Lifetimes of the $2_1^{+}, 4_1^{+}, 6_1^{+}, 2_{\gamma }^{+}$, and $3_{\gamma }^{+}$ states in ${}^{104,106}\mathrm{Ru}$ were measured by using the recoil-distance Doppler-shift technique and the Cologne Plunger device. Low-lying excited states in both nuclei were populated in a ${}^{104}\mathrm{Ru}({}^{18}\mathrm{O},{}^{18}\mathrm{O}){}^{104}\mathrm{Ru}$* inelastic scattering and in a ${}^{104}\mathrm{Ru}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{106}\mathrm{Ru}$ two-neutron transfer reaction using the Cologne FN Tandem accelerator. The experimental energy levels and deduced electromagnetic transition probabilities are compared in the context of $\gamma$ softness and the mapped interacting boson model with input from the microscopic self-consistent mean-field calculation using a Gogny interaction. The newly obtained results for the $\gamma$ band give a more detailed insight about the triaxial behavior of ${}^{104,106}\mathrm{Ru}$. The results will be discussed in the context of $\gamma$ soft and rigid triaxial behavior which is present in the neutron-rich Ru isotopes.

In the quasiclassical approximation it is studied excitation of the 8.2 eV isomer ${}^{229m}\mathrm{Th}$ in the electron bridges (EB), initiated by a laser pulse. While the nucleus and atomic electron are treated quantum mechanically, the laser pulse is described by a time-dependent wave packet, formed by classic electromagnetic waves. Two types of the EB are taken into consideration: via the continuous electron spectrum and via discrete atomic levels. In calculations of the excitation probability of ${}^{229m}\mathrm{Th}$ by a laser pulse I employ the generalized formalism of Floquet functions, which allows one to solve the time-dependent Schrödinger equation by the methods of stationary scattering theory. The task is solved for weak lasers as well as for the conventional lasers of arbitrary intensity. In the first case the results well correlate with those obtained previously when treating the laser pulse as a bunch of uncorrelated photons. If conventional lasers generate EB through an atomic level, its population suffers Rabi oscillations. Therefore application of the $\pi$ pulses may strongly enhance the effect of the isomer excitation. For the same EB the excitation probability of the isomer as a function of the laser carrier frequency is shown to have two peaks associated with two resonant levels.

By using the symmetric-asymmetric Gaussian barrier distribution (SAGBD) model, Wong formula, and coupled channel approach, heavy ion fusion dynamics is investigated for ${}^{12}\mathrm{C}+{}^{248}\mathrm{Cm}$ and ${}^{16}\mathrm{O}+{}^{244}\mathrm{Pu}$ reactions at energies lying below and near the Coulomb barrier. Coupling of various channels linked with the structure of participants to the relative motion of the collision partners is done by considering a Gaussian type of weight function in the SAGBD model and cross sections are found to be enhanced relative to the calculations obtained by the simple barrier penetration model. In the SAGBD model, the channel coupling effects are calculated in terms of channel coupling parameter ($\lambda$) and percentage reduction in the height of apparent fusion barrier with respect to the Coulomb barrier ($V_{\mathrm{CBRED}}$). The channel coupling parameter estimates the cumulative influence of dominant intrinsic channels, which are responsible for the sub-barrier fusion enhancement. The SAGBD calculations appropriately explain the dynamics of ${}^{12}\mathrm{C}+{}^{248}\mathrm{Cm}$ and ${}^{16}\mathrm{O}+{}^{244}\mathrm{Pu}$ reactions at energies lying around the Coulomb barrier. The coupled channel analysis of the present reactions is done by using the code ccfull and the coupled channel calculations unambiguously identify the dominant influences of the rotational states up to ${10}^{+}$ spin states of the ground state rotational band of target isotopes in both reactions. In addition, the couplings to higher order deformation, such as ${\beta }_4$ for target and low lying quantum states of the projectile, are necessarily required to reproduce the experimental data of ${}^{12}\mathrm{C}+{}^{248}\mathrm{Cm}$ and ${}^{16}\mathrm{O}+{}^{244}\mathrm{Pu}$ reactions. Apart from the fusion analysis, the dynamical cluster-decay model (DCM) is applied to understand the fission dynamics of the ${}^{260}\mathrm{No}^{*}$ nucleus formed via the above-mentioned reactions. The decay study is carried out at the center-of-mass energies spread, $E_{\mathrm{c}.\mathrm{m}.}$ ($\approx 79$ to 109 MeV) by including the quadrupole deformations (${\beta }_2$) and optimum orientations (${\theta }_i^{\mathrm{opt}}$) of the decaying fragments. According to the experimental observation, the noncompound nucleus (nCN) fission component competes with the compound nucleus (CN) fission processes. Consequently, the possibility of nCN contribution is also explored in the decay of the ${}^{260}\mathrm{No}^{*}$ compound nucleus. With an aim to have a comprehensive analysis of CN and nCN fission mechanisms, the role of the center-of-mass energy ($E_{\mathrm{c}.\mathrm{m}.}$) and angular momentum ($\ell$) is explored in terms of various parameters of DCM such as fragmentation potential, preformation probability, barrier modification, etc.

