arXiv subjects
Publications and source records attributed to G. Hagen.
Ab initio has been used as a label in nuclear theory for over two decades. Its meaning has evolved and broadened over the years. We present our interpretation, briefly review its historical use, and discuss its present-day relation to theoretical uncertainty quantification.
The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. Our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.
For the first time, the $(d,{}^2\text{He})$ reaction was successfully used in inverse kinematics to extract the Gamow-Teller transition strength in the $β^{+}$ direction from an unstable nucleus. The nucleus studied was $^{14}$O, and the Gamow-Teller transition strength to $^{14}$N was extracted up to an excitation energy of 22 MeV. The measurement of the $(d,{}^2\text{He})$ reaction in inverse kinematics was made possible by the combination of an active target time projection chamber and a magnetic spectrometer. The data were used to test shell-model and state-of-the-art coupled cluster calculations. Shell-model calculations reproduce the measured Gamow-Teller strength distribution up to about 15 MeV reasonably well, after the application of a phenomenological quenching factor. Coupled-cluster calculation reproduces the full strength distribution well without such quenching, owing to the large model space, the inclusion of strong correlations, and the coupling of the weak interaction to two nucleons through two-body currents. This indicates that such calculations provide a very promising path for answering long-standing questions about the observed quenching of Gamow-Teller strengths in nuclei.
The root mean square radii of the proton density distribution in $^{16-24}$O derived from measurements of charge changing cross sections with a carbon target at $\sim$900$A$ MeV together with the matter radii portray thick neutron skin for $^{22 - 24}$O despite $^{22,24}$O being doubly magic. Imprints of the shell closures at $N$ = 14 and 16 are reflected in local minima of their proton radii that provide evidence for the tensor interaction causing them. The radii agree with it ab initio calculations employing the chiral NNLO$_{\mathrm{sat}}$ interaction, though skin thickness predictions are challenged. Shell model predictions agree well with the data.
We present the results of a National Science Foundation (NSF) Project Scoping Workshop, the purpose of which was to assess the current status of calculations for the nuclear matrix elements governing neutrinoless double-beta decay and determine if more work on them is required. After reviewing important recent progress in the application of effective field theory, lattice quantum chromodynamics, and ab initio nuclear-structure theory to double-beta decay, we discuss the state of the art in nuclear-physics uncertainty quantification and then construct a road map for work in all these areas to fully complement the increasingly sensitive experiments in operation and under development. The road map contains specific projects in theoretical and computational physics as well as an uncertainty-quantification plan that employs Bayesian Model Mixing and an analysis of correlations between double-beta-decay rates and other observables. The goal of this program is a set of accurate and precise matrix elements, in all nuclei of interest to experimentalists, delivered together with carefully assessed uncertainties. Such calculations will allow crisp conclusions from the observation or non-observation of neutrinoless double-beta decay, no matter what new physics is at play.
Coupled cluster theory is an attractive tool to solve the quantum many-body problem because its singles and doubles (CCSD) approximation is computationally affordable and yields about 90% of the correlation energy. Capturing the remaining 10%, e.g. via including triples, is numerically expensive. Here we assume that short-range three-body correlations dominate and - following Lepage [How to renormalize the Schrödinger equation, arXiv:nucl-th/9706029] - that their effects can be included within CCSD by renormalizing the three-body contact interaction. We renormalize this contact in $^{16}$O and obtain accurate CCSD results for $^{24}$O, $^{20-34}$Ne, $^{40,48}$Ca, $^{78}$Ni, $^{90}$Zr, and $^{100}$Sn.
We compute spectral function for $^4$He by combining coupled-cluster theory with an expansion of integral transforms into Chebyshev polynomials. Our method allows to estimate the uncertainty of spectral reconstruction. The properties of the Chebyshev polynomials make the procedure numerically stable and considerably lower in memory usage than the typically employed Lanczos algorithm. We benchmark our predictions with other calculations in the literature and with electron scattering data in the quasi-elastic peak. The spectral function formalism allows one to extend ab-initio lepton-nucleus cross sections into the relativistic regime. This makes it a promising tool for modeling this process at higher energy transfers. The results we present open the door for studies of heavier nuclei, important for the neutrino oscillation programs.
