We develop a new method to describe properties of truly open-shell nuclei. This method is based on single-reference coupled-cluster theory and the equation-of-motion method with extensions to nuclei with $A\pm 2$ nucleons outside a closed shell. We perform proof-of-principle calculations for the ground states of the helium isotopes $^{3-6}$He and the first excited $2^+$ state in $^6$He. The comparison with exact results from matrix diagonalization in small model spaces demonstrates the accuracy of the coupled-cluster methods. Three-particle--one-hole excitations of $^4$He play an important role for the accurate description of $^6$He. For the open-shell nucleus $^6$He, the computational cost of the method is comparable with the coupled-cluster singles-and-doubles approximation while its accuracy is similar to coupled-cluster with singles, doubles and triples excitations.
An overview of the ab initio no-core shell model is presented. Recent results for light nuclei obtained with the chiral two-nucleon and three-nucleon interactions are highlighted. Cross section calculations of capture reactions important for astrophysics are discussed. The extension of the ab initio no-core shell model to the description of nuclear reactions by the resonating group method technique is outlined.
A brief review of recent microscopic calculations of nuclear pairing gap is given. A semi-microscopic model is suggested in which the ab-initio effective pairing interaction is supplemented with a small phenomenological addendum. It involves a parameter which is universal for all medium and heavy nuclei. Calculations for several isotopic and isotonic chains of semi-magic nuclei confirm the relevance of the model.
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 show the first results for the elastic scattering of neutrons off oxygen and calcium isotopes obtained from ab initio optical potentials. The potential is derived using self consistent Green's function theory (SCGF) with the saturating chiral interaction NNLO$_{\textrm{sat}}$. Our calculations are compared to available scattering data and show that it is possible to reproduce low energy scattering observables in medium mass nuclei from first principles.
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 obtain properties of $^{12}$C in the {\it ab initio} no-core nuclear shell-model. The effective Hamiltonians are derived microscopically from the realistic CD-Bonn and the Argonne V8' nucleon-nucleon (NN) potentials as a function of the finite harmonic oscillator basis space. Binding energies, excitation spectra and electromagnetic properties are presented for model spaces up to $5\hbarΩ$. The favorable comparison with available data is a consequence of the underlying NN interaction rather than a phenomenological fit.
We construct effective 2- and 3-body Hamiltonians for the p-shell by performing 12\hbarΩab initio no-core shell model (NCSM) calculations for A=6 and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the 0\hbarΩspace. We then separate these effective Hamiltonians into 0-, 1- and 2-body contributions (also 3-body for A=7) and analyze the systematic behavior of these different parts as a function of the mass number A and size of the NCSM basis space. The role of effective 3- and higher-body interactions for A>6 is investigated and discussed.
We perform an ab initio shell-model calculation for ^{18}O in a restricted no-core model space, microscopically deriving a two-body effective interaction and introducing a minimal refinement of one-body energies in the spsd or spsdpf model space. Low-lying energy levels, except for the experimental 0_{2}^{+} and 2_{3}^{+} states, are better described in the spsdpf space than in the spsd space. The structure of low-lying energy levels is discussed with an emphasis on many-particle many-hole states beyond the four-particle two-hole configuration.
We demonstrate the existence of multiple converging sequences in the ab initio no-core shell model. By examining the underlying theory of effective operators, we expose the physical foundations for the alternative pathways to convergence. This leads us to propose a revised strategy for evaluating effective interactions for $A$-body calculations in restricted model spaces. We suggest that this strategy is particularly useful for applications to nuclear processes in which states of both parities are used simultaneously, such as for transition rates. We demonstrate the utility of our strategy wit…
With a view toward describing reactions of intermediate-mass nuclei from first principles, we present first results for the norm and Hamiltonian overlaps (kernels) for the p-α, p-16O and p-20Ne cluster systems using realistic nucleon-nucleon interactions. This is achieved in the framework of a new ab initio approach that combines the symmetry-adapted no-core shell model (SA-NCSM) with the resonating group method (RGM). In this model, a physically relevant basis based on the SU(3) symmetry is used. The structure of the clusters is provided by the ab initio SA-NCSM, which enables the description…
We derive ab initio optical potentials from self-consistent Green's function (SCGF) theory and compute the elastic scattering of neutrons off oxygen and calcium isotopes. The comparison with scattering data is satisfactory at low scattering energies. The method is benchmarked against no-core shell model with continuum (NCSMC) calculations, showing that virtual excitations of the target are crucial to predict proper fragmentation and absorption at higher energies. This is a significant step toward deriving optical potentials for medium mass nuclei and complex many-body systems in general.
This review presents some of the challenges in constructing models of atomic nuclei starting from theoretical descriptions of the strong interaction between nucleons. The focus is on statistical computing and methods for analyzing the link between bulk properties of atomic nuclei, such as radii and binding energies, and the underlying microscopic description of the nuclear interaction. The importance of careful model calibration and uncertainty quantification of theoretical predictions is highlighted.
