arXiv subjects

P. Maris

Publications and source records attributed to P. Maris.

At least 19 recordsLinked to original sources

arXiv2025

Separable character of ab initio No-Core Shell Model one-body densities

Motivated by recent findings on the separability of optical potentials that are derived from folding off-shell densities with off-shell nucleon-nucleon amplitudes, we study the off-shell character of one-body density matrices created within the No-Core Shell Model (NCSM). Concentrating on nuclei with a 0$^+$ ground state from $^4$He through $^{48}$Ca, we investigate the off-shell character of their one-body density matrices in momentum space when using the momentum transfer and the average momentum as variables. A singular value decomposition of the one-body density matrices reveals that they can be characterized by only very few terms, depending on the mass number of the nucleus. These findings are independent of the nucleon-nucleon interactions employed, as well as from computational specifics as grid spacing and size of the model space.

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arXiv2023

Nuclear structure and elastic scattering observables obtained consistently with different NN interactions

Nucleon-nucleon ($NN$) interactions based on chiral effective theories are commonly used in ab initio calculations of light nuclei. Here we present a study based on three different NN interactions (up to next-to-next-to-leading order) for which structure and elastic proton scattering observables are consistently calculated for $^4$He, $^{12}$C, and $^{16}$O. The interactions are compared at the two-body level in terms of Wolfenstein amplitudes, and their predictions for ground state energies, point-proton radii, and charge form factors, as well as proton elastic scattering observables in the leading-order spectator expansion in the energy range between 65 and 160 MeV projectile energy are presented. To gain further insight into differences visible in elastic scattering observables, we investigate the behavior of the calculated effective nucleon-nucleus interactions for the $^{12}$C nucleus based on the different $NN$ interactions.

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arXiv2023

Uncertainties in ab initio nuclear structure calculations with chiral interactions

We present theoretical ground state energies and their uncertainties for p-shell nuclei obtained from chiral effective field theory internucleon interactions as a function of chiral order, fitted to two- and three-body data only. We apply a Similary Renormalization Group transformation to improve the numerical convergence of the many-body calculations, and discuss both the numerical uncertainties arising from basis truncations and those from omitted induced many-body forces, as well as chiral truncation uncertainties. With complete Next-to-Next-to-Leading (N2LO) order two- and three-body interactions, we find significant overbinding for the ground states in the upper p-shell, but using higher-order two-body potentials, in combination with N2LO three-body forces, our predictions agree with experiment throughout the p-shell to within our combined estimated uncertainties. The uncertainties due to chiral order truncation are noticeably larger than the numerical uncertainties, but they are expected to become comparable to the numerical uncertainties at complete N3LO.

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arXiv2023

Chiral uncertainties in ab initio nucleon-nucleus elastic scattering

The effective interaction between a nucleon and a nucleus is one of the most important ingredients for reaction theories. Theoretical formulations were introduced early by Feshbach and Watson, and efforts of deriving and computing those `optical potentials' in a microscopic fashion have a long tradition. However, only recently the leading order term in the Watson multiple scattering approach could be calculated fully {\it ab initio}, meaning that the same nucleon-nucleon (NN) interaction enters both the structure as well as the reaction pieces on equal footing. This allows the uncertainties from the underlying chiral effective NN interaction to be systematically explored in nucleon-nucleus elastic scattering observables. In this contribution the main ingredients for arriving at the {\it ab initio} leading order of the effective nucleon-nucleus interaction in the Watson approach will be reviewed. Concentrating on one specific chiral NN interaction from the LENPIC collaboration and light nuclei with a 0$^+$ ground state, the leading order nucleon-nucleus interaction is calculated using up to the third chiral order (N2LO) in the nucleon-nucleon potential, and elastic scattering observables are extracted. Then pointwise as well as correlated uncertainty quantification is used for the estimation of the chiral truncation error. Elastic scattering observables for $^4$He, $^{12}$C, and $^{16}$O for between 65 and 200 MeV projectile energy will be analyzed.

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arXiv2022

Probing the quadrupole transition strength of 15C via deuteron inelastic scattering

Deuteron elastic scattering from 15C and inelastic scattering reactions to the first excited state of 15C were studied using a radioactive beam of 15C in inverse kinematics. The scattered deuterons were measured using HELIOS. The elastic scattering differential cross sections were analyzed using the optical model. A matter deformation length {\delta}d = 1.04(11) fm has been extracted from the differential cross sections of inelastic scattering to the first excited state. The ratio of neutron and proton matrix elements Mn/Mp = 3.6(4) has been determined from this quadrupole transition. Neutron effective charges and core-polarization parameters of 15C were determined and discussed. Results from ab-initio no-core configuration interaction calculations were also compared with the experimental observations. This result supports a moderate core decoupling effect of the valence neutron in 15C similarly to its isotone 17O, in line with the interpretation of other neutron-rich carbon isotopes.

