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Register a new userNuclear Structure Calculations with Coupled Cluster Methods from Quantum Chemistry
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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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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.
Emergent properties such as nuclear saturation and deformation, and the effects on shell structure due to the proximity of the scattering continuum and particle decay channels are fascinating phenomena in atomic nuclei. In recent years, ab initio approaches to nuclei have taken the first steps towards tackling the computational challenge of describing these phenomena from Hamiltonians with microscopic degrees of freedom. This endeavor is now possible due to ideas from effective field theories, novel optimization strategies for nuclear interactions, ab initio methods exhibiting a soft scaling with mass number, and ever-increasing computational power. This paper reviews some of the recent accomplishments. We also present new results. The recently optimized chiral interaction NNLO$_{rm sat}$ is shown to provide an accurate description of both charge radii and binding energies in selected light- and medium-mass nuclei up to $^{56}$Ni. We derive an efficient scheme for including continuum effects in coupled-cluster computations of nuclei based on chiral nucleon-nucleon and three-nucleon forces, and present new results for unbound states in the neutron-rich isotopes of oxygen and calcium. The coupling to the continuum impacts the energies of the $J^pi = {1/2}^-,{3/2}^-,{7/2}^-,{3/2}^+$ states in $^{17,23,25}$O, and - contrary to naive shell-model expectations - the level ordering of the $J^pi = {3/2}^+,{5/2}^+,{9/2}^+$ states in $^{53,55,61}$Ca.
Broydens method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the unitary gas problem, the nuclear density functional theory with Skyrme functionals, and the nuclear coupled-cluster theory. The stability of the method, its ease of use, and its rapid convergence rates make Broydens method a tool of choice for large-scale nuclear structure calculations.
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.
A finite rank separable approximation for the quasiparticle RPA calculations with Skyrme interactions that was proposed in our previous work is extended to take into account the coupling between one- and two-phonon terms in the wave functions of excited states. It is shown that characteristics calculated within the suggested approach are in a good agreement with available experimental data.
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