV model on a more rigorous microscopic foundation. We show that vector-coherent-state theory provides exact rotor expansions of Elliotts su(3) operators as well as boson expansions of the giant-resonance excitation operators. The rotor expansion leads to simple analytic expressions for su(3) matrix elements that are exact in many situations and, in general, accurate to high order in a small parameter L /2 λ + μ , for λ ⩾ μ , and in L / λ + 2 μ , for λ μ . These expressions provide useful and accurate hand-calculator alternatives to implementation of the exact algorithms available for the computation of su(3) matrix elements in an so(3) basis. They also provide valuable insights into the physical content of the su(3) model in rotor-model terms. Another recent development shows that the rigid-rotor and SU(3) models can survive the effects of strong representation mixing due, for example, to spin-orbit and other interactions, albeit in a “softened form”. We incorporate this development into the CRV model and show that, as a consequence, nuclear rotational bands and their vibrational excitations have natural microscopic origins in valence-shell su(3) representations with strong renormalization and “softening” due to the effects of coupling to higher shells and representation mixing. Some implications of the results for the microscopic interpretation of rotational spectra in heavy nuclei are discussed.

An effective shell-model theory of collective states

Abstract A simple quadrupole-quadrupole model is used to illustrate how the coupling between different symplectic shells can be eliminated to obtain effective interactions and operators that act only within shells. The physical content of the model is transparent and relates to the calculation of core-polarization effects due to extra-core particles in the unified model. But, since the symplectic shell model is based on a group, rather than an independent-particle structure, it avoids the necessity of distinguishing core and extra-core particles or of introducing redundant collective variables and thus fully respects the Pauli principle.

Electron scattering in the microscopic Sp(3, R) model

Abstract A generating function formalism is presented for calculating the longitudinal and transverse electron scattering form factors of doubly even light nuclei in the microscopic Sp(3, R) model, and a practical computational method for carrying out the calculations is given. The method is applied to calculate the longitudinal elastic (0 → 0) and inelastic (0 → 2) form factors of 20 Ne in the SU(3), Sp(1, R), and S0(3) × D submodels. These results are compared with experiment and with other calculations.

The geometric SO(3) × D model: A practical microscopic theory of quadrupole collective motion

Abstract A practical microscopic theory is presented for quadrupole collective states. It is a submodel of the sp(3, R ) model in which some degrees of freedom are suppressed in order to gain computational viability with a modest computer. Applications are made to even sd-shell nuclei using the Brink-Boeker force and no adjustable parameters.

An application of boson second quantization techniques to the calculation of electron scattering form factors

Abstract It is suggested that boson second quantization, in terms of harmonic oscillator bosons, may be much more useful than its fermion counterpart for shell-model calculations in an LS coupled basis. The bosons carry the fundamental representation of SU(3). The combined set of boson creation and annihilation operators also carry the fundamental representation of Sp(3, R). Boson second quantization therefore provides a mechanism for expressing operators in terms of SU(3) and Sp(3, R) irreducible tensors. This is of major importance for shell-model calculations in an SU(3) basis and for the development of the symplectic shell model. Applications are made to the calculation of electron scattering form factors and it is shown how major simplifications arise when the space is restricted to a single major shell. For example, longitudinal form factors for 0 → 2 transitions in the sd-shell are shown to depend on just three parameters while the corresponding transverse form factors are uniquely determined up to an overall multiplicative constant. Further simplifications result on restriction to a single SU(3) irreducible representation.

Application of the symplectic shell model to the L = 0+ states of 4He

Abstract The nature of the low-lying L = 0 + states of 4 He is analyzed in the framework of the symplectic shell model. A generator coordinate method for microscopic calculations is used to diagonalize the Brink and Boecker force, B1, in the space defined by the 0ħω and 4ħω irreps of spatial symmetry [ f ] = [4] and the 2ħω irrep of symmetry [22]. A mixed Sp(3, R ) calculation is also attempted. Results show that the first L π = 0 + excited state is a vibrational excitation of the ground state.

A symplectic model calculation of transverse electron scattering form factors for 24Mg

Abstract The electron scattering transverse form factors for the transitions 0+ → 21+ and 0+ → 22+ for 24Mg are calculated in the symplectic model. Results show that the predictions of the sp(3, R ) model are improved over calculations restricted to the valence shell. Unlike longitudinal form factor calculations the effects of higher shells are not accounted for by simply introducing an effective charge factor.

Boson representation of the nuclear shell model charge and current densities

Abstract We use boson second quantization, in terms of harmonic-oscillator bosons, to derive simpl expressions for the charge and current density multipoles restricted to the sd shell. For example, it is shown that the shape of the longitudinal FL0+ → 4+(q) and transverse FT0+ → 4+(q) FT0+ → 5+(q) form factors are independent of the nuclear wave functions. Boson second quantization also provides a mechanism for expressing the multipole operators in terms of SU(3) tensors. We perform an SU(3) tensor analysis of the multipole operators, since this is of major importance for shell-model calculations in an SU(3) basis.