Isoscalar $E0, E1$, and $E2$ strength in ${}^{44}\mathrm{Ca}$

Isoscalar giant resonances in ${}^{44}\mathrm{Ca}$ have been studied with inelastic scattering of 240 MeV α particles at small angles including $0^{\circ }$. A majority of the energy weighted sum rule was identified for $E0$ and $E2$ ($\approx 70\%$), and nearly half was identified for $E1$. The strength distributions are compared with the predictions from Hartree-Fock based random phase approximation calculations with the KDE0v1 Skyrme-type interaction. The giant monopole resonance energy moments for ${}^{40,44,48}\mathrm{Ca}$ increase with mass, contrary to what would be expected with a negative symmetry energy, $K_{\tau }$.

Figure 1

Inelastic α spectra obtained for ${}^{44}\mathrm{Ca}$ are shown. The lines are examples of continua chosen for analyses.

Figure 2

The angular distributions of the ${}^{44}\mathrm{Ca}$ cross sections for three excitation ranges of the GR peak and the continuum are plotted vs center-of-mass scattering angle. Each bin is 480 keV wide and the average energies for each bin are shown. The lines through the data points indicate the multipole fits. The contributions of each multipole are shown. The statistical errors are smaller than the data points.

Figure 3

Strength distributions obtained for ${}^{44}\mathrm{Ca}$ are shown by the histograms. Error bars represent the uncertainty based on the fitting of the angular distributions and different choices for the continuum, as described in the text. Gaussian fits to the $E1$ distributions for the individual peaks (blue and purple) and their sum (red) are shown. The green lines are the strength distributions obtained with the HF-RPA calculations using the KDE0v1 interaction, smeared to more closely represent the data as discussed in the text. The orange lines are the HF-RPA strength distributions without smearing and with the strength scaled to fit on the figure.

Figure 4

Experimental results for ISGMR energies in ${}^{40}\mathrm{Ca}$ [8], ${}^{44}\mathrm{Ca}$ (present work), and ${}^{48}\mathrm{Ca}$ [2] (blue diamonds) are compared with theoretical predictions. The results of fully self-consistent HF-RPA calculations [4] with KDE0v1 [6] are shown using the experimental excitation energy range ($E=9.5-40\mathrm{MeV}$) (red squares).

Figure 5

Values of $K_A$ from the scaling energy $\sqrt{m_3/m{}_1}$ for the Ca isotopes are plotted against $A$. A fit to the data (red line) using the Leptodermous expansion with the parameters indicated is shown. The green line is shown as a reference and is also from the Leptodermous expansion but with $K_{\tau }=-550\mathrm{MeV}$.