The HADES Collaboration has extracted dilepton mass spectra for ${\pi }^{-}$ induced reactions on the proton from a comparison of data taken on C and ${\mathrm{CH}}_2$ targets. The spectra were interpreted in terms of different versions of vector-meson dominance. Here we present results obtained from the theory and generator gibuu. We first check the subtraction procedure used and then discuss the obtained mass spectra for the proton target. We point out that any conclusions on the version of VMD requires the knowledge of the $\rho$ spectral function in the interesting mass region.

Background: Low-energy $\beta$ and electron-capture (EC) decays are important systems in neutrino mass determination experiments. An isotope with an ultralow-$Q$-value $\beta$ decay to an excited state in the daughter with $Q_{\mathrm{es}}<1$ keV could provide a promising alternative candidate for future experiments. ${}^{75}\mathrm{Se}$ EC decay and ${}^{75}\mathrm{Ge}\beta$ decay represent such candidates, but a more precise determination of the mass of the common daughter, ${}^{75}\mathrm{As}$, is required to evaluate whether their potential decay branches are energetically allowed and ultralow.

Purpose: Our purpose is to perform a precise atomic mass measurement of ${}^{75}\mathrm{As}$ and combine the result with the precisely known atomic masses of ${}^{75}\mathrm{Se}$ and ${}^{75}\mathrm{Ge}$, along with nuclear energy level data for ${}^{75}\mathrm{As}$ to evaluate potential ultralow-$Q$-value decay branches in the EC decay of ${}^{75}\mathrm{Se}$ and the $\beta$ decay of ${}^{75}\mathrm{Ge}$.

Method: The LEBIT Penning trap mass spectrometer at the Facility for Rare Isotope Beams was used to perform a high-precision measurement of the atomic mass of ${}^{75}\mathrm{As}$ via cyclotron frequency ratio measurements of ${}^{75}\mathrm{As}^{+}$ to a ${}^{12}\mathrm{C}_6$ reference ion.

Results: The ${}^{75}\mathrm{As}$ mass excess was determined to be $\mathrm{ME}\left({}^{75}\mathrm{As}\right)=-73035.98\left(43\right)$ keV, from which the ground-state to ground-state $Q$ values for ${}^{75}\mathrm{Se}$ EC decay and ${}^{75}\mathrm{Ge}\beta$ decay were determined to be 866.50(44) and 1179.01(44) keV, respectively. These results were compared to energies of excited states in ${}^{75}\mathrm{As}$ at 865.4(5) and 1172.0(6) keV to determine $Q$ values of 1.1(7) and 7.0(7) keV for the potential ultralow EC-decay and $\beta$-decay branches of ${}^{75}\mathrm{Se}$ and ${}^{75}\mathrm{Ge}$, respectively.

Conclusion: The candidate ultralow-$Q$-value EC-decay and $\beta$-decay branches of ${}^{75}\mathrm{Se}$ and ${}^{75}\mathrm{Ge}$ to excited states in ${}^{75}\mathrm{As}$, identified by Gamage et al. [N. D. Gamage, R. Bhandari, M. H. Gamage, R. Sandler, and M. Redshaw, Hyperfine Interact. 240, 43 (2019)] are seen to be energetically allowed. The ${}^{75}\mathrm{Se}$ EC decay to the 865.4 -keV excited state in ${}^{75}\mathrm{As}$ is potentially ultralow with $Q_{\mathrm{es}}\approx 1$ keV. However, a more precise determination of the 865.4(5)-keV level in ${}^{75}\mathrm{As}$ is required to draw a more definite conclusion about the energy of this potential decay channel.

