Ab Initio No-core Shell Model Research Articles

Uncertainty quantification of collective nuclear observables from the chiral potential parametrization

Abstract We perform an uncertainty estimate of quadrupole moments and B(E2) transition rates that inform nuclear collectivity. In particular, we study the low-lying states of 6Li and 12C using the ab initio symmetry-adapted no-core shell model. For a narrow standard deviation of approximately 1% on the low-energy constants which parametrize high-precision chiral potentials, we find output standard deviations in the collective observables ranging from approximately 3-6%. The results mark the first step towards a rigorous uncertainty quantification of collectivity in nuclei that aims to account for all sources of uncertainty in ab initio descriptions of challenging collective and clustering observables.

Direct Observation of Competing M1 and M3 Transitions in ^{10}B.

Excited states in ^{10}B were populated with the ^{10}B(p,p^{'}γ)^{10}B^{*} reaction at 8.5MeV and their γ decay was investigated via coincidence γ-ray spectroscopy. The emitted γ rays were measured using large-volume LaBr_{3}:Ce and CeBr_{3} detectors placed in anti-Compton shields. This allowed the observation of weak γ-ray transitions, such as the M3 transition between the J^{π},T=0^{+},1 isobaric analog state (IAS) and the J^{π},T=3^{+},0 ground state and the E2 transition between the J^{π},T=2_{1}^{+},0 state and the IAS, i.e., performing measurements of branching ratios at the level of λ≥10^{-4}. For the first time in ^{10}B, the competing M1 and M3 transitions from the decay of the IAS have been observed in a γ spectroscopy experiment. The experimental results are compared with abinitio no-core shell model calculation using the newest version of the local position-space chiral N^{3}LO nucleon-nucleon interaction. The calculations reproduce correctly the ordering of the bound states in ^{10}B, and are in reasonable agreement with the observed branching ratios and reduced transition probabilities.

Intruder band mixing in an ab initio description of 12Be

The spectrum of ▪ exhibits exotic features, e.g., an intruder ground state and shape coexistence, normally associated with the breakdown of a shell closure. While previous phenomenological treatments indicated the ground state has substantial contributions from intruder configurations, it is only with advances in computational abilities and improved interactions that this intruder mixing is observed in ab initio no-core shell model (NCSM) predictions. In this work, we extract electromagnetic observables and symmetry decompositions from the NCSM wave functions to demonstrate that the low-lying positive parity spectrum can be explained in terms of mixing of rotational bands with very different intrinsic structure coexisting within the low-lying spectrum. These observed bands exhibit an approximate SU(3) symmetry and are qualitatively consistent with Elliott model predictions.

Direct ab initio calculation of the 4He nuclear electric dipole polarizability

The calculation of nuclear electromagnetic sum rules by directly solving for numerous eigenstates in a large basis is numerically challenging and has not been performed for A>2 nuclei. With the significant progress of high performance computing, we show that calculating sum rules using numerous discretized continuum states obtained with the ab initio no-core shell model in the harmonic oscillator basis is achievable numerically. Specifically, we calculate the 4He electric dipole (E1) polarizability, that is an inverse energy weighted sum rule, employing the Daejeon16 NN interaction. We demonstrate that the calculations are numerically tractable as the dimension of the basis increases and are convergent. Our results for the 4He electric dipole polarizability are consistent with the most recent experimental data and are compared with those of other theoretical studies employing different techniques and various interactions.

Nuclear structure properties of Si and P isotopes with the microscopic effective interactions

In the present work, we have reported comprehensive study of the sd-shell nuclei Si and P with neutron number varying from N=9 to N=20 using the microscopic effective valence shell interactions, namely, N3LO, JISP16 and DJ16A. These effective sd-shell interactions are developed using the ab initio no-core shell model wave functions and the Okubo-Lee-Suzuki transformation method. For comparison, we have also performed shell model calculations with the empirical USDB interaction. Energy spectra and electromagnetic properties of these isotopic chains have been studied. Theoretically calculated shell model results are compared with the available experimental data, to check the predictive strength of these microscopic interactions. It is found that the binding energies of the ground states are better reproduced with the DJ16A interaction as compared to other microscopic interactions and a proton subshell closure at Z=14 is obtained in Si. Spin-tensor decomposition of two-body interaction is presented to understand the contributions from central, vector and tensor components into these interactions. Spectroscopic strengths of 23Al(d,n)24Si are examined for the newly performed experiment at NSCL.

