We explore the impact of optimizations of the single-particle basis on the convergence behavior and robustness of ab initio no-core shell model calculations. Our focus is on novel basis sets defined by the natural orbitals of a correlated one-body density matrix that is obtained in second-order many-body perturbation theory. Using a perturbatively improved density matrix as starting point informs the single-particle basis about the dominant correlation effects on the global structure of the many-body state, while keeping the computational cost for the basis optimization at a minimum. Already the comparison of the radial single-particle wavefunctions reveals the superiority of the natural-orbital basis compared to a Hartree-Fock or harmonic oscillator basis, and it highlights pathologies of the Hartree-Fock basis. We compare the model-space convergence of energies, root-mean-square radii, and selected electromagnetic observables with all three basis sets for selected p-shell nuclei using chiral interactions with explicit three-nucleon terms. In all cases the natural-orbital basis provides the fastest and most robust convergence, making it the most efficient basis for no-core shell model calculations. As an application we present no-core shell model calculations for the ground-state energies of all oxygen isotopes and assess the accuracy of the normal-ordered two-body approximation of the three-nucleon interaction in the natural-orbital basis.
A brief review of models to describe nuclear structure and reactions properties is presented, starting from the historical shell model picture and encompassing modern ab initio approaches. A selection of recent theoretical results on observables for exotic light and medium-mass nuclei is shown. Emphasis is given to the comparison with experiment and to what can be learned about three-body forces and continuum properties.
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 …
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…
We perform \textit{ab initio} no-core shell-model calculations for $A=18$ and $19$ nuclei in a $4\hbarΩ$, or $N_{\rm max}=4$, model space by using the effective JISP16 and chiral N3LO nucleon-nucleon potentials and transform the many-body effective Hamiltonians into the $0\hbarΩ$ model space to construct the $A$-body effective Hamiltonians in the $sd$-shell. We separate the $A$-body effective Hamiltonians with $A=18$ and $A=19$ into inert core, one-, and two-body components. Then, we use these core, one-, and two-body components to perform standard shell-model calculations for the $A=18$ and $…
We implement the ab initio no-core shell model approach to study neutron-rich $^{18}$C, $^{19}$C and $^{20}$C isotopes. For this purpose, we employ charge-dependent Bonn 2000 (CDB2K), inside non-local outside Yukawa (INOY) and chiral next-to-next-to-next-to-leading order (N$^{3}$LO) nucleon-nucleon interactions. Low-lying energy spectra, electromagnetic properties and point-proton radii for these nuclei up to basis space $N_{\rm max}$ = 4 are calculated. Binding energies obtained with INOY interaction are in better agreement with the experimental values as compared to other \textit{ab initio} …
We introduce the extension of the ab initio no-core shell model with continuum to describe three-body cluster systems. We present results for the ground state of 6He and show improvements with respect to the description obtained within the no-core shell model and the no-core shell model/resonating group methods.
In this work we present $ab~initio$ shell-model calculations for electric quadrupole moments and magnetic dipole moments of $sd$ shell nuclei using valence-space Hamiltonians derived with two $ab~initio$ approaches: the in-medium similarity renormalization group (IM-SRG) and the coupled-cluster effective interaction (CCEI). Results are in a reasonable agreement with the available experimental data as well as with the results from the phenomenological USDB effective interaction. This work will add more information to the available $ab~initio$ results for the spectroscopy of $sd$ shell nuclei.
