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Phenomenological R-matrix has been a standard framework for the evaluation of resolved resonance cross section data in nuclear physics for many years. It is a powerful method for comparing different types of experimental nuclear data and combining the results of many different experimental measurements in order to gain a better estimation of the true underlying cross sections. Yet a practical challenge has always been the estimation of the uncertainty on both the cross sections at the energies of interest and the fit parameters, which can take the form of standard level parameters. Frequentist (χ2-based) estimation has been the norm. In this work, a Markov Chain Monte Carlo sampler, emcee, has been implemented for the R-matrix code AZURE2, creating the Bayesian R-matrix Inference Code Kit (BRICK). Bayesian uncertainty estimation has then been carried out for a simultaneous R-matrix fit of the 3He (α,γ)7Be and 3He (α,α)3He reactions in order to gain further insight into the fitting of capture and scattering data. Both data sets constrain the values of the bound state α-particle asymptotic normalization coefficients in 7Be. The analysis highlights the need for low-energy scattering data with well-documented uncertainty information and shows how misleading results can be obtained in its absence.

The effect of the isovector imaginary optical potential has been studied experimentally by using the particle-evaporation technique for the $^{11}\mathrm{B}+^{48}\mathrm{Ca}$ reaction with a 21.8 MeV $^{11}\mathrm{B}$ beam. Spectra of neutron, proton, and $\ensuremath{\alpha}$ particles emitted from the neutron-rich compound nucleus $^{59}\mathrm{Mn}$ have been measured and analyzed with traditional optical model potentials with their original parametrizations as well as with adjusted isovector imaginary components. It is shown that the isovector component of the imaginary potential is indispensable in the reproduction of proton and $\ensuremath{\alpha}$-particle yields from this reaction and even needs to be enhanced compared with the suggestions of the original model parametrizations. This can lead to important consequences for astrophysical reaction-rate calculations.

The secondary $\ensuremath{\gamma}$ rays emitted following a nuclear reaction are often relatively straightforward to detect experimentally. Despite the large volume of such data, a practical formalism for describing these $\ensuremath{\gamma}$ rays in terms of partial-wave $T$-matrix elements has never been given. The partial-wave formalism is applicable when $R$-matrix methods are used to describe the reaction in question. This paper supplies the needed framework, and it is demonstrated by the application to the $^{15}\mathrm{N}(p,{\ensuremath{\alpha}}_{1}\ensuremath{\gamma})^{12}\mathrm{C}$ reaction.

Background: Spectroscopic factors, overlaps, and isospin symmetry are often used in conjunction with single-particle wave functions for the phenomenological analysis of nuclear structure and reactions. Many differing prescriptions for connecting these quantities to physically relevant asymptotic normalization constants or widths are available in the literature, but their relationship and degree of validity are not always clear. Purpose: This paper derives relationships among the above quantities of interest using well-defined methodology and starting assumptions. Method: $R$-matrix theory is used as the primary tool to interoperate between the quantities of interest to this work. Particular attention is paid to effects arising from beyond the nuclear surface, where isospin symmetry is strongly violated. Results: Relationships among the quantities of interest are derived. Example applications of these methods to mirror levels in nucleon+${}^{12}{\rm C}$, nucleon+${}^{16}{\rm O}$, and nucleon+${}^{26}{\rm Al}$ are presented. A new approach to multi-level mirror symmetry is derived and applied to the first three $2^+$ states of ${}^{18}{\rm O}$ and ${}^{18}{\rm Ne}$. Conclusions: The relationship between the quantities of interest is clarified and certain procedures are recommended. It is found that the asymptotic normalization constant of the second $2^+$ state in ${}^{18}{\rm Ne}$ deduced from the mirror state in ${}^{18}{\rm O}$ is significantly larger than found in previous work. This finding has the effect of increasing the ${}^{17}{\rm F}(p,\gamma){}^{18}{\rm Ne}$ reaction rate in novae., Comment: 27 pages, 10 figures

We evaluated polyvinyl toluene (PVT) scintillators fabricated with different emitting dopants and scintillator optical configurations for fast neutron imaging. A neutron imaging apparatus was constructed to study scintillators under MeV neutron exposure. PVT with 2% Xylyl Flrpic emitter was identified as the brightest. The addition of a black backing to the scintillator, compared with a specular reflector film backing, improved the resolution of the neutron image obtained with the PVT scintillator by about 2 ×. It is concluded that a PVT imaging screen with 2% Xylyl Flrpic, configured with a black backing, provides the best quality fast neutron image of the scintillators tested.

