The nuclear scissors mode within two approaches (Wigner function moments versus RPA)

Two complementary methods to describe the collective motion, RPA and Wigner function moments method, are compared on an example of a simple model - harmonic oscillator with quadrupole-quadrupole residual interaction. It is shown that they give identical formulae for eigenfrequencies and transition probabilities of all collective excitations of the model including the scissors mode, which here is the subject of our special attention. The exact relation between the variables of the two methods and the respective dynamical equations is established. The normalization factor of the "synthetic" scissors state and its overlap with physical states are calculated analytically. The orthogonality of the spurious state to all physical states is proved rigorously.Comment: 39 page

A new type of nuclear collective motion - the spin scissors mode

The coupled dynamics of low lying modes and various giant resonances are studied with the help of the Wigner Function Moments method on the basis of Time Dependent Hartree-Fock equations in the harmonic oscillator model including spin-orbit potential plus quadrupole-quadrupole and spin-spin residual interactions. New low lying spin dependent modes are analyzed. Special attention is paid to the spin scissors mode.Comment: 21 page

Orbital and spin scissors modes in superfluid nuclei

Nuclear scissors modes are considered in the frame of Wigner function moments method generalized to take into account spin degrees of freedom and pair correlations simultaneously. A new source of nuclear magnetism, connected with counter-rotation of spins up and down around the symmetry axis (hidden angular momenta), is discovered. Its inclusion into the theory allows one to improve substantially the agreement with experimental data in the description of energies and transition probabilities of scissors modes in rare earth nuclei.Comment: arXiv admin note: text overlap with arXiv:1301.251

Nuclear Scissors with Pairing and Continuity Equation

The coupled dynamics of the isovector and isoscalar giant quadrupole resonances and low lying modes (including scissors) are studied with the help of the Wigner Function Moments (WFM) method generalized to take into account pair correlations. Equations of motion for collective variables are derived on the basis of the Time Dependent Hartree-Fock-Bogoliubov (TDHFB) equations in the harmonic oscillator model with quadrupole-quadrupole (QQ) residual interaction and a Gaussian pairing force. Special care is taken of the continuity equation.Comment: 28 pages, 3 figure

Electric 1+1^+ state below nuclear scissors

The solution of time dependent Hartree-Fock-Bogoliubov equations by the Wigner function moments method predicts four low-lying $1^+$ states. Three of them are known as various scissors modes. Fourth state is disposed below all scissors modes and has the electrical nature. It is found that it represents one of three branches of $2^+$ state which can exist in spherical nuclei and which is split %due to a deformation. in deformed nuclei. It is discovered, that the antiferromagnetic properties of nuclei lead to the splitting of $2^+$ states already at the zero deformation.Comment: 20 pages, 6 figures, 2 table

Nuclear Scissors Mode with Pairing

The coupled dynamics of the scissors mode and the isovector giant quadrupole resonance are studied using a generalized Wigner function moments method taking into account pair correlations. Equations of motion for angular momentum, quadrupole moment and other relevant collective variables are derived on the basis of the time dependent Hartree-Fock-Bogoliubov equations. Analytical expressions for energy centroids and transitions probabilities are found for the harmonic oscillator model with the quadrupole-quadrupole residual interaction and monopole pairing force. Deformation dependences of energies and $B(M1)$ values are correctly reproduced. The inclusion of pair correlations leads to a drastic improvement in the description of qualitative and quantitative characteristics of the scissors mode.Comment: 36 pages, 5 figures, the results of calculation by another method and the section concerning currents are adde

Semirelativistic stability of N-boson systems bound by 1/r pair potentials

We analyze a system of self-gravitating identical bosons by means of a semirelativistic Hamiltonian comprising the relativistic kinetic energies of the involved particles and added (instantaneous) Newtonian gravitational pair potentials. With the help of an improved lower bound to the bottom of the spectrum of this Hamiltonian, we are able to enlarge the known region for relativistic stability for such boson systems against gravitational collapse and to sharpen the predictions for their maximum stable mass.Comment: 11 pages, considerably enlarged introduction and motivation, remainder of the paper unchange

Toroidal quadrupole transitions associated to collective rotational-vibrational motions of the nucleus

In the frame of the algebraic Riemann Rotational Model one computes the longitudinal, transverse and toroidal multipoles corresponding to the excitations of low-lying levels in the ground state band of several even-even nuclei by inelastic electron scattering (e,e'). Related to these transitions a new quantity, which accounts for the deviations from the Siegert theorem, is introduced. The intimate connection between the nuclear vorticity and the dynamic toroidal quadrupole moment is underlined. Inelastic differential cross-sections calculated at backscattering angles shows the dominancy of toroidal form-factors over a broad range of momentum transfer.Comment: 11 pages in LaTex, 3 figures available by fax or mail, accepted for publication in J.Phys.