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arXiv2022

SS-HORSE Extension of the No-Core Shell Model: Application to Resonances in $^7{\mathrm He}$

Theoretical ab initio studies of resonances in the unbound ${\rm^{7}He}$ nucleus are presented. We perform no-core shell model calculations with $NN$ interactions Daejeon16 and JISP16 and utilize the SS-HORSE method to calculate the $S$ matrix for two-body channels $n{-}{\rm^{6}He}$ and $n{-}{\rm^{6}He^{*}}$ with ${\rm^{6}He}$ respectively in the ground and excited $2^{+}$ states as well as for the four-body democratic decay channel ${{\rm^{4}He}+n+n+n}$. The resonant energies and widths areobtained by numerical location of the $S$-matrix poles. We describe all experimentally known ${\rm^{7}He}$ resonances and suggest an interpretation of an observed wide resonance of unknown spin-parity.

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arXiv2022

Nuclear properties with semilocal momentum-space regularized chiral interactions beyond N2LO

We present a comprehensive investigation of few-nucleon systems as well as light and medium-mass nuclei up to $A=48$ using the current Low Energy Nuclear Physics International Collaboration two-nucleon interactions in combination with the third-order (N$^2$LO) three-nucleon forces. To address the systematic overbinding of nuclei starting from $A \sim 10$ found in our earlier study utilizing the N$^2$LO two- and three-nucleon forces, we take into account higher-order corrections to the two-nucleon potentials up through fifth order in chiral effective field theory. The resulting Hamiltonian can be completely determined using the $A=3$ binding energies and selected nucleon-deuteron cross sections as input. It is then shown to predict other nucleon-deuteron scattering observables and spectra of light $p$-shell nuclei, for which a detailed correlated truncation error analysis is performed, in agreement with experimental data. Moreover, the predicted ground state energies of nuclei in the oxygen isotopic chain from $^{14}$O to $^{26}$O as well as $^{40}$Ca and $^{48}$Ca show a remarkably good agreement with experimental values, given that the Hamiltonian is fixed completely from the $A \leq 3$ data, once the fourth-order (N$^3$LO) corrections to the two-nucleon interactions are taken into account. On the other hand, the charge radii are found to be underpredicted by $\sim 10\%$ for the oxygen isotopes and by almost $20\%$ for $^{40}$Ca and $^{48}$Ca.

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arXiv2022

Effective operators for valence space calculations from the {\itshape ab initio} No-Core Shell Mode

In recent years, remarkable progress has been achieved in developing novel non-perturbative techniques for constructing valence space shell model Hamiltonians from realistic internucleon interactions. One of these methods is based on the Okubo--Lee--Suzuki (OLS) unitary transformation applied to no-core shell model (NCSM) solutions. In the present work, we implement the corresponding approach to solve for valence space effective electromagnetic operators. To this end, we use the NCSM results for $A=16-18$, obtained at $N_{\rm max}=4$, to derive a charge-dependent version of the effective interaction for the $sd$ shell, which allows us to exactly reproduce selected NCSM spectra of $^{18}$O, $^{18}$F and $^{18}$Ne within the two valence nucleon space. We then deduce effective single-particle matrix elements of electric quadrupole ($E2$) and magnetic dipole ($M1$) operators by matching them to the electromagnetic transitions and moments for $^{17}$O and $^{17}$F from the NCSM at $N_{\rm max}=4$. Thus, effective $E2$ and $M1$ operators are obtained as sets of single-particle matrix elements for the valence space ($sd$ shell) which allow us to reproduce the NCSM results for $A=17$ exactly. Systematic comparison of a large set of $sd$ shell results on quadrupole and magnetic dipole moments and transitions for $A=18$ using effective $E2$ and $M1$ operators that we derive from the full NCSM calculations demonstrates a remarkable agreement.

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arXiv2021

Ab initio nucleon-nucleus elastic scattering with chiral effective field theory uncertainties

