A correlation function of two particles with small relative velocities obeys a sum rule—the momentum integral of the function is determined due to the completeness of quantum states of the particles. The original sum rule derived in 1995 suffered from a serious problem: the momentum integral was ultraviolet divergent in physically interesting cases. We resolve the problem by considering the sum rule not of a single correlation function but of a sum or difference of two appropriately chosen correlation functions. The improved sum rule is shown to work well for the exact Coulomb correlation functions. We argue that the sum rule can be used to test an accuracy and range of applicability of correlation functions computed in approximate models. The neutron-proton correlation function is discussed as an example.

A new precision half-life measurement of ${}^{29}\mathrm{P}$ was conducted using the TwinSol $\beta$-counting station at the University of Notre Dame Nuclear Science Laboratory. The resulting value of $t_{1/2}^{\mathrm{new}}=4.1055\left(44\right)\mathrm{s}$ is the most precise ${}^{29}\mathrm{P}$ half-life measurement to date. Utilizing this measurement and reevaluating the world data leads to a new world average of $t_{1/2}^{\mathrm{world}}=4.1031\left(58\right)\mathrm{s}$, which improves the Birge ratio from 3.11 to 1.45 and is 2.3 times more precise than the previous world value. The new Cabibbo-Kobayashi-Maskawa matrix element $V_{\mathrm{ud}}$ for ${}^{29}\mathrm{P}$ shifts closer into agreement with the superallowed pure Fermi value. The uncertainty in the mixed transition value of $V_{\mathrm{ud}}$, however, is still dominated by the Fermi to Gamow-Teller mixing ratio $\rho$. Using the new world half-life and assuming the validity of the standard model, a new predicted value for $\rho$ and its associated correlation parameters have been evaluated in order to guide future determination of $\rho$.

The equation of state (EoS) of neutron star matter, constrained by the existence of two-solar-mass stars and gravitational wave signals from neutron star mergers, is analyzed using the Landau theory of relativistic Fermi liquids. While the phase diagram of dense and cold QCD matter is still open for scenarios ranging from hadronic to quark matter in the center of neutron stars, a Fermi-liquid treatment is motivated by a microscopic approach starting from a chiral nucleon-meson field theory combined with nonperturbative functional renormalization group methods. In this scheme effects of multipionic fluctuations and repulsive nuclear many-body correlations suggest that the transition to chiral symmetry restoration is shifted to densities above those typically encountered in the neutron star core. Under such conditions a Fermi-liquid description in terms of nucleon quasiparticles appears to be justified. The leading Landau parameters are derived and discussed. Our results are contrasted with a well-known Fermi liquid, namely liquid ${}^3\mathrm{He}$.

Coherent elastic neutrino scattering on the ${}^{40}\mathrm{Ar}$ nucleus is computed with coupled-cluster theory based on nuclear Hamiltonians inspired by effective field theories of quantum chromodynamics. Our approach is validated by calculating the charge form factor and comparing it to data from electron scattering. We make predictions for the weak form factor, the neutron radius, and the neutron skin and estimate systematic uncertainties. The neutron-skin thickness of ${}^{40}\mathrm{Ar}$ is consistent with results from density-functional theory. Precision measurements from coherent elastic neutrino-nucleus scattering could potentially be used to extract these observables and help to constrain nuclear models.

Neutron and proton spectral functions of ${}^{40}\mathrm{Ar}, {}^{40}\mathrm{Ca}$, and ${}^{48}\mathrm{Ti}$ isotopes are computed using the ab initio self-consistent Green's function approach. The resulting radii and charge distributions are in good agreement with available experimental data. The spectral functions of Ar and Ti are then utilized to calculate inclusive ($e,e^{\prime }$) cross sections within a factorization scheme and are found to correctly reproduce the recent Jefferson Lab measurements. Based on these successful agreements, the weak charged and neutral current double-differential cross sections for neutrino-${}^{40}\mathrm{Ar}$ scattering are predicted in the quasielastic region. Results obtained by replacing the (experimentally inaccessible) neutron spectral distribution of ${}^{40}\mathrm{Ar}$ with the (experimentally accessible) proton distribution of ${}^{48}\mathrm{Ti}$ are compared and the accuracy of this approximation is assessed.