The ab initio no-core shell model (NCSM) is extended to include a realistic three-body interaction in calculations for p-shell nuclei. The NCSM formalism is reviewed and new features needed in calculations with three-body forces are discussed in detail. We present results of first applications to 6,7Li, 6He, 7,8,10Be, 10,11,12B, 12N and 10,11,12,13C using the Argonne V8' nucleon-nucleon (NN) potential and the Tucson-Melbourne TM'(99) three-nucleon interaction (TNI). In addition to increasing the total binding energy, we observe a substantial sensitivity in the low-lying spectra to the presence…
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.
We present the first ab initio calculations of nuclear ground states up into the domain of heavy nuclei, spanning the range from 16-O to 132-Sn based on two- plus three-nucleon interactions derived within chiral effective field theory. We employ the similarity renormalization group for preparing the Hamiltonian and use coupled-cluster theory to solve the many-body problem for nuclei with closed sub-shells. Through an analysis of theoretical uncertainties resulting from various truncations in this framework, we identify and eliminate the technical hurdles that previously inhibited the step beyo…
Recently, charge radii and ground-state electromagnetic moments of Li and Be isotopes were measured precisely. We have performed large-scale ab initio no-core shell model calculations for these isotopes using high-precision nucleon-nucleon potentials. The isotopic trends of our computed charge radii and quadrupole and magnetic-dipole moments are in good agreement with experimental results with the exception of the 11Li charge radius. The magnetic moments are in particular well described, whereas the absolute magnitudes of the quadrupole moments are about 10% too small. The small magnitude of t…
The spherical Hartree-Fock approximation is applied to the $abinitio$ no-core shell model, with a realistic effective nucleon-nucleon interaction in order to investigate the range of its utility. Hartree-Fock results for binding energies, one-body density distributions and occupation probabilities are compared with results from exact diagonalization in similar model spaces. We show that this mean field approximation, especially with second order corrections, is able to provide some useful approximatons for $^4He$ and $^{16}O$. We also explore the physical insights provided by the Hartree-Fock …
An {\em ab initio} (i.e., from first principles) theoretical framework capable of providing a unified description of the structure and low-energy reaction properties of light nuclei is desirable to further our understanding of the fundamental interactions among nucleons, and provide accurate predictions of crucial reaction rates for nuclear astrophysics, fusion-energy research, and other applications. In this contribution we review {\em ab initio} calculations for nucleon and deuterium scattering on light nuclei starting from chiral two- and three-body Hamiltonians, obtained within the framewo…
The ${^3{\rm He}}(α,γ){^7{\rm Be}}$ and ${^3{\rm H}}(α,γ){^7{\rm Li}}$ astrophysical $S$ factors are evaluated at low collision energies (less than 2.5 MeV in the centre-of-mass frame) within the no-core shell model with continuum approach using a renormalized chiral nucleon-nucleon interaction.
Variational calculations for s-shell hypernuclei are performed by explicitly including $Σ$ degrees of freedom. Four sets of YN interactions (SC97d(S), SC97e(S), SC97f(S) and SC89(S)) are used. The bound-state solution of $_Λ^5$He is obtained and a large energy expectation value of the tensor $ΛN-ΣN$ transition part is found. The internal energy of the $^4$He subsystem is strongly affected by the presence of a $Λ$ particle with the strong tensor $ΛN-ΣN$ transition potential.
An ab-initio calculation scheme for finite nuclei based on self-consistent Green's functions in the Gorkov formalism is developed. It aims at describing properties of doubly-magic and semi-magic nuclei employing state-of-the-art microscopic nuclear interactions and explicitly treating pairing correlations through the breaking of U(1) symmetry associated with particle number conservation. The present paper introduces the formalism, necessary to undertake applications at (self-consistent) second-order using two-nucleon interactions, in a detailed and self-contained fashion. First applications of…
Working in the framework of the ab-initio no-core shell model, we derive two-body effective interactions microscopically for specific harmonic-oscillator basis spaces from the realistic Argonne V8' nucleon-nucleon potential. However, our two-body effective interaction is only the dominant part of the A-body (A >= 3) effective interaction, which also contains three-, four- and, in general, up to A-body components. We model these multi-body components as a simple two-parameter, basis-space-dependent interaction. We then investigate the coupling needed to provide accurate descriptions of selected…
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.
