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

doi:10.1016/0375-9474(86)90270-8

Nuclear Physics A

Volume 454, Issue 2, 16 June 1986, Pages 288-300

https://doi.org/10.1016/0375-9474(86)90270-8 Get rights and content

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 ²⁰Ne in the SU(3), Sp(1, R), and S0(3) × D submodels. These results are compared with experiment and with other calculations.

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SU(3) quasi-dynamical symmetry as an organizational mechanism for generating nuclear rotational motions
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The phenomenological symplectic model with a Davidson potential is used to construct rotational states for a rare-earth nucleus with microscopic wave functions. The energy levels and E2 transitions obtained are in remarkably close agreement (to within a few percent) with those of the rotor model with vibrational shape fluctations that are adiabatically decoupled from the rotational degrees of freedom. An analysis of the states in terms of their SU(3) content shows that SU(3) is a very poor dynamical symmetry but an excellent quasi-dynamical symmetry for the model. It is argued that such quasi-dynamical symmetry can be expected for any Hamiltonian that reproduces the observed low-energy properties of a well-deformed nucleus, whenever the latter are well-described by the nuclear rotor model.
Transverse form factors in the collective and symplectic models
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Transverse electron scattering form factors are calculated for 0⁺ → 2⁺ excitations in ¹⁶O, ²⁴Mg and ⁴⁰Ca. The objective is to learn about the current flows associated with nuclear collective motions. The 2⁺ states considered in ¹⁶O and ⁴⁰Ca are giant quadrupole vibrational excitations. In ²⁴Mg, the 2⁺ state is the first excited rotational state. The form factors have been computed microscopically within the framework of the symplectic model and, in order to interpret the dynamical content of collective flows of the model, the results are compared with form factors calculated with collective models, for different collective flows. For the giant resonance state, we calculate the form factor for irrotational-flow vibrational motion and, for the rotational state, we use the rotor model with both rigid and irrotational current flows.
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A symplectic model calculation of transverse electron scattering form factors for <sup>24</sup>Mg
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Electron scattering multipoles for symplectic shell model applications
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The charge and current density multipoles used in calculating electron scattering form factors are given in a form suitable for second-quantized SU (3) shell-model applications. The expressions are exact representations of the density multipoles, extend over all major oscillator shells, and are tailored for symplectic shell-model applications. Through a SU(3) tensor decomposition of these multipoles, the importance of considering multiple irreps in symplectic model calculations for ds-shell nuclei is explored, as well as the extent to which higher shell correlations will influence form factor predictions. Results for SU(3) model applications to ²⁰Ne, ²²Ne, and ²⁴Mg are given and the significance of the theory for symplectic model applications is discussed. The relation of this general fermion formulation to a restricted harmonic oscillator boson representation is also demonstrated.

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

Abstract

Nucl. Phys.

Sov. J. Nucl. Phys.

Phys. Lett.

Phys. Lett.

Ann. Rev. Nucl. Sci.

Progr. Theor. Phys.

Phys. Lett.

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Ann of Phys.

Nucl. Phys.