I have analyzed experimental $2n$ transfer data for ground and first-excited $0^{+}$ states in even ${}^{92–100}\mathrm{Mo}$ nuclei, using a generalized coexistence model. Output of the analysis is the mixing intensity for each nucleus in terms of a dimensionless parameter R, which is limited to a narrow range. Throughout the allowed range, the mixing is found to be monotonic in A, and is largest in ${}^{100}\mathrm{Mo}$.

Background: Uncertainty quantification for nuclear theories has gained a more prominent role in the field, with more groups attempting to understand the uncertainties in their calculations. However, recent studies have shown that the uncertainties on the optical potentials are too large for the theory to be useful.

Purpose: The purpose of this work is to explore possible experimental conditions that may reduce the uncertainties on elastic scattering and single-nucleon transfer cross sections that come from the fitting of the optical model parameters to experimental data.

Method: Using Bayesian methods, we explore the effect of the uncertainties of optical model parameters on the angular grid of the differential cross section, including cross-section data at nearby energies, and changes in the experimental error bars. We also study the effect on the resulting uncertainty when other observables are included in the fitting procedure, particularly the total (reaction) cross sections.

Results: We study proton and neutron elastic scattering on ${}^{48}\mathrm{Ca}$ and ${}^{208}\mathrm{Pb}$. We explore the parameter space with the Markov-chain Monte Carlo method, produce posterior distributions for the optical model parameters, and construct the corresponding 95% confidence intervals on the elastic-scattering cross sections. We also propagate the uncertainties on the optical potentials to the ${}^{48}\mathrm{Ca}(d,p){}^{49}\mathrm{Ca}$(g.s.) and ${}^{208}\mathrm{Pb}(d,p){}^{209}\mathrm{Pb}$(g.s.) cross sections.

Conclusions: We find little sensitivity to the angular grid and an improvement of up to a factor of 2 on the uncertainties by including data at a nearby energy. Although reducing the error bars on the data does reduce the uncertainty, the gain is often considerably smaller than one would naively expect. We also find that the inclusion of total reaction cross section can improve the uncertainty although the magnitude of the effect depends strongly on the cases considered.

Microscopic coupled-channel calculations of inelastic proton scattering are performed to study neutron excitations in the $2_1^{+}$ states of ${}^{18}\mathrm{O}$, ${}^{10}\mathrm{Be}$, ${}^{12}\mathrm{Be}$, and ${}^{16}\mathrm{C}$. The proton-nucleus potentials in the coupled-channel calculation are microscopically derived by folding the Melbourne $g$-matrix $NN$ interaction with the matter and transition densities of the target nuclei obtained via structure model calculations of the antisymmetrized molecular dynamics. The calculated results reasonably reproduce the elastic and inelastic proton scattering cross section, and support the dominant contribution of neutrons in the $2_1^{+}$ excitation of ${}^{12}\mathrm{Be}$ and ${}^{16}\mathrm{C}$ as well as ${}^{18}\mathrm{O}$. The sensitivity of the inelastic scattering cross sections to the neutron transition density is discussed as well as the exotic behavior of the neutron transition density with amplitude in the outer regions of ${}^{12}\mathrm{Be}$ and ${}^{16}\mathrm{C}$.

