Microscopic analysis of the low-energy M1(K=1) spin and orbital scissors modes

A low-energy $M1(K=1)$ spin-scissors resonance (SSR) located just below the ordinary orbital scissors resonance (OSR) was recently predicted in deformed nuclei within the Wigner Function Moments (WFM) approach. We analyze this prediction using fully self-consistent Skyrme Quasiparticle Random Phase Approximation (QRPA) method. The Skyrme forces SkM*, SVbas and SG2 are implemented to explore SSR and OSR in $^{160,162,164}$Dy and $^{232}$Th. The calculations show that isotopes $^{160,162,164}$Dy indeed have at 1.5-2.4 MeV (below OSR)$K^{\pi}=1^+$ states with a large $M1(K=1)$ spin strength. These states are dominated by $pp[411\uparrow, 411\downarrow]$ and $nn[521\uparrow, 521\downarrow]$ spin-flip configurations corresponding to $pp[2d_{3/2}, 2d_{5/2}]$ and $nn[2f_{5/2}, 2f_{7/2}]$ structures in the spherical limit. So the predicted SSR is actually reduced to low-orbital (l=2,3) spin-flip states. Moreover, following our analysis and in contradiction with the spin-scissors treatment of WFM, the deformation is not the principle origin of the low-energy spin $M1(K=1)$ states but only a factor affecting their features. In $^{232}$Th, the $M1(K=1)$ spin strength is found very small. The spin and orbital strengths are generally mixed and exhibit the interference: weak destructive in SSR range and strong constructive in OSR range. The two groups of $1^+$ states observed experimentally at 2.4-4 MeV in $^{160,162,164}$Dy and at 2-4 MeV in $^{232}$Th are rather explained by fragmentation of the orbital strength than by the occurrence of spin-flip states. The best agreement with the experimental data is obtained for the force SG2.