Chiral Nucleon-nucleon Interaction Research Articles

Ab initio calculations for well deformed nuclei: 40Mg and 42Si

We performed ab initio valence-space in-medium similarity renormalization group calculations based on chiral nucleon-nucleon and three-nucleon interactions to study the neutron-rich nuclei around N=28, where the experimental and theoretical evidence point to a rapid transition from spherical to rotational regimes. First, the rotational spectra of 40Mg, 42Si, and 44S are established theoretically, anchored by the calculated E2 transition strength. The results suggest that 40Mg and 42Si exhibit large deformations. After that, the erosion of the N=28 shell closure, especially the evolutions of shape deformation and the emergence of shape coexistence, are discussed in N=28 even-even isotones ranging from 40Mg to 48Ca. Finally, the shell evolution of N=28 in Mg and Si chains is discussed based on the experimental and predicted excitation energies of low-lying states. The results from our ab initio calculations align well with available experimental data, furnishing essential insights into the structure of neutron-rich nuclei, particularly deformations in the vicinity of 40Mg and 42Si.

Wave-function-based emulation for nucleon-nucleon scattering in momentum space

Emulators for low-energy nuclear physics can provide fast & accurate predictions of bound-state and scattering observables for applications that require repeated calculations with different parameters, such as Bayesian uncertainty quantification. In this paper, we extend a scattering emulator based on the Kohn variational principle (KVP) to momentum space (including coupled channels) with arbitrary boundary conditions, which enable the mitigation of spurious singularities known as Kohn anomalies. We test it on a modern chiral nucleon-nucleon (NN) interaction, including emulation of the coupled channels. We provide comparisons between a Lippmann-Schwinger equation emulator and our KVP momentum-space emulator for a representative set of neutron-proton (np) scattering observables, and also introduce a quasi-spline-based approach for the KVP-based emulator. Our findings show that while there are some trade-offs between accuracy and speed, all three emulators perform well. Self-contained Jupyter notebooks that generate the results and figures in this paper are publicly available.

Machine learning light hypernuclei

We employ a feed-forward artificial neural network to extrapolate at large model spaces the results of ab-initio hypernuclear No-Core Shell Model calculations for the Λ separation energy BΛ of the lightest hypernuclei, Λ3H, Λ4H and Λ4He, obtained in computationally accessible harmonic oscillator basis spaces using chiral nucleon-nucleon, nucleon-nucleon-nucleon and hyperon-nucleon interactions. The overfitting problem is avoided by enlarging the size of the input dataset and by introducing a Gaussian noise during the training process of the neural network. We find that a network with a single hidden layer of eight neurons is sufficient to extrapolate correctly the value of the Λ separation energy to model spaces of size Nmax=100. The results obtained are in agreement with the experimental data in the case of Λ3H and the 0+ state of Λ4He, although they are off of the experiment by about 0.3 MeV for both the 0+ and 1+states of Λ4H and the 1+ state of Λ4He. We find that our results are in excellent agreement with those obtained using other extrapolation schemes of the No-Core Shell Model calculations, showing this that an ANN is a reliable method to extrapolate the results of hypernuclear No-Core Shell Model calculations to large model spaces.

Chiral uncertainties in ab initio elastic nucleon-nucleus 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 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 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 4He, 12C, and 16O for between 65 and 200 MeV projectile energy will be analyzed.

Neutron-deuteron scattering cross sections with chiral NN interactions using wave-packet continuum discretization

In this work we present a framework that allows to solve the Faddeev equations for three-nucleon scattering using the wave-packet continuum-discretization method. We perform systematic benchmarks using results in the literature and study in detail the convergence of this method with respect to the number of wave packets. We compute several different elastic neutron-deuteron scattering cross-section observables for a variety of energies using chiral nucleon-nucleon interactions. For the interaction $\text{N2LO}_{\text{opt}}$ we find good agreement with data for nucleon scattering-energies $E_\text{Lab} \leq 70$ MeV and a slightly larger maximum of the neutron analyzing power $A_y(n)$ at $E_\text{Lab} = 10$ MeV and 21 MeV compared with other interactions. This work represents a first step towards a systematic inclusion of three-nucleon scattering observables in the construction of next-generation nuclear interactions.

Accurate Relativistic Chiral Nucleon-Nucleon Interaction up to Next-to-Next-to-Leading Order.