Isospin symmetry breaking (ISB) effects in the charge radius difference $\mathrm{\Delta }{R}_{\mathrm{ch}}$ of mirror nuclei are studied using the test example of ${}^{48}\mathrm{Ca}$ and ${}^{48}\mathrm{Ni}$. This choice allows for a transparent study of ISB contributions since pairing and deformation effects, commonly required for the study of mirror nuclei, can be neglected in this specific pair. The connection of $\mathrm{\Delta }{R}_{\mathrm{ch}}$ with the nuclear equation of state and the effect of ISB on such a relation are discussed according to an energy density functional approach. We find that nuclear ISB effects may shift the estimated value for the symmetry energy slope parameter $L$ by about 6 to 14 MeV while Coulomb corrections can be neglected. ISB effects on the ground-state energy and charge radii in mirror nuclei have been recently predicted by ab initio calculations to be relatively small, pointing to a negligible effect for the extraction of information on the nuclear EoS. These contrasting results call for a dedicated theoretical effort to solve this overarching problem that impacts not only the neutron-skin thickness or the difference in mass and charge radii of mirror nuclei but also other observables such as the isobaric analog state energy.

We study the temporal formation of quantum-mechanical bound states within a one-dimensional attractive square-well potential by first solving the time-independent Schrödinger equation and then studying a time-dependent system with an external time-dependent potential. For this we introduce Gaussian potentials with different spatial and temporal extensions and generalize this description also for subsequent pulses and for random noisy potentials. Our main goal is to study the timescales in which the bound state is populated and depopulated. Particularly, we clarify a likely connection between the uncertainty relation for energy and time and the transition time between different energy eigenstates. We demonstrate that the formation of states is not delayed due to the uncertainty relation but follows the pulse shape of the perturbation. In addition we investigate the (non-)applicability of first-order perturbation theory on the considered quantum system.

In the present work, measurement and analysis of forward recoil range distribution of various reaction residues populated in the interaction of ${}^{19}\mathrm{F}$ projectile with ${}^{159}\mathrm{Tb}$ target nucleus have been performed. The aim is to disentangle the contribution of complete fusion (CF) and incomplete fusion (ICF) components at two different above-barrier energies $\approx 83$ and 94 MeV. The recoil-catcher technique with off-line $\gamma$-ray spectroscopy has been performed. The complete and incomplete fusion events have been identified by full and partial linear momentum transfer, respectively. A single Gaussian distribution has been observed in case of residues populated via complete fusion processes. However, the recoil range distribution for $\alpha$-emitting channels was found to be deconvoluted into more than one Gaussian peak indicating the involvement of both full and partial linear momentum transfer components due to the presence of CF and ICF processes. The analysis of data suggests that projectile breaks up as soon as it comes near the vicinity of target nuclear field leading to different linear momentum transfer components. Further, the analysis done within the framework of universal fusion function indicates a significant break-up fusion probability of ${}^{19}\mathrm{F}$ projectile. As such, at lower energies ${}^{19}\mathrm{F}$ is found to behave similar to other $\alpha$-cluster beams.

We argue that the STAR data on $J/\psi$ photoproduction in $d+\mathrm{Au}$ ultraperipheral collisions (UPCs) at the momentum transfer $t\ne 0$ primarily probes elastic and possibly nucleon-dissociative $J/\psi$ photoproduction on quasifree nucleons, while being essentially insensitive to expectedly weak nuclear modifications of the gluon distribution in the deuteron. Analyzing the STAR detector capabilities for selection of UPC events, we explore the possibility that the contribution of nucleon-dissociative $J/\psi$ photoproduction is negligibly small and obtain a very good description of the $t$ dependence of the STAR total cross section.