Ab initio no-core shell-model study of 18-24Ne isotopes

We report ab initio no-core shell-model (NCSM) study of 18−24Ne isotopes for energy spectra, electromagnetic properties, and point-proton radii using three realistic NN interactions. We have used inside nonlocal outside Yukawa (INOY), charge-dependent Bonn 2000 (CDB2K) and the chiral next-to-next-to-next-to-leading order (N3LO) interactions. We are able to reach basis size up to N max = 6 for 18Ne and N max = 4 for the 19−24Ne isotopes with m-scheme dimensions up to 1.0 × 109 in case of 24Ne. We observed better results for INOY interaction in terms of the binding energies of the ground state, and overall all three interactions provide good agreement with the experimental low-energy spectra. Our results for reduced M1 transition strengths and magnetic moments are close to the experimental values. We found that for long-range observables such as the E2 transition strengths, the electric quadrupole moments, and the point-proton radii (r p ), we need higher N max calculations to obtain results comparable to the experimental data. We have observed almost 6% increment in the converged r p as we increase the model space from N max = 4 to N max = 6.

Quantifying uncertainties due to irreducible three-body forces in deuteron-nucleus reactions

Background: Deuteron-induced nuclear reactions are an essential tool for probing the structure of nuclei as well as astrophysical information such as $(n,\ensuremath{\gamma})$ cross sections. The deuteron-nucleus system is typically described within a Faddeev three-body model consisting of a neutron ($n$), a proton ($p$), and the target nucleus ($A$) interacting through pairwise phenomenological potentials. While Faddeev techniques enable the exact description of the three-body dynamics, their predictive power is limited in part by the omission of irreducible neutron-proton-nucleus three-body force ($n\text{\ensuremath{-}}p\text{\ensuremath{-}}A$ 3BF).Purpose: Our goal is to quantify systematic uncertainties stemming from the reduction of deuteron-nucleus ($d+A$) dynamics to a picture of three pointlike nuclear clusters interacting via pairwise nucleon-nucleus forces, using as testing grounds $d+\ensuremath{\alpha}$ scattering and the $^{6}\mathrm{Li}$ ground state. We particularly focus on quantifying uncertainties arising from the full antisymmetrization of the ($A+2$)-body system with the target nucleus fixed in its ground state.Methods: We adopt the ab initio no-core shell model coupled with the resonating group method (NCSM/RGM) to compute microscopic $n\text{\ensuremath{-}}\ensuremath{\alpha}$ and $p\text{\ensuremath{-}}\ensuremath{\alpha}$ interactions, and use them in a three-body description of the $d+\ensuremath{\alpha}$ system by means of momentum-space Faddeev-type equations. Simultaneously, we also carry out ab initio calculations of $d+\ensuremath{\alpha}$ scattering and $^{6}\mathrm{Li}$ ground state by means of six-body NCSM/RGM calculations to serve as a benchmark for the three-body model predictions given by the Faddeev calculations.Results: By comparing the Faddeev and NCSM/RGM results, we show that the irreducible $n\text{\ensuremath{-}}p\text{\ensuremath{-}}\ensuremath{\alpha}$ 3BF has a non-negligible effect on bound state and scattering observables alike. Specifically, the Faddeev approach yields a $^{6}\mathrm{Li}$ ground state that is approximately 600 keV shallower than the one obtained with the NCSM/RGM. Additionally, the Faddeev calculations for $d+\ensuremath{\alpha}$ scattering yield a ${3}^{+}$ resonance that is located approximately 400 keV higher in energy compared to the NCSM/RGM result. The shape of the $d+\ensuremath{\alpha}$ angular distributions computed using the two approaches also differ, owing to the discrepancy in the predictions of the ${3}^{+}$ resonance energy.Conclusions: The Faddeev three-body model predictions for $d+\ensuremath{\alpha}$ scattering and $^{6}\mathrm{Li}$ using microscopic $n\text{\ensuremath{-}}\ensuremath{\alpha}$ and $p\text{\ensuremath{-}}\ensuremath{\alpha}$ potentials differ from those computed microscopically with the NCSM/RGM. These discrepancies are due to the $n\text{\ensuremath{-}}p\text{\ensuremath{-}}\ensuremath{\alpha}$ 3BF, which arises from two-nucleon exchange terms in the microscopic $d\text{\ensuremath{-}}\ensuremath{\alpha}$ interaction and are not accounted for in the three-body model Faddeev calculations. This study lays the foundation for future parametrizations of the 3BF due to Pauli exclusion principle effects in improved three-body calculations of deuteron-induced reactions.