There has been significant recent progress in solving the long-standing problems of how nuclear shell structure and collective motion emerge from underlying microscopic inter-nucleon interactions. We review a selection of recent significant results within the ab initio No Core Shell Model (NCSM) closely tied to three major factors enabling this progress: (1) improved nuclear interactions that accurately describe the experimental two-nucleon and three-nucleon interaction data; (2) advances in algorithms to simulate the quantum many-body problem with strong interactions; and (3) continued rapid …
The existence of multi-neutron systems has always been a debatable question. Indeed, both inter-nucleon correlations and a large continuum coupling occur in these states. We then employ the ab-initio no-core Gamow shell model to calculate the resonant energies and widths of the trineutron and tetraneutron systems with realistic interactions. Our results indicate that trineutron and tetraneutron are both unbound and bear broad widths. The calculated energy and width of tetraneutron are also comparable with recent experimental data. Moreover, our calculations suggest that the energy of trineutro…
In the shell-model framework, valence-space Hamiltonians connecting multiple major-oscillator shells are of key interest for investigating the physics of neutron-rich nuclei, which have been the subject of intense experimental activity for decades. Here we present an extension of the ab initio valence-space in-medium similarity renormalization group which allows the derivation of such Hamiltonians nonperturbatively. Starting from initial two- and three-nucleon forces from chiral effective field theory, we then calculate properties of nuclei in the important island-of-inversion region above oxy…
Constructing microscopic effective interactions (`optical potentials') for nucleon-nucleus (NA) elastic scattering requires in first order off-shell nucleon-nucleon (NN) scattering amplitudes between the projectile and the struck target nucleon and nonlocal one-body density matrices. While the NN amplitudes and the {\it ab intio} no-core shell-model (NCSM) calculations always contain the full spin structure of the NN problem, one-body density matrices used in traditional microscopic folding potential neglect spin contributions inherent in the one-body density matrix. Here we derive and show th…
We present No-Core Full Configuration results for the ground state energies of all particle-stable p-shell nuclei, as well as the excitation energies of more than 40 narrow states, excluding isobaric analog states. We used the chiral LENPIC nucleon-nucleon plus three-nucleon interaction at N2LO with semi-local coordinate space regulators, and also the phenomenological Daejeon16 nucleon-nucleon potential. With simple exponential extrapolations of the total energies of each state, binding energies and spectra are found to be in good agreement with experiment. Both interactions produce a trend to…
In the present work, we have done a comprehensive study of low-lying energy spectrum for oxygen and fluorine chains using $ab~initio$ no core shell model. We have used inside nonlocal outside Yukawa (INOY) potential, which is a two body interaction but also has the effect of three body forces by short range and nonlocal character. Also, we have performed calculations with N3LO and N2LOopt interactions and compared corresponding results with the experimental data and phenomenological USDB interaction. We have reached up to $N_{max}$=6 for $^{18-21}$O and $^{18-19}$F, $N_{max}$=4 for other oxyge…
Nuclear structure and reaction theory are undergoing a major renaissance with advances in many-body methods, realistic interactions with greatly improved links to Quantum Chromodynamics, the advent of high performance computing, and improved computational algorithms. State-of-the-art two- and three-nucleon interactions obtained from chiral Effective Field Theory provide a theoretical foundation for nuclear theory with controlled approximations. With highly efficient numerical codes, tuned to the current generation of supercomputers, we can perform ab-initio nuclear structure calculations for a…
Ab initio many-body methods address closed-shell nuclei up to mass A ~ 130 on the basis of realistic two- and three-nucleon interactions. Several routes to address open-shell nuclei are currently under investigation, including ideas which exploit spontaneous symmetry breaking. Singly open-shell nuclei can be efficiently described via the sole breaking of $U(1)$ gauge symmetry associated with particle number conservation, to account for their superfluid character. The present work formulates and applies Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-sta…
Background: Low-energy transfer reactions in which a proton is stripped from a deuteron projectile and dropped into a target play a crucial role in the formation of nuclei in both primordial and stellar nucleosynthesis, as well as in the study of exotic nuclei using radioactive beam facilities and inverse kinematics. Ab initio approaches have been successfully applied to describe the $^3$H$(d,n)^4$He and $^3$He$(d,p)^4$He fusion processes. Purpose: An ab initio treatment of transfer reactions would also be desirable for heavier targets. In this work, we extend the ab initio description of $(d,…