The CNO cycle is the main energy source in massive stars during their hydrogen burning phase, and, for our sun, it contributes at the $\approx 1\%$ level. As the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction is the slowest in the cycle, it determines the CNO energy production rate and thus the CNO contribution to the solar neutrino flux. These CNO neutrinos are produced primarily from the $\beta$ decay of ${}^{15}\mathrm{O}$ and, to a lesser extent, from the decay of ${}^{13}\mathrm{N}$. Solar CNO neutrinos are challenging to detect, but they can provide independent new information on the metallicity of the solar core. Recently, CNO neutrinos from ${}^{15}\mathrm{O}$ have been identified for the first time with the Borexino neutrino detector at the INFN Gran Sasso underground laboratory. There are, however, still some considerable uncertainties in the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction rate under solar temperature conditions. The low energy reaction data presented here, measured at the CASPAR underground accelerator, aim at connecting existing measurements at higher energies and attempts to shed light on the discrepancies between the various data sets, while moving towards a better understanding of the ${}^{14}\mathrm{N}(p,\gamma ){}^{15}\mathrm{O}$ reaction cross section. The present measurements span proton energies between 0.27 and 1.07 MeV, closing a critical gap in the existing data. A multichannel $R$-matrix analysis was performed with the entire new and existing data sets and is used to extrapolate the astrophysical $S$ factors of the ground state and the 6.79 MeV transition to low energies. The extrapolations are found to be in agreement with previous work, but find that the discrepancies between measured data and $R$-matrix fits, both past and present, still exist. We examine the possible reasons for these discrepancies and thereby provide recommendations for future studies.

The ${\pi }^{-}+{}^2\mathrm{H}\to n+n, {\pi }^{-}+{}^3\mathrm{H}\to n+n+n, {\pi }^{-}+{}^3\mathrm{He}\to n+d$, and ${\pi }^{-}+{}^3\mathrm{He}\to p+n+n$ capture reactions from the lowest $1S$ atomic orbitals are studied under full inclusion of final state interactions. Our results are obtained with the single-nucleon and two-nucleon transition operators derived at leading order in chiral effective field theory. The initial and final three-nucleon states are calculated with the chiral nucleon-nucleon semilocal momentum space potential up to ${\mathrm{N}}^4{\mathrm{LO}}^{+}$, augmented by the consistently regularized chiral ${\mathrm{N}}^2\mathrm{LO}$ three-nucleon potential. We found that absorption rates depend strongly on the nuclear pion absorption operator used, and its two-body parts change the rates by a few orders of magnitude. The final state interactions between nucleons generated by the two-nucleon forces are also important, while the three-nucleon interaction plays a visible role only in the ${\pi }^{-}+{}^3\mathrm{He}\to n+d$ reaction. Our absorption rate for the ${\pi }^{-}+{}^2\mathrm{H}\to n+n$ process is in good agreement with the experimental data from the hadronic ground-state broadening in pionic deuterium. The capture rates on ${}^3\mathrm{He}$ are also generally consistent with the spectroscopic data within error bars, though our central values are found to be systematically below the data. We show that for the three-body breakup processes the dominant contributions to the absorption rates arise from the quasi-free scattering and final-state interaction kinematical configurations.

In the nuclear shell model the $j-1$ anomaly is associated with unusual ordering of the $j$ and $j-1$ states of a $j^{-3}$ split multiplet. In the mass regions placed away from the doubly magic nuclei, the $j-1$ levels are found to be below the respective $j$ states. The anomalous ordering of the levels is most prominent in the silver isotopic chain, but a similar effect is observed also in other systems with pure three-hole configurations. The correlation between the $\mathrm{\Delta }E=E_{j-1}-E_j$ energy splitting, observed in some odd-mass nuclei, and the even-even core's $2^{+}$ level energy is well pronounced in the (28,50) neutron and proton shells and to a lesser extent in the lower and higher (20,28) and (50, 82) shells.

Theoretical ab initio studies of resonances in the unbound ${}^7\mathrm{He}$ 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 $n+{}^6\mathrm{He}$ and $n+{}^6\mathrm{He}^{*}$ with ${}^6\mathrm{He}$ respectively in the ground and excited $2^{+}$ states as well as for the four-body democratic decay channel ${}^4\mathrm{He}+n+n+n$. The resonant energies and widths are obtained by numerical location of the $S$-matrix poles. We describe all experimentally known ${}^7\mathrm{He}$ resonances and suggest an interpretation of an observed wide resonance of unknown spin-parity.