Nuclear physics uncertainties in light hypernuclei

The energy levels of light hypernuclei are experimentally accessible observables that contain valuable information about the interaction between hyperons and nucleons. In this work we study strangeness $S = -1$ systems $^{3,4}_\Lambda$H and $^{4,5}_\Lambda$He using the ab initio no-core shell model (NCSM) with realistic interactions obtained from chiral effective field theory ($\chi$EFT). In particular, we quantify the finite precision of theoretical predictions that can be attributed to nuclear physics uncertainties. We study both the convergence of the solution of the many-body problem (method uncertainty) and the regulator- and calibration data-dependence of the nuclear $\chi$EFT Hamiltonian (model uncertainty). For the former, we implement infrared correction formulas and extrapolate finite-space NCSM results to infinite model space. We then use Bayesian parameter estimation to quantify the resulting method uncertainties. For the latter, we employ a family of 42 realistic Hamiltonians and measure the standard deviation of predictions while keeping the leading-order hyperon-nucleon interaction fixed. Following this procedure we find that model uncertainties of ground-state $\Lambda$ separation energies amount to $\sim 20(100)$ keV in $^3_\Lambda$H($^4_\Lambda$H,He) and $\sim 400$ keV in $^5_\Lambda$He. Method uncertainties are comparable in magnitude for the $^4_\Lambda$H,He $1^+$ excited states and $^5_\Lambda$He, which are computed in limited model spaces, but otherwise much smaller. This knowledge of expected theoretical precision is crucial for the use of binding energies of light hypernuclei to infer the elusive hyperon-nucleon interaction.

Ab initio no-core shell model study of neutron-rich 18,19,20C isotopes

We implement the ab initio no-core shell model approach to study neutron rich 18C, 19C and 20C 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 (N3LO) nucleon-nucleon interactions. Low-lying energy spectra, electromagnetic properties and point-proton radii for these nuclei up to basis space Nmax = 4 are calculated. Binding energies obtained with INOY interaction are in better agreement with the experimental values as compared to other ab initio interactions. We also show behavior of ground state energy and point-proton radii with the NCSM parameters, ħΩ and Nmax. We report a strong sensitivity of the B(E2) values from the first excited 2+ to ground state of 18C and 20C to the nuclear interaction. Shell model calculations with YSOX interaction are also performed, and corresponding results are compared with ab initio one.

AbInitio Prediction of the ^{4}He(d,γ)^{6}Li Big Bang Radiative Capture.

The rate at which helium (^{4}He) and deuterium (d) fuse together to produce lithium-6 (^{6}Li) and a γ ray, ^{4}He(d,γ)^{6}Li, is a critical puzzle piece in resolving the discrepancy between big bang predictions and astronomical observations for the primordial abundance of ^{6}Li. The accurate determination of this radiative capture rate requires the quantitative and predictive description of the fusion probability across the big bang energy window (30 keV≲E≲400 keV), where measurements are hindered by low counting rates. We present first-principle (or, abinitio) predictions of the ^{4}He(d,γ)^{6}Li astrophysical S factor using validated nucleon-nucleon and three-nucleon interactions derived within the framework of chiral effective field theory. By employing the abinitio no-core shell model with continuum to describe ^{4}He-d scattering dynamics and bound ^{6}Li product on an equal footing, we accurately and consistently determine the contributions of the main electromagnetic transitions driving the radiative capture process. Our results reveal an enhancement of the capture probability below 100keV owing to previously neglected magnetic dipole (M1) transitions and reduce by an average factor of 7 the uncertainty of the thermonuclear capture rate between 0.002 and 2GK.

Nuclear ab initio calculations of 6He β-decay for beyond the Standard Model studies

Precision measurements of β-decay observables offer the possibility to search for deviations from the Standard Model. A possible discovery of such deviations requires accompanying first-principles calculations. Here we compute the nuclear structure corrections for the β-decay of 6He which is of central interest in several experimental efforts. We employ the impulse approximation together with wave functions calculated using the ab initio no-core shell model with potentials based on chiral effective field theory. We use these state-of-the-art calculations to give a novel and comprehensive analysis of theoretical uncertainties. We find that nuclear corrections, which we compute within the sensitivity of future experiments, create significant deviation from the naive Gamow-Teller predictions, making their accurate assessment essential in searches for physics beyond the Standard Model.

Λnn bound state and resonance

We perform the ab initio no-core shell model (NCSM) calculation to investigate the bound state problem of the three-body $\Lambda nn$ system in chiral next-to-next-to-leading-order NN and chiral leading-order YN interactions. The calculations show that no $\Lambda nn$ bound state exists, but predict a low-lying $\Lambda nn$ resonant state near the threshold with the energy of $E_r= 0.124$ MeV and the width of about $\Gamma=1.161$ MeV. In searching for $\Lambda nn$ resonances, we extend the NCSM calculation to the continuum state by employing the J-matrix formalism in the scattering theory with the hyperspherical oscillator basis.