As ab-initio calculations of atomic nuclei enter the A=40-100 mass range, a great challenge is how to approach the vast majority of open-shell (degenerate) isotopes. We add realistic three-nucleon interactions to the state of the art many-body Green's function theory of closed-shells, and find that physics of neutron driplines is reproduced with very good quality. Further, we introduce the Gorkov formalism to extend ab-initio theory to semi-magic, fully open-shell, isotopes. Proof-of-principle calculations for Ca-44 and Ni-74 confirm that this approach is indeed feasible. Combining these two a…
We use properties of doubly-magic nuclei and ab-initio calculations of low-density neutron matter to constrain Skyrme equations of state for neutron-rich conditions. All of these properties are consistent with a Skyrme functional form and a neutron-matter equation of state that depends on three parameters. With a reasonable range for the neutron-matter effective mass, the values of the two other Skyrme parameters are well constrained. This leads to predictions for other quantities. The neutron skins for $^{208}$Pb and $^{48}$Ca are predicted to be 0.182(10) fm and 0.173(5) fm, respectively. Ot…
The symplectic symmetry of eigenstates for the $0^+_{gs}$ in $^{16}$O and the $0^+_{gs}$ and lowest $2^+$ and $4^+$ configurations of $^{12}$C that are well-converged within the framework of the no-core shell model with the JISP16 realistic interaction is examined. These states are found to project at the 85-90% level onto very few symplectic representations including the most deformed configuration, which confirms the importance of a symplectic no-core shell model and reaffirms the relevance of the Elliott $\mathrm{SU}(3)$ model upon which the symplectic scheme is built.
We investigate cross sections for neutrino-12C exclusive scattering and for muon capture on 12C using wave functions obtained in the ab initio no-core shell model. In our parameter-free calculations with basis spaces up to the 6 hbarOmega we show that realistic nucleon-nucleon interactions, like e.g. the CD-Bonn, under predict the experimental cross sections by more than a factor of two. By including a realistic three-body interaction, Tucson-Melbourne TM'(99), the cross sections are enhanced significantly and a much better agreement with experiment is achieved. At the same time,the TM'(99) in…
Toward $\textit{Ab Initio}$ Quantum Simulations of Atomic Nuclei Using Noisy Qubits
State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University（北京大学物理学院核物理与技术国家重点实验室）；Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences（中国科学院近代物理研究所南方核科学理论中心）
We present an \emph{ab initio} calculation of spectroscopic factors for neutron and proton removal from $^{24}$O using the coupled-cluster method and a state-of-the-art chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order. In order to account for the coupling to the scattering continuum we use a Berggren single-particle basis that treats bound, resonant, and continuum states on an equal footing. We report neutron removal spectroscopic factors for the $^{23}$O states $J^π = 1/2^+$, $5/2^+$, $3/2^-$ and $1/2^-$, and proton removal spectroscopic factors for the $^{23}$N sta…
In a recent Letter [Phys. Rev. Lett. 99, 092501 (2007)], Roth and Navratil present an importance-truncation scheme for the no-core shell model. The authors claim that their truncation scheme leads to converged results for the ground state of 40-Ca. We believe that this conclusion cannot be drawn from the results presented in the Letter. Furthermore, the claimed convergence is at variance with expectations of many-body theory. In particular, coupled-cluster calculations indicate that a significant fraction of the correlation energy is missing.
We propagate the statistical uncertainty of experimental NN scattering data into the binding energy of $^3$H and $^4$He. We also study the sensitivity of the magnetic moment and proton radius of the $^3$H to changes in the NN interaction. The calculations are made with the no-core full configuration method in a sufficiently large harmonic oscillator basis. For those light nuclei we obtain $ΔE$($^3$H) = 0.015 MeV and $ΔE$($^4$He) = 0.055 MeV.
In the framework of the ab-initio no-core shell model (NCSM), we describe the longitudinal-longitudinal distribution function, part of the inclusive (e,e') longitudinal response. In the two-body cluster approximation, we compute the effective operators consistent with the unitary transformation used to obtain the effective Hamiltonian. When short-range correlations are probed, the results display independence from the model space size and length scale. Long-range correlations are more difficult to model in the NCSM and they can be described only by increasing the model space or increasing the …
The relation of the shell, collective and cluster models of the atomic nuclei is discussed from the viewpoint of symmetries. In the fifties the U(3) symmetry was found as their common part for a single shell problem. For multi major-shell excitations, considered here, the U(3)$\otimes$U(3) dynamical symmetry turns out to be their intersection.
