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Register a new userCoupled cluster approach to nuclear physics
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Authors
D.J. Dean
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Using many-body perturbation theory and coupled-cluster theory, we calculate the ground-state energy of He-4 and O-16. We perform these calculations using a no-core G-matrix interaction derived from a realistic nucleon-nucleon potential. Our calculations employ up to two-particle-two-hole coupled-cluster amplitudes.
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We perform coupled-cluster calculations for the doubly magic nuclei 4He, 16O, 40Ca and 48Ca, for neutron-rich isotopes of oxygen and fluorine, and employ bare and secondary renormalized nucleon-nucleon interactions. For the nucleon-nucleon interaction from chiral effective field theory at order next-to-next-to-next-to leading order, we find that the coupled-cluster approximation including triples corrections binds nuclei within 0.4 MeV per nucleon compared to data. We employ interactions from a resolution-scale dependent similarity renormalization group transformations and assess the validity of power counting estimates in medium-mass nuclei. We find that the missing contributions due to three-nucleon forces are consistent with these estimates. For the unitary correlator model potential, we find a slow convergence with respect to increasing the size of the model space. For the G-matrix approach, we find a weak dependence of ground-state energies on the starting energy combined with a rather slow convergence with respect to increasing model spaces. We also analyze the center-of-mass problem and present a practical and efficient solution.
Atomic nuclei are complex, quantum many-body systems whose structure manifests itself through intrinsic quantum states associated with different excitation modes or degrees of freedom. Collective modes (vibration and/or rotation) dominate at low energy (near the ground-state). The associated states are usually employed, within a truncated model space, as a basis in (coherent) coupled channels approaches to low-energy reaction dynamics. However, excluded states can be essential, and their effects on the open (nuclear) system dynamics are usually treated through complex potentials. Is this a complete description of open system dynamics? Does it include effects of quantum decoherence? Can decoherence be manifested in reaction observables? In this contribution, I discuss these issues and the main ideas of a coupled-channels density-matrix approach that makes it possible to quantify the role and importance of quantum decoherence in low-energy nuclear reaction dynamics. Topical applications, which refer to understanding the astrophysically important collision $^{12}$C + $^{12}$C and achieving a unified quantum dynamical description of relevant reaction processes of weakly-bound nuclei, are highlighted.
Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by a continuous-scale invariance, which is broken to a discrete one when three or more particles come into play. This symmetry induces a universal behavior for different systems, independent of the details of the underlying interaction, rooted in the smallness of the ratio $ell/a_B ll 1$, where the length $a_B$ is associated to the binding energy of the two-body system $E_2=hbar^2/m a_B^2$ and $ell$ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the on-set of system-specific non-universal effects. In this work we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which $a_Brightarrowinfty$, and show that nuclear systems belong to this class of universality.
We provide a brief commentary on recent work by Hammer and Son on the scaling behavior of nuclear reactions involving the emission of several loosely bound neutrons. In this work they discover a regime, termed unnuclear physics, in which these reactions are governed by an approximate conformal symmetry of the nuclear force. Remarkably, the scaling exponents that govern nuclear reactions can be related to the energies of ultracold atomic drops confined in harmonic potentials. We also comment on the importance and the limitations of this approximate symmetry in the physics of neutron stars.
We present several coupled-cluster calculations of ground and excited states of 4He and 16O employing methods from quantum chemistry. A comparison of coupled cluster results with the results of exact diagonalization of the hamiltonian in the same model space and other truncated shell-model calculations shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei, with much less computational effort than traditional large-scale shell-model approaches. Unless truncations are made, for nuclei like 16O, full-fledged shell-model calculations with four or more major shells are not possible. However, these and even larger systems can be studied with the coupled cluster methods due to the polynomial rather than factorial scaling inherent in standard shell-model studies. This makes the coupled cluster approaches, developed in quantum chemistry, viable methods for describing weakly bound systems of interest for future nuclear facilities.
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