The low-lying level structure of ${}^{59}\mathrm{V}$ and ${}^{61}\mathrm{V}$ was investigated for the first time. The neutron knockout reaction and inelastic proton scattering were applied for ${}^{61}\mathrm{V}$ while the neutron knock-out reaction provided the data for ${}^{59}\mathrm{V}$. Four and five new transitions were determined for ${}^{59}\mathrm{V}$ and ${}^{61}\mathrm{V}$, respectively. Based on the comparison to our shell-model calculations using the Lenzi-Nowacki-Poves-Sieja (LNPS) interaction, three of the observed $\gamma$ rays for each isotope could be placed in the level scheme and assigned to the decay of the first $11/2^{-}$ and $9/2^{-}$ levels. The $(p,p^{\prime })$ excitation cross sections for ${}^{61}\mathrm{V}$ were analyzed by the coupled-channels formalism assuming quadrupole plus hexadecapole deformations. Due to the role of the hexadecapole deformation, ${}^{61}\mathrm{V}$ could not be unambiguously placed on the island of inversion.

Background: Heavy-ion fusion cross-sections at sub barrier energies are found to be enhanced by orders of magnitude as compared to the predictions of one-dimensional barrier penetration model (1-D BPM). The coupling of various internal degrees of freedom has been employed to decrypt the mechanism responsible for the observed sub-barrier fusion enhancement. However, the unambiguous role of multi-neutron transfer channels in the sub-barrier domain is still elusive.

Purpose: We aim to explore and disentangle the effects of multi-neutron transfer channels from the inelastic excitations in the vicinity of the Coulomb barrier.

Method: The fusion excitation functions for ${}^{28}\mathrm{Si} + {}^{116,120,124}\mathrm{Sn}$ systems were measured from $\approx 14\%$ below to $\approx 15\%$ above the Coulomb barrier by detecting the evaporation residues (ERs) at the focal plane of the Recoil Mass Separator (RMS), Heavy Ion Reaction Analyzer (HIRA) at the Inter-University Accelerator Centre (IUAC), New Delhi.

Results: The extracted fusion cross sections for the investigated systems at sub-barrier energies are significantly enhanced as compared to the predictions of 1-D BPM calculations. To probe the underlying mechanism responsible for the observed sub-barrier fusion enhancement, the coupled-channels (CC) formalism was employed. Coupled reaction channels (CRC) calculations by incorporating the one-neutron transfer channel to elucidate the significance of the transfer channel on the fusion dynamics were performed. Further, the semiempirical coupled channels (ECC) approach was explored to decipher the possible cause of the observed fusion excitation function trend. A systematic analysis of the neighboring systems available in the literature was also performed.

Conclusions: CC calculations were able to reproduce the measured fusion excitation functions for ${}^{28}\mathrm{Si} + {}^{116,120}\mathrm{Sn}$ systems to a reasonable extent. However, observed sub-barrier fusion enhancement in ${}^{28}\mathrm{Si}+{}^{124}\mathrm{Sn}$ system could not be explained using CC calculations. The influence of multi-neutron transfer channels was highlighted in the coupled-channels calculations. The interplay of collective excitations and neutron transfer was observed.

Observations of neutron stars may be used to study aspects of extremely dense matter, specifically a possibility of phase transitions to exotic states, such as deconfined quarks. We present a novel data analysis method for detecting signatures of dense-matter phase transitions in sets of mass-radius measurements, and study its sensitivity with respect to the size of observational errors and the number of observations. The method is based on machine learning anomaly detection coupled with normalizing flows technique: the algorithm trained on samples of astrophysical observations featuring no phase transition signatures interprets a phase transition sample as an anomaly. For the sake of this study, we focus on dense-matter equations of state leading to detached branches of mass-radius sequences (strong phase transitions), use an astrophysically informed neutron-star mass function, and various magnitudes of observational errors and sample sizes. The method is shown to reliably detect cases of mass-radius relations with phase transition signatures, while increasing its sensitivity with decreasing measurement errors and increasing number of observations. We discuss marginal cases, when the phase transition mass is located near the edges of the mass function range. Evaluated on the current state-of-art selection of real measurements of electromagnetic and gravitational-wave observations, the method gives inconclusive results, which we interpret as due to small available sample size, large observational errors, and complex systematics.