We construct a relativistic chiral nucleon-nucleon interaction up to the next-to-next-to-leading order in covariant baryon chiral perturbation theory. We show that a good description of the np phase shifts up to T_{lab}=200 MeV and even higher can be achieved with a χ[over ˜]^{2}/d.o.f. less than 1. Both the next-to-leading-order results and the next-to-next-to-leading-order results describe the phase shifts equally well up to T_{lab}=200 MeV, but for higher energies, the latter behaves better, showing satisfactory convergence. The relativistic chiral potential provides the most essential inputs for relativistic abinitio studies of nuclear structure and reactions, which has been in need for almost two decades.

AbInitio Computation of the Longitudinal Response Function in ^{40}Ca.

We present a consistent abinitio 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 quasielastic 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 abinitio computations of neutrino-nucleus cross sections relevant for experimental long-baseline neutrino programs.

Low-Density Neutron Matter and the Unitary Limit

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the1S0neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.

Renormalizability of leading order covariant chiral nucleon-nucleon interaction * *Supported by the National Natural Science Foundation of China (11735003, 11975041, 11775148, 11961141004)

In this work, we study the renormalization group invariance of the recently proposed covariant power counting in the case of nucleon-nucleon scattering [Chin. Phys. C 42 (2018) 014103] at leading order. We show that unlike the Weinberg scheme, renormalizaion group invariance is satisfied in the channel. Another interesting feature is that the and channels are correlated. Fixing the relevant low energy constants by fitting to the phase shifts at and 25 MeV with cutoff values MeV, one can describe the phase shifts relatively well. In the limit of , the phase shifts become cutoff-independent, whereas the phase shifts do not. This is consistent with the Wigner bound and previous observations that the channel is best treated perturbatively. As for the and - channels, renormalization group invariance is satisfied.

Microscopic investigation of the Li8(n,γ)Li9 reaction

The $^8$Li($n,\gamma$)$^9$Li reaction plays an important role in several astrophysics scenarios. It cannot be measured directly and indirect experiments have so far provided only cross section limits. Theoretical predictions differ by an order of magnitude. In this work we study the properties of $^9$Li bound states and low-lying resonances and calculate the $^8$Li($n,\gamma$)$^9$Li cross section within the no-core shell model with continuum (NCSMC) with chiral nucleon-nucleon and three-nucleon interactions as the only input. The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states well suited to calculate low-energy nuclear scattering and reactions. Our calculations reproduce the experimentally known bound states as well as the lowest $5/2^-$ resonance of $^9$Li. We predict a $3/2^-$ spin-parity assignment for the resonance observed at 5.38 MeV. In addition to the a very narrow $7/2^-$ resonance corresponding presumably to the experimental 6.43 MeV state, we find several other broad low-lying resonances. Our calculated $^8$Li($n,\gamma$)$^9$Li cross section is within the limits derived from the 1998 National Superconducting Cyclotron Laboratory Coulomb-dissociation experiment [Phys. Rev. C {\bf 57}, 959 (1998)]. However, it is higher than cross sections obtained in recent phenomenological studies. It is dominated by a direct E1 capture to the ground state with a resonant contribution at $\sim0.2$ MeV due to E2/M1 radiation enhanced by the $5/2^-$ resonance.

Merging ab initio theory and few-body approach for (d, p) reactions

A framework for A(d, p)B reactions is introduced by merging the microscopic approach to computing the properties of the nucleon-target systems and the three-body n + p + A reaction formalism, thus providing a consistent link between the reaction cross sections and the underlying microscopic structure. In this first step toward a full microscopic description, we focus on the inclusion of the neutron-target microscopic properties. The properties of the neutron-target subsystem are encapsulated in the Green’s function which is computed with the coupled Cluster theory using a chiral nucleon-nucleon and three-nucleon interactions. Subsequently, this many-body information is introduced in the few-body Green’s Function Transfer approach to (d, p) reactions. Our benchmarks on stable targets 40,48Ca show an excellent agreement with the data. We then proceed to make specific predictions for (d, p) on neutron rich 52,54Ca isotopes. These predictions are directly relevant to testing the new magic numbers N = 32, 34 and are expected to be feasible in the first campaign of the projected FRIB facility.

Investigations of the few-nucleon systems within the LENPIC project

Results presented in this contribution are obtained within the Low Energy Nuclear Physics International Collaboration (LENPIC). LENPIC aims to develop chiral nucleon-nucleon and many-nucleon interactions complete through at least the fourth order in the chiral expansion. These interactions will be used together with consistently derived current operators to solve the structure and reactions of light and medium-mass nuclei including electroweak processes. In this contribution the current status of the chiral nuclear forces and current operators will be briefly discussed. A special role played by the calculations of nucleon-deuteron scattering will be explained.

