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Register a new userVariational approach with the superposition of the symmetry-restored quasi-particle vacua for nuclear shell-model calculations
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We propose a variational calculation scheme utilizing the superposition of the angular-momentum, parity, number projected quasiparticle vacua, that is especially suitable for applying to medium-heavy nuclei in shell-model calculations. We derive a formula for the energy variance with quasi-particle vacua and apply the energy-variance extrapolation to the present scheme for further precise estimation of the exact shell-model energy. The validity of the method is presented for the shell-model calculation of $^{132}$Ba in the $50 leq Z,N leq 82$ model space. We also discuss the feasibility of this scheme in the case of the $^{150}$Nd in the $50 leq Z leq 82$ and $82 leq Z leq 126$ model space and demonstrate that its neutrinoless-double-beta-decay matrix element is obtained showing good convergence.
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We discuss a variational calculation for nuclear shell-model calculations and propose a new procedure for the energy-variance extrapolation (EVE) method using a sequence of the approximated wave functions obtained by the variational calculation. The wave functions are described as linear combinations of the parity, angular-momentum projected Slater determinants, the energy of which is minimized by the conjugate gradient method obeying the variational principle. The EVE generally works well using the wave functions, but we found some difficult cases where the EVE gives a poor estimation. We discuss the origin of the poor estimation concerning shape coexistence. We found that the appropriate reordering of the Slater determinants allows us to overcome this difficulty and to reduce the uncertainty of the extrapolation.
We have recently extended many-body perturbation theory and coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the restoration of the angular momentum at any truncation order [T. Duguet, J. Phys. G: Nucl. Part. Phys. 42 (2015) 025107]. Following a similar route, we presently extend Bogoliubov many-body perturbation theory and Bogoliubov coupled cluster theory performed on top of a Bogoliubov reference state breaking global gauge symmetry to allow for the restoration of the particle number at any truncation order. Eventually, formalisms can be merged to handle $SU(2)$ and $U(1)$ symmetries at the same time. Several further extensions of the newly proposed many-body formalisms can be foreseen in the mid-term future. The long-term goal relates to the ab initio description of near-degenerate finite quantum systems with an open-shell character.
A novel machine learning approach is used to provide further insight into atomic nuclei and to detect orderly patterns amidst a vast data of large-scale calculations. The method utilizes a neural network that is trained on ab initio results from the symmetry-adapted no-core shell model (SA-NCSM) for light nuclei. We show that the SA-NCSM, which expands ab initio applications up to medium-mass nuclei by using dominant symmetries of nuclear dynamics, can reach heavier nuclei when coupled with the machine learning approach. In particular, we find that a neural network trained on probability amplitudes for $s$-and $p$-shell nuclear wave functions not only predicts dominant configurations for heavier nuclei but in addition, when tested for the $^{20}$Ne ground state, it accurately reproduces the probability distribution. The nonnegligible configurations predicted by the network provide an important input to the SA-NCSM for reducing ultra-large model spaces to manageable sizes that can be, in turn, utilized in SA-NCSM calculations to obtain accurate observables. The neural network is capable of describing nuclear deformation and is used to track the shape evolution along the $^{20-42}$Mg isotopic chain, suggesting a shape-coexistence that is more pronounced toward the very neutron-rich isotopes. We provide first descriptions of the structure and deformation of $^{24}$Si and $^{40}$Mg of interest to x-ray burst nucleosynthesis, and even of the extremely heavy nuclei such as $^{166,168}$Er and $^{236}$U, that build upon first principles considerations.
In most nuclear many-body methods, observables are calculated using many-body wave functions explicitly. The variational two-particle reduced density matrix method is one of the few exceptions to the rule. Ground-state energies of both closed-shell and open-shell nuclear systems can indeed be evaluated by minimizing a constrained linear functional of the two-particle reduced density matrix. However, it has virtually never been used in nuclear theory, because nuclear ground states were found to be well overbound, contrary to those of atoms and molecules. Consequently, we introduced new constraints in the nuclear variational two-particle reduced density matrix method, developed recently for atomic and molecular systems. Our calculations then show that this approach can provide a proper description of nuclear systems where only valence neutrons are included. For the nuclear systems where both neutrons and protons are active, however, the energies obtained with the variational two-particle reduced density matrix method are still overbound. The possible reasons for the noticed discrepancies and solutions to this problem will be discussed.
We report on a novel ab initio approach for nuclear few- and many-body systems with strangeness. Recently, we developed a relevant no-core shell model technique which we successfully applied in first calculations of lightest $Lambda$ hypernuclei. The use of a translationally invariant finite harmonic oscillator basis allows us to employ large model spaces, compared to traditional shell model calculations, and use realistic nucleon-nucleon and nucleon-hyperon interactions (such as those derived from EFT). We discuss formal aspects of the methodology, show first demonstrative results for ${}_{Lambda}^3$H, ${}_{Lambda}^4$H and ${}^4_Lambda$He, and give outlook.
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