Background: Recent developments in {\it ab initio} nuclear theory demonstrate promising results in medium- to heavy-mass nuclei. A particular challenge for many of the many-body methodologies, however, is an accurate treatment of the electric-quadrupole, $E2$, strength associated with collectivity. Purpose: The valence-space in-medium similarity renormalization group (VS-IMSRG) is a particularly powerful method for accessing medium- and high-mass nuclei but has been found to underpredict $E2$ strengths. The purpose of this work is to evaluate the isospin dependence of this underprediction. Methods: We perform a systematic comparison of valence-space in-medium similarity renormalization group (VS-IMSRG) calculations with available literature. We make use of isoscalar and isovector contributions to the $E2$ matrix elements to assess isoscalar and isovector contributions to the missing strength. Results: It is found that the $E2$ strength is consistent throughout $T_z=\left|\frac{1}{2}\right|$, $T_z=\left|1\right|$, $T_z=\left|\frac{3}{2}\right|$ and $T_z=2$ pairs within the $sd$-shell. Furthermore, no isovector contribution to the deficiency is identified. Conclusions: A comparison with toy-models and coupled-cluster calculations is used to discuss potential origins of the missing strength, which arises from missing many-particle, many-hole excitations out of the model space. The absence of any significant isovector contribution to the missing $E2$ strength indicates that the $E2$ strength discrepancy, and therefore any correction, is largely independent of the isospin of the nuclei in question.
Single-reference coupled-cluster theory is an accurate and affordable computational method for the nuclear many-body problem. For open-shell nuclei, the reference state typically breaks rotational invariance and angular momentum must be restored as a good quantum number. We perform angular-momentum projection after variation and employ the disentangled coupled-cluster formalism and a Hermitian approach. We compare our results with benchmarks for $^8$Be and $^{20}$Ne using a two-nucleon interaction from chiral effective field theory and for $pf$-shell nuclei within the traditional shell model. We compute the rotational band in the exotic nucleus $^{34}$Mg and find agreement with data.
Collinear laser spectroscopy is performed on the nickel isotopes $^{58-68,70}$Ni, using a time-resolved photon counting system. From the measured isotope shifts, nuclear charge radii $R_c$ are extracted and compared to theoretical results. Three ab initio approaches all employ, among others, the chiral interaction NNLO$_{\rm sat}$, which allows an assessment of their accuracy. We find agreement with experiment in differential radii $δ\left\langle r_\mathrm{c}^2 \right\rangle$ for all employed ab initio methods and interactions, while the absolute radii are consistent with data only for NNLO$_{\rm sat}$. Within nuclear density functional theory, the Skyrme functional SV-min matches experiment more closely than the Fayans functional Fy($Δr$,HFB).
Pion exchange is the central ingredient to nucleon-nucleon interactions used in nuclear structure calculations, and one pion exchange (OPE) enters at leading order in chiral effective field theory. In the $^{2S+1}L_J={^1S_0}$ partial wave, however, OPE and a contact term needed for proper renormalization fail to produce the qualitative, and quantitative, features of the scattering phase shifts. Cutoff variation also revealed a surprisingly low breakdown momentum of about 330 MeV in this partial wave. Here we show that potentials consisting of OPE, two pion exchange (TPE), and a single contact address these problems and yield accurate and renormalization group (RG) invariant phase shifts in the $^1S_0$ partial wave. We demonstrate that a leading-order potential with TPE can be systematically improved by adding a contact quadratic in momenta. For momentum cutoffs below about 500 MeV, the removal of relevant physics from TPE loops needs to be compensated by additional contacts to keep RG invariance. Inclusion of the $Δ$ isobar degree of freedom in the potential does not change the strong contributions of TPE.
A measurement of proton inelastic scattering of $^8$He at $8.25A$~MeV at TRIUMF shows a resonance at 3.54(6)~MeV with a width of 0.89(11)~MeV. The energy of the state is in good agreement with coupled cluster and no-core shell model with continuum calculations, with the latter successfully describing the measured resonance width as well. Its differential cross section analyzed with phenomenological collective excitation form factor and microscopic coupled reaction channels framework consistently reveals a large deformation parameter $β_2$ = 0.40(3), consistent with no-core shell model predictions of a large neutron deformation. This deformed double-closed shell at the neutron drip-line opens a new paradigm.