Probing chiral interactions up to next-to-next-to-next-to-leading order in medium-mass nuclei

We study ground-state energies and charge radii of closed-shell medium-mass nuclei based on novel chiral nucleon-nucleon (NN) and three-nucleon (3N) interactions, with a focus on exploring the connections between finite nuclei and nuclear matter. To this end, we perform in-medium similarity renormalization group (IM-SRG) calculations based on chiral interactions at next-to-leading order (NLO), N$^2$LO, and N$^3$LO, where the 3N interactions at N$^2$LO and N$^3$LO are fit to the empirical saturation point of nuclear matter and to the triton binding energy. Our results for energies and radii at N$^2$LO and N$^3$LO overlap within uncertainties, and the cutoff variation of the interactions is within the EFT uncertainty band. We find underbound ground-state energies, as expected from the comparison to the empirical saturation point. The radii are systematically too large, but the agreement with experiment is better. We further explore variations of the 3N couplings to test their sensitivity in nuclei. While nuclear matter at saturation density is quite sensitive to the 3N couplings, we find a considerably weaker dependence in medium-mass nuclei. In addition, we explore a consistent momentum-space SRG evolution of these NN and 3N interactions, exhibiting improved many-body convergence. For the SRG-evolved interactions, the sensitivity to the 3N couplings is found to be stronger in medium-mass nuclei.

Be7 and Li7 nuclei within the no-core shell model with continuum

The production of $^7$Be and $^7$Li nuclei plays an important role in primordial nucleosynthesis, nuclear astrophysics, and fusion energy generation. The $^3\mathrm{He}(\alpha , \gamma) ^7\mathrm{Be}$ and $^3\mathrm{H}(\alpha , \gamma) ^7\mathrm{Li}$ radiative-capture processes are important to determine the $^7$Li abundance in the early universe and to predict the correct fraction of pp-chain branches resulting in $^7$Be versus $^8$B neutrinos. In this work we study the properties of $^7$Be and $^7$Li within the no-core shell model with continuum (NCSMC) method, using chiral nucleon-nucleon interactions as the only input, and analyze all the binary mass partitions involved in the formation of these systems. The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states and thus is well suited to investigate systems with many resonances and pronounced clustering like $^7$Be and $^7$Li. Our calculations reproduce all the experimentally known states of the two systems and provide predictions for several new resonances of both parities. Some of these new possible resonances are built on the ground states of $^6$Li and $^6$He, and thus represent a robust prediction. We do not find any resonance in the p${+}^6$Li mass partition near the threshold. On the other hand, in the p${+}^6$He mass partition of $^7$Li we observe an $S$-wave resonance near the threshold producing a very pronounced peak in the calculated S factor of the $^6\mathrm{He} (\mathrm{p},\gamma) ^7\mathrm{Li}$ radiative-capture reaction, which could be relevant for astrophysics and its implications should be investigated.

Microscopic optical potentials for calcium isotopes

We construct nucleonic microscopic optical potentials by combining the Green's function approach with the coupled-cluster method for $\rm{^{40}Ca}$ and $\rm{^{48}Ca}$. For the computation of the ground-state of $\rm{^{40}Ca}$ and $\rm{^{48}Ca}$, we use the coupled-cluster method in the singles-and-doubles approximation, while for the A = $\pm 1$ nuclei we use particle-attached/removed equation-of-motion method truncated at two-particle-one-hole and one-particle-two-hole excitations, respectively. Our calculations are based on the chiral nucleon-nucleon and three-nucleon interaction $\rm{NNLO_{sat}}$, which reproduces the charge radii of $^{40}$Ca and $^{48}$Ca, and the chiral nucleon-nucleon interaction $\rm{NNLO_{opt}}$. In all cases considered here, we observe that the overall form of the neutron scattering cross section is reproduced for both interactions, but the imaginary part of the potential, which reflects the loss of flux in the elastic channel, is negligible. The latter points to neglected many-body correlations that would appear beyond the coupled-cluster truncation level considered in this work. We show that, by artificially increasing the parameter $\eta$ in the Green's function, practical results can be further improved.

