Two-rotor model of deformed nuclei

Microscopic calculation of the restoring force for scissor isovector vibrations

“…These two quantities cannot be derived directly from the available experimental data. The same applies to the critical angle ~c [6][7][8], which depends, moreover, on the characteristic range of the neutron-proton interaction.…”

“…The restoring force for the A T= 1 scissor vibrations is a response of nuclear matter to the isovector density gradient created by the relative displacement of the neutrons against the protons. This restoring force was calculated earlier [6][7][8] using the approach of Goldhaber and Teller [2] originally applied to giant resonances. They evaluate the increase in potential energy due to the lack of the neutronproton overlap in the isovector vibrations.…”

“…The resulting energy (about 10-12MeV) seems to be several times higher than the energy of the magnetic dipole states, which have been observed in recent experiments on inelastic electron scattering [11,12] and resonance fluorescence following photoexcitation [13] and which have been identified with the isovector scissor vibrations. When the classical hamiltonian is quantized before the transformation to the intrinsic frame, which is considered to be a more appropriate procedure, the energy of the scissor isovector vibration increases by a factor of l/~ [8]. The energy is reduced further by using the rigid-body moment of inertia and lowering the stiffness parameter by a factor 1/2 [8].…”

“…When the classical hamiltonian is quantized before the transformation to the intrinsic frame, which is considered to be a more appropriate procedure, the energy of the scissor isovector vibration increases by a factor of l/~ [8]. The energy is reduced further by using the rigid-body moment of inertia and lowering the stiffness parameter by a factor 1/2 [8].…”

“…The name "giant angle dipole" was also suggested previously [-5]. Estimates for the main characteristics of this type of collective motion were obtained with the TRM [6][7][8] by evaluating the stiffness, associated with this vibration using the procedure of Goldhaber and Teller [2]. The resulting energy (about 10-12MeV) seems to be several times higher than the energy of the magnetic dipole states, which have been observed in recent experiments on inelastic electron scattering [11,12] and resonance fluorescence following photoexcitation [13] and which have been identified with the isovector scissor vibrations.…”