SummaryWhat is the size of the atomic nucleus? This deceivably simple question is difficult to answer. While the electric charge distributions in atomic nuclei were measured accurately already half a century ago, our knowledge of the distribution of neutrons is still deficient. In addition to constraining the size of atomic nuclei, the neutron distribution also impacts the number of nuclei that can exist and the size of neutron stars. We present an ab initio calculation of the neutron distribution of the neutron-rich nucleus 48 Ca. We show that the neutron skin (difference between radii of neutron and proton distributions) is significantly smaller than previously thought. We also make predictions for the electric dipole polarizability and the weak form factor; both quantities are currently targeted by precision measurements. Based on ab initio results for 48 Ca, we provide a constraint on the size of a neutron star.

The electric dipole strength distribution in 48 Ca between 5 and 25 MeV has been determined at RCNP, Osaka, from proton inelastic scattering experiments at forward angles. Combined with photoabsorption data at higher excitation energy, this enables the first extraction of the electric dipole polarizability αD( 48 Ca) = 2.07(22) fm 3 . Remarkably, the dipole response of 48 Ca is found to be very similar to that of 40 Ca, consistent with a small neutron skin in 48 Ca. The experimental results are in good agreement with ab initio calculations based on chiral effective field theory interactions and with state-of-the-art density-functional calculations, implying a neutron skin in 48 Ca of 0.14 − 0.20 fm.Introduction.-The equation of state (EOS) of neutronrich matter governs the properties of neutron-rich nuclei, the structure of neutron stars, and the dynamics of corecollapse supernovae [1,2]. The largest uncertainty of the EOS at nuclear densities for neutron-rich conditions stems from the limited knowledge of the symmetry energy J, which is the difference of the energies of neutron and nuclear matter at saturation density, and the slope of the symmetry energy L, which is related to the pressure of neutron matter. The symmetry energy also plays an important role in nuclei, where it contributes to the formation of neutron skins in the presence of a neutron excess. Calculations based on energy density functionals (EDFs) pointed out that J and L can be correlated with isovector collective excitations of the nucleus such as pygmy dipole resonances [3] and giant dipole resonances (GDRs) [4], thus suggesting that the neutron skin thickness, the difference of the neutron and proton root-mean-square radii, could be constrained by studying properties of collective isovector observables at low energy [5]. One such observable is the nuclear electric dipole polarizability α D , which represents a viable tool to constrain the EOS of neutron matter and the physics of neutron stars [6][7][8][9][10][11].While correlations among α D , the neutron skin and the symmetry energy parameters have been studied extensively with EDFs [12][13][14][15][16], only recently have ab initio calculations based on chiral effective field theory (χEFT) interactions successfully studied such correlations in medium-mass nuclei [17,18]. By using a set of chiral two-plus three-nucleon interactions [19,20] and

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 coupledcluster 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 He, 16,22 O and 40 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 O nucleus, which compares fairly well with data from [Leistenschneider et al. Phys. Rev. Lett. 86, 5442 (2001)]. We also compute the electric dipole polariziability in 40 Ca. Deficiencies of the employed Hamiltonian lead to overbinding, too small charge radii and a too small electric dipole polarizability in 40 Ca.

The electric dipole polarizability quantifies the low-energy behavior of the dipole strength and is related to critical observables such as the radii of the proton and neutron distributions. Its computation is challenging because most of the dipole strength lies in the scattering continuum. In this paper we combine integral transforms with the coupled-cluster method and compute the dipole polarizability using bound-state techniques. Employing different interactions from chiral effective field theory, we confirm the strong correlation between the dipole polarizability and the charge radius, and study its dependence on three-nucleon forces. We find good agreement with data for the 4 He, 40 Ca, and 16 O nuclei, and predict the dipole polarizability for the rare nucleus 22 O.

We compute the electric dipole polarizability of 48 Ca with an increased precision by including more correlations than in previous studies. Employing the coupled-cluster method we go beyond singles and doubles excitations and include leading-order three-particle-three-hole (3p-3h) excitations for the ground state, excited states, and the similarity transformed operator. We study electromagnetic sum rules, such as the bremsstrahlung sum rule m0 and the polarizability sum rule α D using interactions from chiral effective field theory. To gauge the quality of our coupled-cluster approximations we perform several benchmarks with the effective interaction hyperspherical harmonics approach in 4 He and with self consistent Green's function in 16 O. We compute the dipole polarizability of 48 Ca employing the chiral interaction N 2 LOsat [Ekström et al., Phys. Rev. C 91, 051301 (2015)] and the 1.8/2.0 (EM) [Hebeler et al., Phys. Rev. C 83, 031301 (2011)]. We find that the effect of 3p-3h excitations in the ground state is small for 1.8/2.0 (EM) but non-negligible for N 2 LOsat. The addition of these new correlations allows us to improve the precision of our 48 Ca calculations and reconcile the recently reported discrepancy between coupled-cluster results based on these interactions and the experimentally determined α D from proton inelastic scattering in 48 Ca [Birkhan et al., Phys. Rev. Lett. 118, 252501 (2017)]. For the computation of electromagnetic and polarizability sum rules, the inclusion of leading-order 3p-3h excitations in the ground state is important, while less so for the excited states and the similarity-transformed dipole operator.

We present the first laser spectroscopic measurement of the neutron-rich nucleus 68 Ni at the N = 40 subshell closure and extract its nuclear charge radius. Since this is the only short-lived isotope for which the dipole polarizability αD has been measured, the combination of these observables provides a benchmark for nuclear structure theory. We compare them to novel coupled-cluster calculations based on different chiral two-and three-nucleon interactions, for which a strong correlation between the charge radius and dipole polarizability is observed, similar to the stable nucleus 48 Ca. Three-particle-three-hole correlations in coupled-cluster theory substantially improve the description of the experimental data, which allows to constrain the neutron radius and neutron skin of 68 Ni.

Abstract. We review the Lorentz integral transform coupled-cluster method for the calculation of the electric dipole polarizability. We benchmark our results with exact hyperspherical harmonics calculations for 4 He and then we move to a heavier nucleus studying 16 O. We observe that the implemented chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order underestimates the electric dipole polarizability.

Here we summarize how the LIT and CC methods can be coupled, in order to allow for ab initio calculations of reactions in medium mass nuclei. Results on 16 O are reviewed and preliminary calculations on 40 Ca are presented.