Lifetime of the hypertriton

Conflicting values of the hypertriton lifetime τ(3ΛH) were derived in relativistic heavy ion (RHI) collision experiments over the last decade. A very recent ALICE Collaboration measurement is the only experiment where the reported τ(3ΛH) comes sufficiently close to the free-Λ lifetime τΛ, as expected naively for a very weakly bound Λ in 3ΛH. We revisited theoretically this 3ΛH lifetime puzzle [1], using 3ΛH and 3He wave functions computed within the ab initio no-core shell model employing interactions derived from chiral effective field theory to calculate the two-body decay rate Γ(3ΛH → 3He + π−). We found significant but opposing contributions arising from ΣNN admixtures in 3ΛH and from π− − 3He final-state interaction. To derive τ(3ΛH), we evaluated the inclusive π− decay rate Γπ− (3ΛH) by using the measured branching ratio Γ(3ΛH → 3He + π−)/Γπ− (3ΛH) and added the π0 contributions through the ΔI = 1/2rule. The resulting τ(3ΛH) varies strongly with the rather poorly known Λ separation energy Esep(3ΛH) and it is thus possible to associate each one of the distinct RHI τ(3ΛH) measurements with its own underlying value of Esep(3ΛH).

Systematic Nuclear Uncertainties in the Hypertriton System

The hypertriton bound state is relevant for inference of knowledge about the hyperon–nucleon (YN) interaction. In this work we compute the binding energy of the hypertriton using the ab initio hypernuclear no-core shell model (NCSM) with realistic interactions derived from chiral effective field theory. In particular, we employ a large family of nucleon–nucleon interactions with the aim to quantify the theoretical precision of predicted hypernuclear observables arising from nuclear-physics uncertainties. The three-body calculations are performed in a relative Jacobi-coordinate harmonic oscillator basis and we implement infrared correction formulas to extrapolate the NCSM results to infinite model space. We find that the spread of the predicted hypertriton binding energy, attributed to the nuclear-interaction model uncertainty, is about 100 keV. In conclusion, the sensitivity of the hypertriton binding energy to nuclear-physics uncertainties is of the same order of magnitude as experimental uncertainties such that this bound-state observable can be used in the calibration procedure to constrain the YN interactions.

Using spin alignment of inelastically excited nuclei in fast beams to assign spins: The spectroscopy of O13 as a test case

Excited states in 13O were investigated using inelastic scattering of an E/A=69.5-MeV 13O beam off of a 9Be target. The excited states were identified in the invariant-mass spectra of the decay products. Both single proton and sequential two-proton decays of the excited states were examined. For a number of the excited states, the protons were emitted with strong anisotropy where emissions transverse to the beam axis are favored. The measured proton-decay angular distributions were compared to predictions from distorted-wave born-approximation (DWBA) calculations of the spin alignment which was shown to be largely independent of the excitation mechanism. The deduced $^{13}$O level scheme is compared to ab initio no-core shell model with continuum (NCSMC) predictions. The lowest-energy excited states decay isotropically consistent with predictions of strong proton 1s1/2 structure. Above these states in the level scheme, we observed a number of higher-spin states not predicted within the model. Possibly these are associated with rotational bands built on deformed cluster configurations predicted by antisymmetrized molecular dynamics (AMD) calculations. The spin alignment mechanism is shown to be useful for making spin assignments and may have widespread use.

Ab initio calculations of electric dipole moments of light nuclei

In any finite system, the presence of a non-zero permanent electric dipole moment (EDM) would indicate CP violation beyond the small violation predicted in the Standard Model. Here, we use the ab initio no-core shell model (NCSM) framework to theoretically investigate the magnitude of the nuclear EDM. We calculate EDMs of several light nuclei using chiral two- and three-body interactions and a PT-violating Hamiltonian based on a one-meson-exchange model. We present a benchmark calculation for $^3$He, as well as results for the more complex nuclei $^{6,7}$Li, $^9$Be, $^{10,11}$B, $^{13}$C, $^{14,15}$N, and $^{19}$F. Our results suggest that different nuclei can be used to probe different terms of the PT violating interaction. These calculations allow us to suggest which nuclei may be good candidates in the search for a measurable permanent electric dipole moment.

