Opensd-shell nuclei from first principles

Abstract

We extend the ab initio coupled-cluster effective interaction (CCEI) method to open-shell nuclei with protons and neutrons in the valence space, and compute binding energies and excited states of isotopes of neon and magnesium. We employ a nucleon-nucleon and three-nucleon interaction from chiral effective field theory evolved to a lower cutoff via a similarity renormalization group transformation. We find good agreement with experiment for binding energies and spectra, while charge radii of neon isotopes are underestimated. For the deformed nuclei 20 Ne and 24 Mg we reproduce rotational bands and electric quadrupole transitions within uncertainties estimated from an effective field theory for deformed nuclei, thereby demonstrating that collective phenomena in sd-shell nuclei emerge from complex ab initio calculations.Introduction -Nuclei are complex many-body systems that present us with a wealth of interesting quantum mechanical phenomena that emerge along the entire chart of nuclei. These phenomena involve: exotic clustering behavior and extended density distributions of loosely bound nuclei [1, 2], melting and re-organization of shellstructure in neutron nuclei [3][4][5], Borromean nuclei [6,7], and emergence of collective behavior in nuclei, such as rotational and vibrational states [8,9] as well as nuclear super conductivity and pairing [10].Recently there has been an explosion of nuclear manybody methods with a sufficiently soft computational scaling to allow a reliable description of binding energies and spectra in nuclei up through the sd-shell starting from nucleon-nucleon and three-nucleon forces from chiral effective field theory (EFT) [11][12][13][14][15][16]. In spite of this progress, emergence of collective phenomena in nuclei still poses significant challenges to ab initio methods. Rotational states in p-shell nuclei have been successfully computed in the no-core shell-model and in Green'sfunction Monte-Carlo approaches [17][18][19][20][21], while in the sd-shell, deformed nuclei have only been accurately described in shell-model calculations using phenemenological interactions [22]. A symplectic approach has been proposed [23] to enable extension of the no-core shellmodel to larger model spaces and higher-mass nuclei, yet prototypical deformed nuclei like 20 Ne and 48 Cr remain out of reach in the aforementioned approaches. Furthermore, as deformed nuclei are truly open-shell, they

In-medium similarity renormalization group for closed and open-shell nuclei

“…[194]. While the ordering of the lowlying states is the same as for the IMSRG interactions, the positions and spacings of the levels are notably different.…”

“…While the ordering of the lowlying states is the same as for the IMSRG interactions, the positions and spacings of the levels are notably different. We assume that this is caused by fixing A to the mass number of the 16 O core (and its vicinity) instead of the target nucleus when the interaction is constructed [190,194]. This issue will be investigated further elsewhere.…”

“…Ground-state rotational bands of 20 Ne and 24 Mg, based on the N N + 3N (400) interaction at λ = 1.88 fm −1 . We compare results for effective interactions derived by IMSRG valence-space decoupling (e max = 14, E 3max = 14, ω = 20 MeV (dashed lines) and 24 MeV (solid lines)), the A-independent CCEI interaction [194] (e max = 12, E 3max = 14, ω = 20 MeV), and the phenomenological USDB interaction [8] to experimental data [189,193]. The dashed lines represent the neutron separation energies.…”

Computational Nuclear Physics and Post Hartree-Fock Methods

“…However, coupled cluster theory is non-variational and if we want to find properties of excited states, additional calculations via for example equation of motion methods are needed [17,35]. If correlations are strong, a single-reference ansatz may not be the best starting point and a multi-reference approximation is needed [74]. Furthermore, we cannot quantify properly the error we make when truncations are made in the cluster operator.…”

Alpha particle clusters and their condensation in nuclear systems

“…At the end of this section, let us also mention that for light doubly open shell nuclei as, e.g., 20 Ne, there is also recent progress using the symplectic NCSM and ab-initio shell model approaches, see [45,143,144].…”