The magnetic dipole response in deformed nuclei is investigated. Spurious states due to the rotation of the whole nucleus are removed by restricting the residual interaction in such a way that it commutes with the total angular momentum as a ground state expectation value in the quasi-particle random phase approximation. By this one guarantees that the spurious state due to rotations lies at energy zero and that it is a solution of the quasi-particle random phase equation (QRPA) and can easily be removed. The Hamiltonian is chosen to be a deformed Saxon Woods potential with a pairing force and an isoscalar and isovector generalized quadrupole-quadrupole and spin-spin interaction. The generalized isoscalar quadrupole operator is defined as the commutator of the independent quasi-particle Hamiltonian with the total angular momentum. The restoration of rotational symmetry mentioned above determines the isoscalar coupling constant. The generalized isovector quadrupole-quadrupole force does not commute with the total angular momentum. But one can find a linear “isovector” combination of the proton and the neutron total angular momentum which produces by a commutator with the independent quasiparticle Hamiltonian an “isovector” quadrupole operator which yields an isovector quadrupole-quadrupole force which always commutes with the total angular momentum. Thus one gets no restriction of the isovector quadrupole-quadrupole force constant. We fit it to the isovector giant quadrupole resonance ( E(E2) = 130 A 1 3 MeV ). The Hamiltonian contains in addition a spin-spin force, which always commutes with the total angular momentum and therefore does not spoil the restoration of rotational symmetry. The proton-proton, neutron-neutron and proton-neutron spin force constant is determined by solving the nuclear matter problem with the Reid soft core interaction within the Brückner theory and translating the result with the help of the Migdal force into finite nuclei. This yields an almost pure repulsive isovector spin-spin force. This Hamiltonian predicts a high lying ΔN = 2 scissors mode which lies between 17 and 26 MeV. It is spread over very many 1 + states with an average spacing of 15 keV. This highlying scissors mode consists of several hundred states and the overlap with an artificially constructed scissors mode is of the order of 38%, while the low lying scissors mode which shows up as 1 + states around 3 MeV has an overlap with the scissors mode of more than 50 %. In the same energy range as the high lying scissors mode lies also the isovector giant quadrupole resonance. Even at 180°, that means at completely backward angles, the E2 is comparable with the M1 excitation. This is due to the transversal quadrupole transition probability which is not disappearing in electron scattering at 180°. The same Hamiltonian is nicely describing the low lying scissors mode around 3 MeV in the rare earth and the transuranic nuclei. It gives the energies and the reduced magnetic dipole transition probabilities. It also can reproduce the formfactors measured by inelastic electron scattering. The Hamiltonian also reproduces the spin-flip states between 5 and 9 MeV excitation energy, which can be measured by inelastic proton scattering. One obtains in this region two maxima. The lowest one around 6 MeV is mainly of isoscalar nature and is weaker than the spin flip maximum at 7 to 8 MeV, which is mainly of isovector nature. The detailed form of this two-spin flip maxima depend very sensitively on the ratio of the isoscalar and isovector strength of the spin-spin force. In conclusion one can say: There exist a high lying scissors mode, but it is strongly fragmented over several hundred 1 + states between 17 and 26 MeV and even in electron scattering at backward angles the cross section for the excitation of the isovector giant quadrupole resonance is of comparable size. Thus it will be difficult to establish experimentally the existence of this high lying scissors mode.
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