Orbital and spin scissors modes in superfluid nuclei

Nuclear scissors modes are considered in the frame of the 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.

Figure 1

Pictorial representation of two intermingled scissors: the orbital (neutrons versus protons) scissors + spin (spin-up nucleons versus spin-down nucleons) scissors. Arrows inside ellipses show the direction of spin projections; p corresponds to protons; n corresponds to neutrons.

Figure 2

The pair-field (gap) ${\mathrm{\Delta }}_0\left(r\right)$, the function $\underline{\mathrm{\Delta }}=\left|V_0\right|I_{pp}^{\kappa \mathrm{\Delta }}\left(r\right)$, and the nuclear density $n\left(r\right)$ as functions of distance $r$. The solid lines—calculations without the spin-spin interaction $H_{ss}$, the dashed lines—$H_{ss}$ is included.

Figure 3

(a), (b) The energies $E$ and (c), (d) $B\left(M1\right)$ factors as functions of the spin-orbital strength constant $\eta$. (a), (c) Solid lines are without the spin-spin interaction $H_{ss}$, dashed lines are with $H_{ss}$ included. (b), (d) The same as in panels (a) and (c) but with pair correlations included.

Figure 4

(a) Protons with spins $\uparrow$ (up) and $\downarrow$ (down) having nonzero orbital angular momenta at equilibrium. (b) Protons from panel (a) vibrating against one another.

Figure 5

(a) The energies $E$ and (b) $B\left(M1\right)$ factors as a functions of the spin-orbital strength constant ${\kappa }_{\mathrm{Nils}}$. The dashed lines—calculations without $L_{10}^{-}\left(\mathrm{eq}\right)$, the solid lines—$L_{10}^{-}\left(\mathrm{eq}\right)$ are taken into account. $H_{ss}$ and pairing are included.

Figure 6

(a) The energies $E$ and (b) $B\left(M1\right)$ factors as a function of the mass number $A$ for nuclei listed in Table 3.