Structural phenomena in nuclei, from shell structure and clustering to superfluidity and collective rotations and vibrations, reflect emergent degrees of freedom. Ab initio theory describes nuclei directly from a fully microscopic formulation. We can therefore look to ab initio theory as a means of exploring the emergence of effective degrees of freedom in nuclei. For the illustrative case of emergent rotational bands in the Be isotopes, we establish an understanding of the underlying oscillator space and angular momentum (orbital and spin) structure. We consider no-core configuration interact…
Although the modern shell-model picture of atomic nuclei is built from single-particle orbits with good total angular momentum $j$, leading to $j$-$j$ coupling, phenomenological models suggested decades ago that for $0p$-shell nuclides a simpler picture can be realized via coupling of total spin $S$ and total orbital angular momentum $L$. I revisit this idea with large-basis, no-core shell model (NCSM) calculations using modern \textit{ab initio} two-body interactions, and dissect the resulting wavefunctions into their component $L$- and $S$-components. Remarkably, there is broad agreement wit…
Nuclear structure and reaction theory are undergoing a major renaissance with advances in many-body methods, strong interactions with greatly improved links to Quantum Chromodynamics (QCD), the advent of high performance computing, and improved computational algorithms. Predictive power, with well-quantified uncertainty, is emerging from non-perturbative approaches along with the potential for new discoveries such as predicting nuclear phenomena before they are measured. We present an overview of some recent developments and discuss challenges that lie ahead. Our focus is on explorations of al…
We realize the treatment of bound and continuum nuclear systems in the proximity of a three-body breakup threshold within the ab initio framework of the no-core shell model with continuum. Many-body eigenstates obtained from the diagonalization of the Hamiltonian within the harmonic-oscillator expansion of the no-core shell model are coupled with continuous microscopic three-cluster states to correctly describe the nuclear wave function both in the interior and asymptotic regions. We discuss the formalism in detail and give algebraic expressions for the case of core+$n$+$n$ systems. Using simi…
In the present paper, we have calculated the energy spectra for neutron rich $^{18-22}$N isotopes using no core shell model (NCSM).To calculate the energy spectrum we have used three different $NN$ potentials, inside non-local outside Yukawa (INOY), next-to-next-to-next-leading order (N3LO) from chiral effective field theory and charge-dependent Bonn 2000 (CDB2K). The INOY potential, which is a two body interaction but also have the effect of three body forces by short range and non local character present in it. The calculations have been done at $\hbarΩ$=20 MeV, 14 MeV and 12 MeV using INOY,…
The Nilsson orbitals used in the substitutions occurring in the proxy-SU(3) scheme, which are the orbitals bearing the maximum value of total angular momentum in each shell, have an extremely simple structure in the shell model basis |N l j Omega>, with each Nilsson orbital corresponding to a single shell model eigenvector. This simple structure is valid at all deformations for these orbitals, while in other orbitals it is valid only at small deformations. Nilsson 0[110] pairs are found to correspond to |1 1 1 0> pairs in the spherical shell model basis, paving the way for using the proxy-SU(3…
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 ampli…
Ab initio approaches to the nuclear many-body problem have seen their reach considerably extended over the past decade. However, collective excitations have been scarcely addressed so far due to the prohibitive cost of solving the corresponding equations of motion. Here, a numerically efficient method to compute electromagnetic response functions at zero- and finite-temperature in superfluid and deformed nuclei from an ab initio standpoint is presented and applied to $^{16}$O, $^{28}$Si, $^{46}$Ti and $^{56}$Fe. This work opens the path to systematic ab initio calculations of nuclear responses…
In the present work we perform a systematic shell model study of Gamow-Teller transition strength distributions in $sd$ shell nuclei using $ab~initio$ effective interactions. The $ab~initio$ effective interactions are based on in-medium similarity renormalization group (IM-SRG) and coupled-cluster effective interaction (CCEI) approaches. The aim of the present work is to test the predictive power of $ab~initio$ effective interactions by using the available experimental data of Gamow-Teller strength distributions in $sd$ shell nuclei. We perform calculations for $^{20}$Ne $\rightarrow$ $^{20}$F…
[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {\it ab initio} no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. [Purpose:] Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that t…
Precise theoretical calculations of open-shell atomic systems are critical for extracting fundamental physics parameters from precision experiments. Here we present proof-of-principle calculations illustrating the effectiveness of the valence-space formulation of the ab initio in-medium similarity renormalization group, widely used in nuclear theory, as a new ab initio method for atomic systems. We adapt this approach to study properties of closed- and open-shell many-electron systems from helium to calcium. Ground-state energies, excitation spectra, and ionization energies are obtained for se…
