No abstract

The reach of ab initio many-body theories is rapidly extending over the nuclear chart. However, dealing fully with three-nucleon, possibly four-nucleon, interactions makes the solving of the A-body Schrödinger equation particularly cumbersome, if not impossible beyond a certain nuclear mass. Consequently, ab initio calculations of mid-mass nuclei are typically performed on the basis of the so-called normal-ordered two-body (NO2B) approximation that captures dominant effects of three-nucleon forces while effectively working with twonucleon operators. A powerful idea currently employed to extend ab initio calculations to open-shell nuclei consists of expanding the exact solution of the A-body Schrödinger equation while authorizing the approximate solution to break symmetries of the Hamiltonian. In this context, operators are normal ordered with respect to a symmetry-breaking reference state such that proceeding to a naive truncation may lead to symmetry-breaking approximate operators. The purpose of the present work is to design a normal-ordering approximation of operators that is consistent with the symmetries of the Hamiltonian while working in the context of symmetry broken (and potentially restored) methods. Focusing on many-J. Ripoche CEA, DAM,

Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei. In their best current level of implementation, their accuracy is of the order of a few per cent error on the ground-state correlation energy. Recently implemented variants of these methods are operating a breakthrough in the description of medium-mass open-shell nuclei at a polynomial computational cost while putting state-of-the-art models of inter-nucleon interactions to the test.Purpose: As progress in the design of inter-nucleon interactions is made, and as questions one wishes to answer are refined in connection with increasingly available experimental data, further efforts must be made to tailor many-body methods that can reach an even higher precision for an even larger number of observable/quantum states/nuclei. It is the objective of the present work to contribute to such a quest by designing and testing a new many-body scheme. Methods:We formulate a truncated configuration interaction method that consists of diagonalizing the Hamiltonian in a highly truncated subspace of the total N -body Hilbert space. The reduced Hilbert space is generated via the particle-number projected BCS state along with projected seniority-zero two and four quasi-particle excitations. Furthermore, the extent by which the underlying BCS state breaks U (1) symmetry is optimized in presence of the projected two and four quasi-particle excitations. This constitutes an extension of the so-called restricted variation after projection method in use within the frame of multi-reference energy density functional calculations. The quality of the newly designed method is tested against exact solutions of the so-called attractive pairing Hamiltonian problem.Results: By construction, the method reproduce exact results for N = 2 and N = 4. For N = (8,16,20), the error on the ground-state correlation energy is less than (0.006, 0.1, 0.15) % across the entire range of inter-nucleon coupling defining the pairing Hamiltonian and driving the normal-to-superfluid quantum phase transition. The presently proposed method offers the advantage to automatically access the low-lying spectroscopy, which it does with high accuracy. Conclusions:The numerical cost of the newly designed variational method is polynomial (N 6 ) in system size. It achieves an unprecedented accuracy on the ground-state correlation energy, effective pairing gap and onebody entropy as well as on the excitation energy of low-lying states of the attractive pairing Hamiltonian. This constitutes a strong enough motivation to envision its application to realistic nuclear Hamiltonians in view of providing a complementary, accurate and versatile ab initio description of mid-mass open-shell nuclei in the future.