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 …
This contribution reviews a number of applications of the ab initio no-core shell model (NCSM) within nuclear physics and beyond. We will highlight a nuclear-structure study of the A = 12 isobar using a chiral NN + 3NF interaction. In the spirit of this workshop we will also mention the new development of the NCSM formalism to describe open channels and to approach the problem of nuclear reactions. Finally, we will illustrate the universality of the many-body problem by presenting the recent adaptation of the NCSM effective-interaction approach to study the many-boson problem in an external tr…
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…
We present the first ab initio coupled-cluster calculations of medium-mass nuclei with explicit chiral three-nucleon (3N) interactions. Using a spherical formulation of coupled cluster with singles and doubles excitations including explicit 3N contributions, we study ground states of 16,24-O, 40,48-Ca and 56-Ni. We employ chiral NN plus 3N interactions softened through a similarity renormalization group (SRG) transformation at the three-body level. We investigate the impact of all truncations and quantify the resulting uncertainties---this includes the contributions from triples excitations, t…
A new convenient method for precise theoretical calculations of quantities of traditional theory of nuclear reactions such as widths of resonances (including sub-threshold), and asymptotic normalization coefficients is proposed. This method may be considered as a step on the road to full theoretical ab initio description of light nuclei spectroscopic data. As an illustration of this method the computational results for all relevant two-body channels for all known and some theoretically predicted states of 7Li nucleus are shown. Well-proven on a large amount of data Daejeon16 potential was used…
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…
According to microscopic calculations with antisymmetrized molecular dynamics, we studied cluster features in stable and unstable nuclei. A variety of structure was found in stable and unstable nuclei in the $p$-shell and $sd$-shell regions. The structure of excited states of $^{12}$Be was investigated, while in $sd$-shell nuclei we focused on molecular states and deformed states. The deformed states in $^{28}$Si and $^{40}$Ca were discussed in connection with the high-lying molecular states. Appealing molecular states in $^{36}$Ar and $^{24}$Mg were suggested. The results signified that both …
No-Core Gamow Shell Model (NCGSM) is applied for the first time to study selected well-bound and unbound states of helium isotopes. This model is formulated on the complex energy plane and, by using a complete Berggren ensemble, treats bound, resonant, and scattering states on equal footing. We use the Density Matrix Renormalization Group method to solve the many-body Schrödinger equation. To test the validity of our approach, we benchmarked the NCGSM results against Faddeev and Faddeev-Yakubovsky exact calculations for $^3$H and $^4$He nuclei. We also performed {\textit ab initio} NCGSM calcu…
The emergence of rotational bands is observed in no-core configuration interaction (NCCI) calculations for the odd-mass Be isotopes (7<=A<=13) with the JISP16 nucleon-nucleon interaction, as evidenced by rotational patterns for excitation energies, quadrupole moments, and E2 transitions. Yrast and low-lying excited bands are found. The results demonstrate the possibility of well-developed rotational structure in NCCI calculations using a realistic nucleon-nucleon interaction.
We study the use of truncated normal-ordered three-nucleon interactions in ab initio nuclear structure calculations starting from chiral two- plus three-nucleon Hamiltonians evolved consistently with the similarity renormalization group (SRG). We present three key steps: (i) a rigorous benchmark of the normal-ordering approximation in the importance-truncated no-core shell model (IT-NCSM) for 4-He, 16-O, and 40-Ca; (ii) a direct comparison of the IT-NCSM results with coupled-cluster calculations at the singles and doubles level (CCSD) for 16-O; and (iii) first applications of SRG-evolved chira…
We propose an importance truncation scheme for the no-core shell model, which enables converged calculations for nuclei well beyond the p-shell. It is based on an a priori measure for the importance of individual basis states constructed by means of many-body perturbation theory. Only the physically relevant states of the no-core model space are considered, which leads to a dramatic reduction of the basis dimension. We analyze the validity and efficiency of this truncation scheme using different realistic nucleon-nucleon interactions and compare to conventional no-core shell model calculations…
We study the efficacy of a new ab initio framework that combines the symmetry-adapted (SA) no-core shell-model approach with the resonating group method (RGM) for unified descriptions of nuclear structure and reactions. We obtain ab initio neutron-nucleus interactions for $^4$He, $^{16}$O, and $^{20}$Ne targets, starting with realistic nucleon-nucleon potentials. We discuss the effect of increasing model space sizes and symmetry-based selections on the SA-RGM norm and direct potential kernels, as well as on phase shifts, which are the input to calculations of cross sections. We demonstrate the…
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…
Based on the spectator expansion of the multiple scattering series we employ a chiral next-to-next-to-leading order (NNLO) nucleon-nucleon interaction on the same footing in the structure as well as in the reaction calculation to obtain an in leading-order consistent effective potential for nucleon-nucleus elastic scattering, which includes the spin of the struck target nucleon. As an example we present proton scattering off $^{12}$C.
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…
The microscopic structure of neutron-rich sd-shell nuclei is investigated by using the spherical shell-model in the sd-pf valence space with the extended pairing plus quadrupole-quadrupole forces accompanied by the monopole interaction (EPQQM). The calculation reproduces systematically the known energy levels for even-even and odd-mass nuclei including the recent data for 43S, 46S and 47Ar. In particular, the erosion of the N=28 shell closure in 42Si can be explained. Our EPQQM results are compared with other shell-model calculations with the SDPF-NR and SDPF-U effective interactions.