Resonance energies $E_{\lambda }$, neutron widths ${\mathrm{\Gamma }}_{n,\lambda }$, and radiation widths ${\mathrm{\Gamma }}_{\gamma ,\lambda }$ for the compound system ${}^{175}\mathrm{Lu}+n$ were determined up to 1 keV from time-of-flight data reported in literature and recently measured at the GELINA facility of JRC-Geel (Belgium). The statistical analysis of the obtained resonance parameters provides an $s$-wave neutron strength function [$S_0=1.96\left(8\right)$], mean level spacing [$D_0=3.24\left(9\right)\mathrm{eV}$], and average radiation width ($\langle {\mathrm{\Gamma }}_{{\gamma }_0}\rangle =61.3\left(59\right)\mathrm{meV}$) which are substantially different from those compiled in libraries dedicated to statistical calculations. The largest difference lies on the average radiation width, for which a value of 77(5) meV is recommended. ${}^{175}\mathrm{Lu}$ neutron cross sections were calculated with the talys code by using our $s$-wave average parameters as constraints. At $kT=30\mathrm{keV}$, we obtain a total neutron capture cross section equal to 1125(62) mbarns, confirming the lower values reported in the 1990s.

High spin states in ${}^{196}\mathrm{Hg}$ were populated in the ${}^{198}\mathrm{Pt}(\alpha ,6n)$ reaction at 65 MeV and $\gamma \text{−}\gamma$ coincidence measurements were performed using the AFRODITE array at iThemba LABS. The level scheme was extended and new rotational bands were observed. A new dipole band was found. The previously reported dipole band was linked to other known states. Excitation energies, spins, and parities of all bands were determined. The bands were assigned nucleon configurations based on cranked shell model calculations.

We discuss heavy-ion fusion reactions of a well-deformed odd-mass nucleus at energies around the Coulomb barrier. To this end, we consider the ${}^{16}\mathrm{O}+{}^{165}\mathrm{Ho}$ reaction and take into account the effect of deformation of ${}^{165}\mathrm{Ho}$ using the orientation average formula. We show that fusion cross sections are sensitive to magnetic substates of the target nucleus, and cross sections for the side collision, which are relevant to a synthesis of superheavy elements, may be enhanced by a factor of around two by aligning the deformed target nuclei. We also discuss the effect of alignment on the fusion barrier distribution. We find that, for a particular choice of alignment, the shape of barrier distribution becomes similar to a typical shape of barrier distribution for a deformed nucleus with a negative hexadecapole deformation parameter, ${\beta }_4$, even if the intrinsic ${\beta }_4$ is positive in the target nucleus.

The first study of resonances in ${}^{17}\mathrm{O}+\alpha$ elastic scattering was carried out using the thick target inverse kinematics method. The data were analyzed in the framework of an R-matrix approach. Many $\alpha$-cluster states were found in the ${}^{21}\mathrm{Ne}$ excitation region of the 9–13 MeV excitation energy including the first observation of a broad $l=0$ state in an odd-even nucleus, which is likely the analog of the broad $0^{+}$ at 8 MeV in ${}^{20}\mathrm{Ne}$. The observed structure in ${}^{21}\mathrm{Ne}$ appeared to be strikingly similar to that populated in the resonant ${}^{16}\mathrm{O}+\alpha$ scattering in ${}^{20}\mathrm{Ne}$. The results are also useful for refinement of data on an ${}^{17}\mathrm{O}(\alpha ,n)$ reaction important for astrophysics.

Response functions, differential cross sections, and total cross sections for several (anti)neutrino induced reactions on ${}^2\mathrm{H}$, ${}^3\mathrm{He}$, and ${}^3\mathrm{H}$ are calculated in momentum space for (anti)neutrino energies up to 160 MeV, using the AV18 nucleon-nucleon potential and a single-nucleon weak current operator. This work is a continuation of our earlier investigations [J. Golak et al., Phys. Rev. C 98, 015501 (2018)].

Background: The influence of inelastic excitations on sub-barrier fusion enhancement is well established; however, the transfer channel effect can be surprising. Recently, it has been shown that the $2n$ transfer channel is mainly responsible for sub-barrier fusion enhancement despite having a positive-$Q$ value for many-neutron transfer channels. Moreover, some systems do not show enhancement even if they possess positive-$Q$-value transfer channels. It has also been reported that enhancement can be found in those systems for which deformation of nuclei increases after neutron transfer.