Background: Effective interactions for nucleon-nucleus ($NA$) elastic scattering from first principles require the use of the same nucleon-nucleon ($NN$) interaction in the structure and reaction calculations, and a consistent treatment of the relevant operators at each order. Purpose: Truncation uncertainties of chiral $NN$ forces have been studied for scattering observables in few-body systems and for bound state properties of light nuclei. We extend this to $NA$ elastic scattering. Methods: With the spectator expansion of multiple scattering theory and the no-core shell model, we use a chiral interaction from the LENPIC collaboration to consistently calculate the leading order effective $NA$ interaction up to third chiral order (N2LO) and extract elastic scattering observables. We quantify the chiral truncation error using pointwise and correlated methods. Results: We analyze proton-$^{16}$O and neutron-$^{12}$C elastic scattering observables between 65 and 185 MeV projectile kinetic energy. We find qualitatively similar results for the chiral truncation uncertainties as in few-body systems, which we assess using similar diagnostic tools. The order-by-order convergence of the scattering observables for $^{16}$O and $^{12}$C is reasonable near 100 MeV, but for higher energies the expansion parameter becomes too large to converge. We find a near-perfect correlation between the neutron differential cross section and the $NN$ Wolfenstein amplitudes for small momentum transfers. Conclusions: The tools used to study the convergence of a chiral $NN$ interaction in few-body systems can be applied to $NA$ scattering with minor changes. The $NN$ interaction used here gives a good description of $^{16}$O and $^{12}$C scattering observables as low as 65 MeV. The very forward direction of the neutron differential cross section mirrors the behavior of the $NN$ interaction amazingly well.

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arXiv2021

Ground-state properties of light $4n$ self-conjugate nuclei in $ab$ $initio$ no-core Monte Carlo shell model calculations with nonlocal $NN$ interactions

We report $J^\pi = 0^+$ ground-state energies and point-proton radii of $^4$He, $^8$Be, $^{12}$C, $^{16}$O and $^{20}$Ne nuclei calculated by the $ab$ $initio$ no-core Monte Carlo shell model with the JISP16 and Daejeon16 nonlocal $NN$ interactions. Ground-state energies are obtained in the basis spaces up to seven oscillator shells ($N_{\rm shell} = 7$) with several oscillator energies ($\hbar \omega$) around the optimal oscillator energy for the convergence of ground-state energies. These energy eigenvalues are extrapolated to obtain estimates of converged ground state energies in each basis space using energy variances of computed energy eigenvalues. We further extrapolate these energy-variance-extrapolated energies obtained in the finite basis spaces to infinite basis-space results with an empirical exponential form. This form features a dependence on the basis-space size but is independent of the value of $\hbar\omega$ used for the harmonic-oscillator basis functions. Point-proton radii for these states of atomic nuclei are also calculated following techniques employed for the energies. From these results, it is found that the Daejeon16 $NN$ interaction provides good agreement with experimental data up to approximately $^{16}$O, while the JISP16 $NN$ interaction provides good agreement with experimental data up to approximately $^{12}$C. Beyond these nuclei, the interactions produce overbinding accompanied by radii that are too small. These findings suggest and encourage further revisions of nonlocal $NN$ interactions towards the investigation of nuclear structure in heavier-mass regions.

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arXiv2021

Quadrupole moments and proton-neutron structure in p-shell mirror nuclei

Electric quadrupole (E2) matrix elements provide a measure of nuclear deformation and related collective structure. Ground-state quadrupole moments in particular are known to high precision in many p-shell nuclei. While the experimental electric quadrupole moment only measures the proton distribution, both proton and neutron quadrupole moments are needed to probe proton-neutron asymmetry in the nuclear deformation. We seek insight into the relation between these moments through the ab initio no-core configuration interaction (NCCI), or no-core shell model (NCSM), approach. Converged ab initio calculations for quadrupole moments are particularly challenging, due to sensitivity to long-range behavior of the wave functions. We therefore study more robustly-converged ratios of quadrupole moments: across mirror nuclides, or of proton and neutron quadrupole moments within the same nuclide. In calculations for mirror pairs in the p shell, we explore how well the predictions for mirror quadrupole moments agree with experiment and how well isospin (mirror) symmetry holds for quadrupole moments across a mirror pair.

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arXiv2021

Nonlocal structure of the leading order \textit{ab initio} effective potentials for proton elastic scattering from light nuclei

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.

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arXiv2021

Nuclear spin features relevant to ab initio nucleon-nucleus elastic scattering

Background: Effective interactions for elastic nucleon-nucleus scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations, as well as a consistent treatment of the relevant operators at each order. Purpose: Previous work using these interactions has shown good agreement with available data. Here, we study the physical relevance of one of these operators, which involves the spin of the struck nucleon, and examine the interpretation of this quantity in a nuclear structure context. Methods: Using the framework of the spectator expansion and the underlying framework of the no-core shell model, we calculate and examine spin-projected, one-body momentum distributions required for effective nucleon-nucleus interactions in $J=0$ nuclear states. Results: The calculated spin-projected, one-body momentum distributions for $^4$He, $^6$He, and $^8$He display characteristic behavior based on the occupation of protons and neutrons in single particle levels, with more nucleons of one type yielding momentum distributions with larger values. Additionally, we find this quantity is strongly correlated to the magnetic moment of the $2^+$ excited state in the ground state rotational band for each nucleus considered. Conclusions: We find that spin-projected, one-body momentum distributions can probe the spin content of a $J=0$ wave function. This feature may allow future \textit{ab initio} nucleon-nucleus scattering studies to inform spin properties of the underlying nucleon-nucleon interactions. The observed correlation to the magnetic moment of excited states illustrates a previously unknown connection between reaction observables such as the analyzing power and structure observables like the magnetic moment.