100Sn is of singular interest for nuclear structure. Its closed-shell proton and neutron configuration exhibit exceptional binding and 100Sn is the heaviest nucleus comprising protons and neutrons in equal number, a feature that enhances the contribution of the short-range, proton-neutron pairing interaction and strongly influences its decay via the weak interaction. Decays studies in the region of 100Sn have attempted to prove its doubly magic character but few have studied it from the ab initio theoretical perspective and none have addressed the odd-proton nuclear forces. Here we present, the first direct measurement of the exotic odd-proton nuclide 100In - the beta-decay daughter of 100Sn - and 99In, only one proton below 100Sn. The most advanced mass spectrometry techniques were used to measure 99In, produced at a rate of only a few ions per second, and to resolve the ground and isomeric states in 101In. The experimental results are confronted with new ab initio many-body approaches. The 100-fold improvement in precision of the 100In mass value exarcebates a striking discrepancy in the atomic mass values of 100Sn deduced from recent beta-decay results.
The accuracy of atomic theory calculations limits the extraction of nuclear charge radii from isotope shift measurements of odd-proton nuclei. For Na isotopes, though precise spectroscopic measurements have existed since more than half a century, calculations by different methods offer a wide range of values. Here, we present accurate atomic calculations to reliably extract the Na charge radii. By combining experimental matter radii with nuclear coupled-cluster calculations based on nucleon-nucleon and three-nucleon forces, we constrain the parameters obtained from the atomic calculations. Therefore, this study guides atomic theory and highlights the importance of using accurate atomic and nuclear computations in our understanding of the size of light nuclei.
We construct an effective shell-model interaction for the valence space spanned by single-particle neutron and single-hole proton states in $^{100}$Sn. Starting from chiral nucleon-nucleon and three-nucleon forces and single-reference coupled-cluster theory for $^{100}$Sn we apply a second similarity transformation that decouples the valence space. The particle-particle components of the resulting effective interaction can be used in shell model calculations for neutron deficient tin isotopes. The hole-hole interaction can be used to calculate the $N = 50$ isotones south of $^{100}$Sn, and the full particle-hole interaction describes nuclei in the region southeast of $^{100}$Sn. We compute low-lying excited states in selected nuclei southeast of $^{100}$Sn, and find reasonable agreement with data. The presented techniques can also be applied to construct effective shell-model interactions for other regions of the nuclear chart.
Chiral effective field theory ($χ$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 $χ$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 $α$-particle threshold, or deformed, or both. Similarly, we find that the $^{6}$Li ground-state resides above the $α$-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 $χ$EFT lack necessary diagrams -- such as three-nucleon forces -- to realistically describe nuclei with mass number $A>4$.
We use coupled-cluster theory and nuclear interactions from chiral effective field theory to compute the nuclear matrix element for the neutrinoless double-beta decay of $^{48}$Ca. Benchmarks with the no-core shell model in several light nuclei inform us about the accuracy of our approach. For $^{48}$Ca we find a relatively small matrix element. We also compute the nuclear matrix element for the two-neutrino double-beta decay of $^{48}$Ca with a quenching factor deduced from two-body currents in recent ab-initio calculation of the Ikeda sum-rule in $^{48}$Ca [Gysbers et al., Nature Physics 15, 428-431 (2019)].
We present a consistent \emph{ab initio} computation of the longitudinal response function $R_L$ in $^{40}$Ca using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon interactions. We validate our approach by comparing our results for $R_L$ in $^4$He and the Coulomb sum rule in $^{40}$Ca against experimental data and other calculations. For $R_L$ in $^{40}$Ca we obtain a very good agreement with experiment in the quasi-elastic peak up to intermediate momentum transfers, and we find that final state interactions are essential for an accurate description of the data. This work presents a milestone towards \emph{ab initio} computations of neutrino-nucleus cross sections relevant for experimental long-baseline neutrino programs.