Splitting of the isovector giant dipole resonance in neutron-rich spherical nuclei

The well-known splitting of the isovector giant dipole resonance is traditionally explained as a phenomenon of the nuclear isospin asymmetry (isospin splitting model) or the nuclear deformation. We suggest a new mechanism of the splitting of the giant multipole resonances in spherical neutron-rich nuclei resulting from the interplay of the isovector and isoscalar sounds with different velocities. Our approach is based on the collisional Landau kinetic theory and can be used for description of the splitting phenomena for both the isoscalar and the isovector modes in a wide region of nuclear masses $A~40\text{−}240$. For the isovector dipole modes, the evaluated values of the splitting energy, the relative strength of the main and satellite resonance peaks, and the contribution to the energy-weighted sum rule are in agreement with experimental data.

Figure 1

Solutions of the dispersion equation (26) for $s^{(1)}$ and $s^{(2)}$ versus the $\omega \tau$ parameter (see numbers near the circles). The full points (solid line) are for the isovector-like sound velocity $s^{(2)}$ with the Landau parameters $F_0^{\text{'}}=1.2,F_{(1)}^{\text{'}}=0$. The open circles are for the isoscalar-like sound velocity $s^{(1)}$; solid line for $F_0=-0.2,F_1=0.6$ and broken line for $F_0=-0.2,F_1=0$.

Figure 2

Giant dipole resonance energies $E_{\mathrm{GDR}}$ multiplied by $A^{1/3}$ (top) and exhaustion $m_1^{(\kappa )}/m_{\mathrm{GDR}}$ of the $\mathrm{EWSR}$ $m_{\mathrm{GDR}}$ of Eq. (64) (in percent, bottom) for the main isotopes along the $\beta$-stability line vs the particle number A. The full points are the experimental data from Refs. 37, 38, 39 (see http://depni.npi.msu.su/cdfe/). The solid and broken lines are the main GDR resonances and their satellites obtained from Eq. (42) with Eq. (43) for $F_0^{\text{'}}=0.6$, $F_0=-0.46$, $F_1=-0.9$, $b_{s,-}=78$ MeV, $r_0=R_0/A^{1/3}=1.1$ fm, and $\tau =1.05\times {10}^{-22}$ s. Points and lines correspond to the estimations (44).

Figure 3

Isovector giant dipole resonance energies $E_{\mathrm{GDR}}$ (top), $\mathrm{EWSR}$ exhaustion $m_1^{(\kappa )}/m_{\mathrm{GDR}}$ (bottom, in percent), and satellite strength $m_0^{(1)}$ divided by the main peak $m_0^{(2)}$ (middle) for the Ca isotopes vs the asymmetry parameter $X=(N-Z)/A$. The full and open circles show the experimental data from Refs. 37, 38, 39 and Ref. 7, respectively. The squares, triangles, and inverted triangles are obtained from the cross sections for the corresponding ($\gamma ,n$) and ($\gamma ,p$) reactions of Refs. 5, 3, 6, 11, as explained in the text. The dots in the top and middle panels present the ISM. The solid and broken lines lines in the bottom panel show the analytical (exact integral) $\mathrm{EWSR}$ exhaustion (63) for the main IVGDR and satellites. The broken-dotted line and frequent broken-dotted line denote the approximations (64) and (65). Other notations and parameters are the same as in Fig. 2.

Figure 4

The same as Fig. 3 for the Sn iso-topes. The full joined circles show the experimental data from Refs. 37, 38, 39 of different groups (see the references therein). The squares and triangles are obtained from the integral cross sections of Ref. 2 and Ref. 12, respectively.

Figure 5

The same as Fig. 3 for the Sm isotopes. The squares and triangles are obtained from the integral cross sections of Refs. 37, 38, 39 and Ref. 15, respectively.