Power counting in chiral effective field theory and nuclear binding

Chiral effective field theory ($\chi$EFT), as originally proposed by Weinberg, promises a theoretical connection between low-energy nuclear interactions and quantum chromodynamics (QCD). However, the important property of renormalization-group (RG) invariance is not fulfilled in current implementations and its consequences for predicting atomic nuclei beyond two- and three-nucleon systems has remained unknown. In this work we present a first and systematic study of recent RG-invariant formulations of $\chi$EFT and their predictions for the binding energies and other observables of selected nuclear systems with mass-numbers up to $A =16$. Specifically, we have carried out ab initio no-core shell-model and coupled cluster calculations of the ground-state energy of $^3$H, $^{3,4}$He, $^{6}$Li, and $^{16}$O using several recent power-counting (PC) schemes at leading order (LO) and next-to-leading order (NLO), where the subleading interactions are treated in perturbation theory. Our calculations indicate that RG-invariant and realistic predictions can be obtained for nuclei with mass number $A \leq 4$. We find, however, that $^{16}$O is either unbound with respect to the four $\alpha$-particle threshold, or deformed, or both. Similarly, we find that the $^{6}$Li ground-state resides above the $\alpha$-deuteron separation threshold. These results are in stark contrast with experimental data and point to either necessary fine-tuning of all relevant counterterms, or that current state-of-the-art RG-invariant PC schemes at LO in $\chi$EFT lack necessary diagrams -- such as three-nucleon forces -- to realistically describe nuclei with mass number $A>4$.

Ab initio benchmarks of neutrinoless double- β decay in light nuclei with a chiral Hamiltonian

We report ab initio benchmark calculations of nuclear matrix elements (NMEs) for neutrinoless double-beta ($0\nu\beta\beta$) decays in light nuclei with mass number ranging from $A=6$ to $A=22$. We use the transition operator derived from light-Majorana neutrino exchange and evaluate the NME with three different methods: two variants of in-medium similarity renormalization group (IMSRG) and importance-truncated no-core shell model (IT-NCSM). The same two-plus-three-nucleon interaction from chiral effective field theory is employed, and both isospin-conserving ($\Delta T=0$) and isospin-changing ($\Delta T=2$) transitions are studied. We compare our resulting ground-state energies and NMEs to those of recent ab initio no-core shell model and coupled-cluster calculations, also with the same inputs. We show that the NMEs of $\Delta T=0$ transitions are in good agreement among all calculations, at the level of 10%. For $\Delta T=2$, relative deviations are more significant in some nuclei. The comparison with the exact IT-NCSM result allows us to analyze these cases in detail, and indicates the next steps towards improving the IMSRG-based approaches. The present study clearly demonstrates the power of consistent cross-checks that are made possible by ab initio methodology. This capability is crucial for providing meaningful many-body uncertainties in the NMEs for the $0\nu\beta\beta$ decays in heavier candidate nuclei, where quasi-exact benchmarks are not available.

Transfer to the continuum of 11Be with the application of ab-initio S-matrix

The 9Be(18O,16O)11Be two-neutron transfer reaction at 84 MeV is measured at forward angles to explore the continuum of 11Be nucleus. Transfer-to-the-continuum (TC) reaction calculations are applied using for the first time an ab-initio S-matrix. It is derived from the ab-initio no-core shell model with continuum (NCSMC) method, recently used to describe the bound and continuum spectrum of 11Be. Previously known levels are confirmed and theoretical and experimental evidence for a 9/2+ state at Ex = 5.8 MeV is given, whose configuration is thought to be 10Be(2+) + n(d5/2).

Clustering and α -capture reaction rate from ab initio symmetry-adapted descriptions of Ne20

We introduce a new framework for studying clustering and for calculating alpha partial widths using ab initio wave functions. We demonstrate the formalism for $^{20}$Ne, by calculating the overlap between the $^{16}$O$+\alpha$ cluster configuration and states in $^{20}$Ne computed in the ab initio symmetry-adapted no-core shell model. We present spectroscopic amplitudes and spectroscopic factors, and compare those to no-core symplectic shell-model results in larger model spaces, to gain insight into the underlying physics that drives alpha-clustering. Specifically, we report on the alpha partial width of the lowest $1^-$ resonance in $^{20}$Ne, which is found to be in good agreement with experiment. We also present first no-core shell-model estimates for asymptotic normalization coefficients for the ground state, as well as for the first excited $4^{+}$ state in $^{20}$Ne that lies in a close proximity to the $^{16}$O$+\alpha$ threshold. This outcome highlights the importance of correlations for developing cluster structures and for describing alpha widths. The widths can then be used to calculate alpha-capture reaction rates for narrow resonances of interest to astrophysics. We explore the reaction rate for the alpha-capture reaction $^{16}$O$(\alpha,\gamma)^{20}$Ne at astrophysically relevant temperatures and determine its impact on simulated X-ray burst abundances.