Purpose: The aim of this work is to examine the role of multineutron transfer channels on sub-barrier fusion enhancement.

Method: Fusion cross sections were measured with a recoil mass separator for the ${}^{40}\mathrm{Ca}+{}^{70}\mathrm{Zn}$ system and analyzed theoretically within the framework of coupled-channels calculations.

Results: Positive $Q$-value neutron transfer channels seem to be essential for the sub-barrier region, since inelastic excitation coupling was unable to reproduce the trend of experimental fusion cross sections. However, up to $2n$ pick-up channel was found to be sufficient for describing the sub-barrier cross sections.

Conclusions: Sub-barrier fusion in the ${}^{40}\mathrm{Ca}+{}^{70}\mathrm{Zn}$ system is hardly affected by transfer of more than two neutrons. The fusion enhancement due to the transfer channel can be observed in systems for which the deformation of colliding nuclei increases after transfer, though the amount of enhancement does not seem to be proportional to the deformation change.

Background: The well-established coupled channel and coupled reaction channel processes contributing to direct reactions make particular contributions to elastic scattering that are absent from local density folding models. Very little has been established concerning the contribution of these processes to the optical model potentials (OMPs) for ${}^3\mathrm{He}$ scattering. For studying such processes, spin-saturated closed shell nuclei such as ${}^{16}\mathrm{O}$ and ${}^{40}\mathrm{Ca}$ are particularly suitable target nuclei and the (${}^3\mathrm{He}$, ${}^4\mathrm{He}$) reaction is easily handled within conventional reaction theory because it avoids complications such as breakup.

Purpose: To establish and characterize the contribution to the ${}^3\mathrm{He}$-nucleus interaction generated by coupling to neutron pickup (outgoing ${}^4\mathrm{He}$) channels; also to study the contribution of collective states and identify effects of dynamical nonlocality from these couplings.

Methods: Coupled reaction channel (CRC) calculations, including coupling to collective states, will provide the elastic channel $S$-matrix $S_{lj}$ resulting from the included processes. Inversion of $S_{lj}$ will produce the local potential that yields, in a single channel calculation, the elastic scattering observables from the coupled channel calculation. Subtracting the bare potential from the CRC calculations yields a local and $l$-independent representation of the dynamical polarization potential (DPP). From the DPPs, because of a range of combinations of channel couplings, the influence of dynamically generated nonlocality can be identified.

Results: Coupling to ${}^4\mathrm{He}$ channels systematically induces repulsion and absorption in the ${}^3\mathrm{He}$ OMP and also a reduction in the rms radius of the real part. The repulsion and absorption is less for ${}^{208}\mathrm{Pb}$ than for the lighter target nuclei although the qualitative effects, including the general undularity of the DPPs, are similar for all cases; therefore coupling to these channels cannot be represented by renormalizing folding model potentials. Evidence is presented for substantial dynamical nonlocality of the induced DPPs; for ${}^{40}\mathrm{Ca}$ this modifies direct reaction angular distributions. The local equivalent DPPs for individual couplings cannot be added to give the overall DPP for the complete set of couplings. For the ${}^{208}\mathrm{Pb}$ case, channel coupling reduces the reaction cross section although it increases it for ${}^{16}\mathrm{O}$, with ${}^{40}\mathrm{Ca}$ an intermediate case.

Conclusions: The DPPs established here strongly challenge the notion that folding models, in particular local density models, provide a satisfactory description of elastic scattering of ${}^3\mathrm{He}$ from nuclei. Coupling to neutron pickup channels induces dynamical nonlocality in the ${}^3\mathrm{He}$ OMP with implications for direct reactions involving ${}^3\mathrm{He}$. Departures from a smooth radial form for the ${}^3\mathrm{He}$ OMP should be apparent in good fits to suitable elastic scattering data.