We report on a phenomenological analysis of all available electron scattering data on ${}^{12}\mathrm{C}$ (about 6600 differential cross section measurements) and on ${}^{16}\mathrm{O}$ (about 250 measurements) within the framework of the quasielastic (QE) superscaling model (including Pauli blocking). All QE and inelastic cross section measurements are included down to the lowest momentum transfer $\mathbf{q}$ (including photoproduction data). We find that there is enhancement of the transverse QE response function ($R_T^{QE}$) and quenching of the QE longitudinal response function ($R_L^{QE}$) at low $\mathbf{q}$ (in addition to Pauli blocking). We extract parametrizations of a multiplicative low $\mathbf{q}$ “longitudinal quenching factor” and an additive “transverse enhancement” contribution. Additionally, we find that the excitation of nuclear states contribute significantly (up to 30%) to the Coulomb sum rule $SL\left(\mathbf{q}\right)$. We extract the most accurate determination of $SL\left(\mathbf{q}\right)$ to date and find it to be in disagreement with random phase approximation (RPA) based calculations but in reasonable agreement with recent theoretical calculations, such as “first principle Green's function Monte Carlo.”

We propose to obtain information on the spin-isospin dependence of the $\mathrm{\Xi }N$ interaction through the energy levels of $\mathrm{\Xi }N\alpha$ and $\mathrm{\Xi }N\alpha \alpha$ systems, with $\alpha$ being a spectator to attract the $\mathrm{\Xi }N$ pair without changing its spin-isospin structure. By using the Gaussian expansion method with the state-of-the-art $\mathrm{\Xi }N$ potential obtained from lattice QCD calculations, it is found that $\mathrm{\Xi }N\alpha \alpha$ has spin-doublet bound states with $J^{\pi }=1^{-}$ and $2^{-}$ in both isospin triplet and singlet channels. The inversion of the $1^{-}-2^{-}$ spin-doublet between the iso-triplet and the iso-singlet is found to be strongly correlated with the relative strengths of the $\mathrm{\Xi }N$ interaction in the ${}^{11}\mathrm{S}_0, {}^{13}\mathrm{S}_1, {}^{31}\mathrm{S}_0$, and ${}^{33}\mathrm{S}_1$ channels. The $(K^{-},K^{+})$ and $(K^{-},K^0)$ reactions on the ${}^{10}\mathrm{B}$ target are proposed to produce those bound states.

Background: Effective interactions for nucleon-nucleus elastic scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations and a consistent treatment of the relevant operators at each order.

Purpose: Systematic investigations of the effect of truncation uncertainties of chiral nucleon-nucleon ($NN$) forces have been carried out for scattering observables in the two- and three-nucleons system as well as for bound-state properties of light nuclei. Here we extend this type of study to proton and neutron elastic scattering for ${}^{16}\mathrm{O}$ and ${}^{12}\mathrm{C}$.

Methods: Using the frameworks of the spectator expansion of multiple scattering theory as well as the no-core shell model, we employ one specific chiral interaction from the LENPIC collaboration and consistently calculate the leading-order effective nucleon-nucleus interaction up to the third chiral order, from which we extract elastic scattering observables. Then we apply pointwise as well as correlated uncertainty quantification for the estimation of the chiral truncation error.

Results: We calculate and analyze proton elastic scattering observables for ${}^{16}\mathrm{O}$ and ${}^{12}\mathrm{C}$ as well as neutron elastic scattering observables for ${}^{12}\mathrm{C}$ between 65 and 185 MeV projectile kinetic energy. We find in all cases qualitatively similar results for the chiral truncation uncertainties as in few-body systems and assess them using similar diagnostic tools. The order-by-order convergence of the scattering observables for ${}^{16}\mathrm{O}$ and ${}^{12}\mathrm{C}$ is very reasonable around 100 MeV, while for higher energies the chiral expansion parameter becomes too large for convergence. Comparing proton and neutron differential cross sections reveals that their description is comparable up to around 100 MeV. We also find a nearly perfect correlation between the differential cross section for neutron scattering and the $NN$ Wolfenstein amplitudes for small momentum transfers.

Conclusions: The diagnostic tools for studying order-by-order convergence in observables in few-body systems can be employed for observables in nucleon-nucleus scattering with only minor modifications provided the momentum scale in the problems is not too large. We also find that the chiral $NN$ interaction on which our study is based gives a very good description of differential cross sections for ${}^{16}\mathrm{O}$ and ${}^{12}\mathrm{C}$ as low as 65-MeV projectile energy, particularly in the forward direction. In addition, the very forward direction of the neutron differential cross section mirrors the behavior of the $NN$ interaction amazingly well.