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Register a new userShell-model coupled-cluster method for open-shell nuclei
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We present an approach to derive effective shell-model interactions from microscopic nuclear forces. The similarity-transformed coupled-cluster Hamiltonian decouples the single-reference state of a closed-shell nucleus and provides us with a core for the shell model. We use a second similarity transformation to decouple a shell-model space from the excluded space. We show that the three-body terms induced by both similarity transformations are crucial for an accurate computation of ground and excited states. As a proof of principle we use a nucleon-nucleon interaction from chiral effective field theory, employ a $^4$He core, and compute low-lying states of $^{6-8}$He and $^{6-8}$Li in $p$-shell model spaces. Our results agree with benchmarks from full configuration interaction.
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We introduce a hybrid many-body approach that combines the flexibility of the No-Core Shell Model (NCSM) with the efficiency of Multi-Configurational Perturbation Theory (MCPT) to compute ground- and excited-state energies in arbitrary open-shell nuclei in large model spaces. The NCSM in small model spaces is used to define a multi-determinantal reference state that contains the most important multi-particle multi-hole correlations and a subsequent second-order MCPT correction is used to capture additional correlation effects from a large model space. We apply this new ab initio approach for the calculation of ground-state and excitation energies of even and odd-mass carbon, oxygen, and fluorine isotopes and compare to large-scale NCSM calculations that are computationally much more expensive.
The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interactions approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow Shell Model (GSM) provides such a framework as it is capable of describing resonant and non-resonant many-body states on equal footing. To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the $psdf$ shell model space. The resulting interaction is expected to describe nuclei with $5 leqslant A leqslant 12$ at the $p-sd$-shell interface. The optimized one-body potential reproduces nucleon-$^4$He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the Helium, Lithium, and Beryllium isotopes up to $A=9$. A very good agreement with experiment was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the $psd$ region of the nuclear chart.
In this contribution, we present the cluster shell model which is analogous to the Nilsson model, but for cluster potentials. Special attention is paid to the consequences of the discrete symmetries of three alpha-particles in an equilateral triangle configuration. This configuration is characterized by a special structure of the rotational bands which can be used as a fingerprint of the underlying geometric configuration. The cluster shell model is applied to the nucleus 13C.
We extend the ab initio coupled-cluster effective interaction (CCEI) method to deformed 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.
A systematic shell model description of the experimental Gamow-Teller transition strength distributions in $^{42}$Ti, $^{46}$Cr, $^{50}$Fe and $^{54}$Ni is presented. These transitions have been recently measured via $beta$ decay of these $T_z$=-1 nuclei, produced in fragmentation reactions at GSI and also with ($^3${He},$t$) charge-exchange (CE) reactions corresponding to $T_z = + 1$ to $T_z = 0$ carried out at RCNP-Osaka.The calculations are performed in the $pf$ model space, using the GXPF1a and KB3G effective interactions. Qualitative agreement is obtained for the individual transitions, while the calculated summed transition strengths closely reproduce the observed ones.
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