Microscopic calculation of the restoring force for scissor isovector vibrations

Abstract

The restoring force for scissor isovector vibrations is calculated microscopically with the wave functions of an axially symmetric Woods-Saxon potential from a density-dependent symmetry energy. The experimental energies of the low-lying magnetic dipole states in rare-earth nuclei are well reproduced. It is found that only outer particles, which contribute to the nuclear moment of inertia, take part in this collective vibration. They are about half of the total number of nucleons.

Low energy orbital magnetic dipole excitations of heavy nonspherical nuclei

“…Mang on the occasion of his 60th birthday Nevertheless, in the majority of subsequent papers these states have been considered to represent the predicted isovector rotational oscillations now generally called scissors modes [3,9,10,11,12,13,14,15]. This view has been questioned by Hamamoto et al [16,17] on the basis of RPA calculations with a schematic force; but the agreement with experimental data was not good enough to make these results particularly convincing.…”

“…The restoring force has been calculated in an extension of the method of Goldhaber and Teller [20], and more recently by relating it to the asymmetry energy of the liquid drop model [11,3]. It has been noted that the restoring force is related to that ofisovector quadrupole vibrations [11].…”

“…The remarkable feature of the restoring potential is that Z and c~ appear only in the linear combination (Z-7 c5 e). -Dealing with isovector rotational and vibrational degrees of freedom separately, Nojarov et al [11] have noticed that for small deformations there is a relationship between the corresponding restoring forces. We obtain this relation from (2.11) by setting Z = 0 or c~ =0, respectively.…”

β-decay properties for neutron-rich Kr–Tc isotopes from deformedpn-quasiparticle random-phase approximation calculations with realistic forces

“…The parameters of the Woods-Saxon potential are taken from Ref. [14]. For the choice of the model space, based on previous experience, we start from the 0hω to one major shell above the Fermi surface of either proton or neutron, depending on which is close to zero-energy, so for most isotopes here with N ≤ 70, the model space is 0 − 5hω.…”

Two-neutrino double beta decay of 76Ge within deformed QRPA

“…The explicit form of single-particle harmonic oscillator wave functions in cylindrical coordinates (r, z, φ) can be found, e.g., in Ref. [37]. For a given shape of the nuclear surface, the shape of the deformed harmonic oscillator is automatically chosen in a way suitable for obtaining good accuracy with a smallest number of basis functions [35].…”