Microscopic optical potentials derived from ab initio translationally invariant nonlocal one-body densities

We derive a microscopic optical potential for intermediate energies using ab initio translationally invariant nonlocal one-body nuclear densities computed within the no-core shell model (NCSM) approach utilizing two- and three-nucleon chiral interactions as the only input. The optical potential is derived at first-order within the spectator expansion of the non-relativistic multiple scattering theory by adopting the impulse approximation and using the same chiral nucleon-nucleon interaction as that used to compute densities. The ground state local and nonlocal densities of 4,6,8He, 12C, and 16O are calculated and applied to optical potential construction. The differential cross sections and the analyzing powers for the elastic proton scattering off of these nuclei are then calculated for different values of the incident proton energy. The impact of nonlocality and the COM removal is discussed. The use of nonlocal densities has a substantial impact on the differential cross sections and improves agreement with experiment in comparison to results generated with the local densities especially for light nuclei.

Leading order relativistic chiral nucleon-nucleon interaction**Supported by National Natural Science Foundation of China (11375024, 11522539, 11335002, 11375120), DFG and NSFC through funds provided to the Sino-German CRC 110 “Symmetries and the Emergence of Structure in QCD” (NSFC Grant No. 11621131001, DFG Grant No. TRR110), the Major State 973 Program of China (2013CB834400), the China Postdoctoral Science Foundation (2016M600845, 2017T100008), the

Motivated by the successes of relativistic theories in studies of atomic/molecular and nuclear systems and the need for a relativistic chiral force in relativistic nuclear structure studies, we explore a new relativistic scheme to construct the nucleon-nucleon interaction in the framework of covariant chiral effective field theory. The chiral interaction is formulated up to leading order with covariant power counting and a Lorentz invariant chiral Lagrangian. We find that the relativistic scheme induces all six spin operators needed to describe the nuclear force. A detailed investigation of the partial wave potentials shows a better description of the and phase shifts than the leading order Weinberg approach, and similar to that of the next-to-leading order Weinberg approach. For the other partial waves with angular momenta , the relativistic results are almost the same as their leading order non-relativistic counterparts.

Quantum Monte Carlo calculations of light nuclei with local chiral two- and three-nucleon interactions

Local chiral effective field theory interactions have recently been developed and used in the context of quantum Monte Carlo few- and many-body methods for nuclear physics. In this work, we go over detailed features of local chiral nucleon-nucleon interactions and examine their effect on properties of the deuteron, paying special attention to the perturbativeness of the expansion. We then turn to three-nucleon interactions, focusing on operator ambiguities and their interplay with regulator effects. We then discuss the nuclear Green's function Monte Carlo method, going over both wave-function correlations and approximations for the two- and three-body propagators. Following this, we present a range of results on light nuclei: Binding energies and distribution functions are contrasted and compared, starting from several different microscopic interactions.

Structure of ^{78}Ni from First-Principles Computations.

Doubly magic nuclei have a simple structure and are the cornerstones for entire regions of the nuclear chart. Theoretical insights into the supposedly doubly magic ^{78}Ni and its neighbors are challenging because of the extreme neutron-to-proton ratio and the proximity of the continuum. We predict the J^{π}=2_{1}^{+} state in ^{78}Ni from a correlation with the J^{π}=2_{1}^{+} state in ^{48}Ca using chiral nucleon-nucleon and three-nucleon interactions. Our results confirm that ^{78}Ni is doubly magic, and the predicted low-lying states of ^{79,80}Ni open the way for shell-model studies of many more rare isotopes.

Testing semilocal chiral two-nucleon interaction in selected electroweak processes

The recently developed semilocal improved chiral nucleon-nucleon interaction is used for the first time to study several electromagnetic and weak processes at energies below the pion production threshold. Cross sections and selected polarization observables for deuteron photodisintegration, nucleon-deuteron radiative capture, three-body $^{3}\mathrm{He}$ photodisintegration, as well as capture rates for decays of the muonic $^{2}\mathrm{H}$ and $^{3}\mathrm{He}$ atoms are calculated. The Lippmann-Schwinger and Faddeev equations in momentum space are solved to obtain nuclear states. The electromagnetic current operator is taken as a single nucleon current supplemented by many-body contributions induced via the Siegert theorem. For muon capture processes the nonrelativistic weak current together with the dominant relativistic corrections is used. Our results compare well with experimental data, demonstrating the same quality as is observed for the semiphenomenological Argonne V18 potential. Compared to the older version of the chiral potential with a nonlocal regularization, a much smaller cut-off dependence is found for the state-of-art chiral local interaction employed in this paper. Finally, estimates of errors due to the truncation of the chiral expansion are given.