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Register a new user$Ab~initio$ description of collectivity for $sd$ shell nuclei
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Praveen Chandra Srivastava Dr.
Publication date
2019
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English
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In the present work, we have reported shell model results for open shell nuclei Ne, Mg and Si isotopes with $10 leq N leq 20$ in $sd$-shell model space. We have performed calculations in $sd$ shell with two $ab~initio$ approaches: in-medium similarity renormalization group (IM-SRG) and coupled-cluster (CC) theory. We have also performed calculations with phenomenological USDB interaction and chiral effective field theory based CEFT interaction. The results for rotational spectra and $B(E2;2_1^+rightarrow 0_1^+)$ transitions are reported for even-mass isotopes. The IM-SRG and CC results are in reasonable agreement with the experimental data except at $N$ =20. This demonstrates a validity of $ab~initio$ description of deformation for doubly open-shell nuclei for $sd$ shell. To see the importance of $pf$ orbitals, we have also compared our results with SDPF-MU interaction by taking account of $2p-2h$ and $4p-4h$ configurations in $sd$-$pf$-shell model space.
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We merge two successful ab initio nuclear-structure methods, the no-core shell model (NCSM) and the multi-reference in-medium similarity renormalization group (IM-SRG) to define a new many-body approach for the comprehensive description of ground and excited states of closed and open-shell nuclei. Building on the key advantages of the two methods---the decoupling of excitations at the many-body level in the IM-SRG and the access to arbitrary nuclei, eigenstates, and observables in the NCSM---their combination enables fully converged no-core calculations for an unprecedented range of nuclei and observables at moderate computational cost. We present applications in the carbon and oxygen isotopic chains, where conventional NCSM calculations are still feasible and provide an important benchmark. The efficiency and rapid convergence of the new approach make it ideally suited for ab initio studies of the complete spectroscopy of nuclei up into the medium-mass regime.
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.
The Quasi-SU(3) symmetry was uncovered in full pf and sdg shell-model calculations for both even-even and odd-even nuclei. It manifests itself through a dominance of single-particle and quadrupole-quadrupole terms in the Hamiltonian used to describe well-deformed nuclei. A practical consequence of the quasi-SU(3) symmetry is an efficient basis truncation scheme. In a recent work was shown that when this type of Hamiltonian is diagonalized in an SU(3) basis, only a few irreducible represntations (irreps) of SU(3) are needed to describe the Yrast band, the leading S = 0 irrep augmented with the leading S = 1 irreps in the proton and neutron subspaces. In the present article the quasi-SU(3) truncation scheme is used, in conjunction with a realistic but schematic Hamiltonian that includes the most important multipole terms, to describe the energy spectra and B(E2) transition strengths of 20-Ne, 22-Ne, 24-Mg and 28-Si. The effect of the size of the Hilbert space on both sets of observables is discussed, as well as the structure of the Yrast band and the importance of the various terms in the Hamiltonian.
Accurate knowledge of the nuclear level density is important both from a theoretical viewpoint as a powerful instrument for studying nuclear structure and for numerous applications. For example, astrophysical reactions responsible for the nucleosynthesis in the universe can be understood only if we know the nuclear level density. We use the configuration-interaction nuclear shell model to predict nuclear level density for all nuclei in the $sd$-shell, both total and for individual spins (only with positive parity). To avoid the diagonalization in large model spaces we use the moments method based on statistical properties of nuclear many-body systems. In the cases where the diagonalization is possible, the results of the moments method practically coincide with those from the shell-model calculations. Using the computed level densities, we fit the parameters of the Constant Temperature phenomenological model, which can be used by practitioners in their studies of nuclear reactions at excitation energies appropriate for the $sd$-shell nuclei.
We propose a novel storage scheme for three-nucleon (3N) interaction matrix elements relevant for the normal-ordered two-body approximation used extensively in ab initio calculations of atomic nuclei. This scheme reduces the required memory by approximately two orders of magnitude, which allows the generation of 3N interaction matrix elements with the standard truncation of $E_{3max}=28$, well beyond the previous limit of 18. We demonstrate that this is sufficient to obtain ground-state energies in $^{132}$Sn converged to within a few MeV with respect to the $E_{3max}$ truncation. In addition, we study the asymptotic convergence behavior and perform extrapolations to the un-truncated limit. Finally, we investigate the impact of truncations made when evolving free-space 3N interactions with the similarity renormalization group. We find that the contribution of blocks with angular momentum $J_{rm rel}>9/2$ is dominated by a basis-truncation artifact which vanishes in the large-space limit, so these computationally expensive components can be neglected. For the two sets of nuclear interactions employed in this work, the resulting binding energy of $^{132}$Sn agrees with the experimental value within theoretical uncertainties. This work enables converged ab initio calculations of heavy nuclei.
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