We investigate the reaction mechanism of the $\varphi$-meson photoproduction off the proton target, i.e., $\gamma p\to \varphi p$, up to $\sqrt{s}=2.8$ GeV. For this purpose, we employ an effective Lagrangian approach in the tree-level Born approximation, and we employ various experimental and theoretical inputs. As a theoretical setup, the vectorlike Pomeron ($C=+1$) is taken into account as a parametrized two-gluon exchange contribution. We also consider $f_1\left(1285\right)$ axial-vector-meson, ($\pi ,\eta$) pseudoscalar-meson, and ($a_0,f_0$) scalar-meson exchanges in the $t$ channel, in addition to the experimentally confirmed nucleon resonances, such as $N^{*}(2000,5/2^{+})$ and $N^{*}(2300,1/2^{+})$, for the direct $\varphi$-meson radiations in the $s$ and $u$ channels. We provide numerical results for the total and differential cross sections as well as the spin-density matrices in the Gottfried-Jackson, Adair, and helicity frames. We observe that, together with the universally accepted pomeron contribution, the considered meson and nucleon-resonance contributions play significant roles in reproducing the experimental data for the forward and backward $\varphi$-meson scattering-angle regions, respectively, indicating the nontrivial interferences between mesonic and baryonic contributions.

Nonperturbative aspects of the quantum many-body problem are revisited, discussed and advanced in the equation of motion framework. We compare the approach to the two-fermion response function truncated on the two-body level by the cluster expansion of the dynamical interaction kernel to the approach known as time blocking approximation. Such a comparison leads to an extended many-body theory with nonperturbative treatment of high-order configurations. The present implementation of the advanced theory introduces a new class of solutions for the response functions, which include explicitly beyond-mean-field correlations between up to six fermions. The novel approach, which includes configurations with two quasiparticles coupled to two phonons ($2\mathrm{q}\otimes 2\mathrm{phonon}$), is discussed in detail for the particle-hole nuclear response and applied to medium-mass nuclei. The proposed developments are implemented numerically on the basis of the relativistic effective meson-nucleon Lagrangian and compared to the models confined by two-fermion and four-fermion configurations, which are considered as state-of-the-art for the response theory in nuclear structure calculations. The results obtained for the dipole response of ${}^{42,48}\mathrm{Ca}$ and ${}^{68}\mathrm{Ni}$ nuclei in comparison to available experimental data show that the higher configurations are necessary for a successful description of both gross and fine details of the spectra in both high-energy and low-energy sectors.

This article describes an original approach to simultaneously analyzing cross sections and data obtained with surrogate reactions, using an efficient Monte Carlo extended $\mathcal{R}$-matrix theory algorithm based on an unique set of nuclear structure parameters. The alternative analytical path based on the manifold Hauser-Feshbach equation was intensively used in this work to gauge the errors carried by the surrogate-reaction method commonly taken to infer neutron-induced cross sections from observed decay probabilities. The present paper emphasizes in particular a dedicated way to treat ingoing direct reaction and outgoing channels widths correlations and to recall the common absence of class-II states width fluctuation factor in standard codes for calculating average fission cross sections. The present approach opens interesting perspectives on the matter of neutron cross section inference as simultaneously measured fission and $\gamma$-emission probabilities become widely available.

We explore Glauber Monte Carlo predictions for the planned ultrarelativistic ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}$ and $p+{}^{16}\mathrm{O}$ collisions, as well as for collisions of ${}^{16}\mathrm{O}$ on heavy targets. In particular, we present specific collective flow measures which are approximately independent on the hydrodynamic response of the system, such as the ratios of eccentricities obtained from cumulants with different numbers of particles, or correlations of ellipticity and triangularity described by the normalized symmetric cumulants. We use the state-of-the-art correlated nuclear distributions for ${}^{16}\mathrm{O}$ and compare the results to the uncorrelated case, finding moderate effects for the most central collisions. We also consider the wounded quark model, which turns out to yield similar results to the wounded nucleon model for the considered measures. The purpose of our study is to prepare some ground for the upcoming experimental proposals, as well as to provide input for possible more detailed dynamical studies with hydrodynamics or transport codes.