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arXiv2020

Light nuclei with semilocal momentum-space regularized chiral interactions up to third order

We present a systematic investigation of few-nucleon systems and light nuclei using the current LENPIC interactions comprising semilocal momentum-space regularized two- and three-nucleon forces up to third chiral order (N$^2$LO). Following our earlier study utilizing the coordinate-space regularized interactions, the two low-energy constants entering the three-body force are determined from the triton binding energy and the differential cross section minimum in elastic nucleon-deuteron scattering. Predictions are made for selected observables in elastic nucleon-deuteron scattering and in the deuteron breakup reactions, for properties of the $A=3$ and $A=4$ nuclei, and for spectra of $p$-shell nuclei up to $A = 16$. A comprehensive error analysis is performed including an estimation of correlated truncation uncertainties for nuclear spectra. The obtained predictions are generally found to agree with experimental data within errors. Similar to the coordinate-space regularized chiral interactions at the same order, a systematic overbinding of heavier nuclei is observed, which sets in for $A \sim 10$ and increases with $A$.

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arXiv2020

Benchmark neutrinoless double-beta decay matrix elements in a light nucleus

We compute nuclear matrix elements of neutrinoless double-beta decay mediated by light Majorana-neutrino exchange in the A = 6 system. The goal is to benchmark two many-body approaches, the No-Core Shell Model and the Multi-Reference In-Medium Similarity Renormalization Group. We use the SRG-evolved chiral N3LO-EM500 potential for the nuclear interaction, and make the approximation that isospin is conserved. We compare the results of the two approaches as a function of the cutoff on the many-body basis space. Although differences are seen in the predicted nuclear radii, the ground-state energies and neutrinoless double-beta decay matrix elements produced by the two approaches show significant agreement. We discuss the implications for calculations in heavier nuclei.

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arXiv2020

Ab initio Leading Order Effective Potentials for Elastic Nucleon-Nucleus Scattering

Background: Calculating microscopic effective interactions (optical potentials) for elastic nucleon-nucleus scattering has already in the past led to a large body of work. For first-order calculations a nucleon-nucleon (\textit{NN}) interaction and a one-body density of the nucleus were taken as input to rigorous calculations of microscopic full-folding calculations. Purpose: 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. Methods: The first order effective folding potential is computed by first deriving a nonlocal scalar density as well as a spin-projected momentum distribution. Those are then integrated with the off-shell Wolfenstein amplitudes $A$, $C$, and $M$. The resulting nonlocal potential serves as input to a momentum-space Lippmann-Schwinger equation, whose solutions are summed to obtain the nucleon-nucleus scattering observables. Results: We calculate elastic scattering observables for $^4$He, $^6$He, $^8$He, $^{12}$C, and $^{16}$O in the energy regime between 100 and 200 MeV projectile kinetic energy, and compare to available data. We also explore the extension down to about 70 MeV, and study the effect of ignoring the spin of the struck nucleon in the nucleus. Conclusions: In our calculations we contrast elastic scattering off closed-shell and open-shell nuclei. We find that for closed-shell nuclei the approximation of ignoring the spin of the struck target nucleon is excellent. We only see effects of the spin of the struck target nucleon when considering $^6$He and $^8$He, which are nuclei with a $N/Z$ ratio larger than 1.

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arXiv2020

Improved description of light nuclei through chiral effective field theory at leading order

We propose an arrangement of the most commonly invoked version of the two-nucleon chiral potential such that the low-lying amplitude zero of the 1S0 partial wave is captured at leading order of the effective expansion. Adopting other partial waves from the LENPIC interaction, we show how this modification yields an improved description of ground-state energies and point-proton radii of three test nuclei.

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arXiv2020

Robust ab initio predictions for nuclear rotational structure in the Be isotopes

No-core configuration interaction (NCCI) calculations for p-shell nuclei give rise to rotational bands, identified by strong intraband E2 transitions and by rotational patterns for excitation energies, electromagnetic moments, and electromagnetic transitions. However, convergence rates differ significantly for different rotational observables and for different rotational bands. The choice of internucleon interaction may also substantially impact the convergence rates. Consequently, there is a substantial gap between simply observing the qualitative emergence of rotation in ab initio calculations and actually carrying out detailed quantitative comparisons. In this contribution, we illustrate the convergence properties of rotational band energy parameters extracted from NCCI calculations, and compare these predictions with experiment, for the isotopes 7-11Be, and for the JISP16 and Daejeon16 interactions.

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