Giant and pigmy dipole resonances in ${}^4\mathrm{He}$, ${}^{16,22}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$ from chiral nucleon-nucleon interactions

We combine the coupled-cluster method and the Lorentz integral transform for the computation of inelastic reactions into the continuum. We show that the bound-state-like equation characterizing the Lorentz integral transform method can be reformulated based on extensions of the coupled-cluster equation-of-motion method, and we discuss strategies for viable numerical solutions. Starting from a chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order, we compute the giant dipole resonances of ${}^4\mathrm{He}$, ${}^{16,22}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$, truncating the coupled-cluster equation-of-motion method at the two-particle–two-hole excitation level. Within this scheme, we find a low-lying $E1$ strength in the neutron-rich ${}^{22}\mathrm{O}$ nucleus, which compares fairly well with data from Leistenschneider et al. [Phys. Rev. Lett. 86, 5442 (2001)]. We also compute the electric dipole polarizability in ${}^{40}\mathrm{Ca}$. Deficiencies of the employed Hamiltonian lead to overbinding, too-small charge radii, and a too-small electric dipole polarizability in ${}^{40}\mathrm{Ca}$.

Figure 1

The relative convergence of the LIT $L({\omega }_0,\Gamma )$ as a function of the number $N$ of Lanczos steps: ${}^4\mathrm{He}$ in panel (a) and ${}^{16}\mathrm{O}$ in panel (b). The LIT are calculated for $\Gamma =10$ MeV.

Figure 2

Convergence of $L({\omega }_0,\Gamma )$ in ${}^4\mathrm{He}$ with $\Gamma =10$ MeV as a function of $K_{\max }$ in the EIHH expansion (a). Convergence of the LIT-CCSD equations with $\Gamma =10$ MeV as a function of $N_{\max }$ for an HO frequency of $\hslash \Omega =20$ MeV (b).

Figure 3

Comparison of $L({\omega }_0,\Gamma )$ in ${}^4\mathrm{He}$ at $\Gamma =20$ (a) and $\Gamma =10$ (b), calculated in the LIT-CCSD scheme with $N_{\max }=18$ and two values of $\hslash \Omega =20$ and 26 MeV against the LIT from EIHH.

Figure 4

Comparison of the ${}^4\mathrm{He}$ dipole response function calculated with LIT-CCSD ($\hslash \Omega =20$ MeV and $N_{\max }=18$) with the EIHH result. Inversions of the LITs with $\Gamma =10$ and 20 are performed.

Figure 5

Comparison of the ${}^4\mathrm{He}$ dipole cross section calculated with LIT-CCSD and experimental data from Arkatov et al. [58], Nilsson et al. [59], and Raut et al. [60]. The gray and blue bands differ simply by a shift of the theoretical threshold [gray] to the experimental one [dark (blue)] (see text).

Figure 6

Convergence of $L({\omega }_0,\Gamma )$ in ${}^{16}\mathrm{O}$ at $\Gamma =20$ MeV (a) and $\Gamma =10$ (b) for different values of $N_{\max }$ and an HO frequency of $\hslash \Omega =26$ MeV.

Figure 7

Comparison of $L({\omega }_0,\Gamma )$ in ${}^{16}\mathrm{O}$ at $\Gamma =10$ calculated in the LIT-CCSD scheme with $N_{\max }=18$ and two values of $\hslash \Omega =20$ and 26 MeV against the LIT of the experimental data from Ahrens et al. [61].

Figure 8

The dipole response function of ${}^{16}\mathrm{O}$ obtained by inverting $L({\omega }_0,\Gamma )$ at $\Gamma =20$ and 10 MeV for different values $\nu$ of the basis functions in Eq. (46).

Figure 9

Comparison of the ${}^{16}\mathrm{O}$ dipole cross section calculated in the LIT-CCSD scheme against experimental data by Ahrens et al. [61] (triangles with error bars) and Ishkhanov et al. [63] (red circles). The gray curve starts from the theoretical threshold, while the dark (blue) curve is shifted to the experimental threshold.

Figure 10

Convergence of $L({\omega }_0,\Gamma )$ in ${}^{22}\mathrm{O}$ at $\Gamma =10$ MeV as a function of $N_{\max }$ for an HO frequency of $\hslash \Omega =24$ MeV.

Figure 11

Comparison of $L({\omega }_0,\Gamma )$ at $\Gamma =10$ MeV for ${}^{22}\mathrm{O}$ and ${}^{16}\mathrm{O}$. Different HO frequencies have been used: $\hslash \Omega =20$ and 24 MeV for ${}^{16}\mathrm{O}$ (dashed and solid blue lines) and $\hslash \Omega =24$ and 26 MeV for ${}^{22}\mathrm{O}$ (dashed and solid black lines).

Figure 12

Comparison of the LIT-CCSD dipole cross section of ${}^{22}\mathrm{O}$ with the photoneutron data of Ref. [2]. The gray curve starts from the theoretical threshold, while the dark (blue) curve is shifted to the experimental threshold.

Figure 13

Convergence of $L({\omega }_0,\Gamma )$ in ${}^{40}\mathrm{Ca}$ at $\Gamma =10$ MeV as a function of $N_{\max }$ for an HO frequency of $\hslash \Omega =20$ MeV (a). Comparison of $L({\omega }_0,\Gamma )$ in ${}^{40}\mathrm{Ca}$ at $\Gamma =10$ calculated in the LIT-CCSD scheme with $N_{\max }=18$ and two values of $\hslash \Omega =20$ and 24 MeV against the LIT of the experimental data from Ahrens et al. [61] (b).

Figure 14

Comparison of the LIT-CCSD dipole cross section of ${}^{40}\mathrm{Ca}$ with the photoabsorption data of Ref. [61]. The gray curve starts from the theoretical threshold, while the dark (blue) curve is shifted to the experimental threshold.