Journal of physics / G 49(1), 010502 (2022). doi:10.1088/1361-6471/ac2827, Published by IOP Publ., Bristol

Fast neutron imaging is a powerful tool to investigate elemental/isotopic compositions of objects, supporting both scientific studies as well as cargo scanning. Current neutron imaging systems are faced with challenges associated with timing, detection efficiency, and/or spatial resolution. Here, we report on the use of a semiconducting lithium indium diselenide neutron sensor coupled to a Timepix ASIC for fast neutron imaging. Using a 15 cm thick copper knife edge, the spatial resolution of the neutron imager was found to be 1.55 mm for 9 MeV neutrons. The experimental detection efficiency at 9 MeV was in general agreement with calculations.

Cross sections of one- and two-neutron removal reactions of 24O, leading to the 23O(½+) ground state and to bound final states of 22O, have been measured at the National Superconducting Cyclotron Laboratory. The experiment was conducted using the S800 spectrograph and a 24O beam energy of 92.3 MeV/u. The measured 23O ground state and 22O inclusive cross section values, of 74(11) mb and 146(33) mb, respectively, are in good agreement with calculations using eikonal reaction dynamics and shell-model nuclear structure overlaps. The widths at half maximum of the associated parallel momentum distributions of these cross sections, deduced from Gaussian fits, are 115(13) MeV/c for 23O and 309(36) MeV/c for 22O in the projectile rest frame. The data and calculations strongly support the shell-model description of 24O as a spherical, doubly-magic structure.

We study derivatives of the shift and penetration factors of collision theory with respect to energy, angular momentum, and charge. Definitive results for the signs of these derivatives are found for the repulsive Coulomb case. In particular, we find that the derivative of the shift factor with respect to energy is positive for the repulsive Coulomb case, a long anticipated but heretofore unproven result. These results are closely connected to the properties of the sum of squares of the regular and irregular Coulomb functions; we also present investigations of this quantity., Comment: 13 pages, 1 figure

A general framework for deconvoluting the effects of energy averaging on charged-particle reaction measurements is presented. There are many potentially correct approaches to the problem; the relative merits of some of them are discussed. These deconvolution methods are applied to recent 12 C ( α , γ ) 16 O measurements.

Some applications of few-nucleon physics to Big Bang Nucleosynthesis, solar neutrinos, and neutron stars have been reviewed. The future in all of these areas is very exciting as improved measurements of the light element abundances, solar neutrino fluxes, and neutron star properties are planned. On the nuclear physics side new theoretical calculations and measurements will improve our understanding of the underlying physics. Together these effors will lead to a greater understanding of both our Universe and few-nucleon dynamics.

Double differential cross sections of neutrons from $d\phantom{\rule{0.16em}{0ex}}+{\phantom{\rule{0.16em}{0ex}}}^{63,65}$Cu reactions have been measured at deuteron energies of 6 and 7.5 MeV. The cross sections measured at backward angles have been compared to theoretical calculations in the framework of the statistical Hauser-Feshbach model. Three different level density models were tested: the Fermi-gas model, the Gilbert-Cameron model, and the microscopic approach through the Hartree-Fock-Bogoliubov method (HFBM). The calculations using the Gilbert-Cameron model are in best agreement with our experimental data. Level densities of the residual nuclei ${}^{64}$Zn and ${}^{66}$Zn have been obtained from statistical neutron evaporation spectra. The angle-integrated cross sections have been analyzed with the exciton model of nuclear reaction.

The D+D reactions are well known and widely used for a variety of purposes, mainly because of the use of the D(d, n)3He reaction as a mono-energetic neutron source. The least studied of the D+D reactions is the D(d, n)pD reaction known as the deuteron breakup reaction, which produces a continuum of neutrons at energies below the monoenergetic peak. The neutron energy distribution as a function of angle for the cross section, d2σdΩdE${{{d^2}\sigma } \over {d\Omega dE}}$, of the D(d,n)pD reaction has been measured using a 6.94-MeV pulsed deuteron beam incident upon a D2 gas target. The time-of-flight technique was used to determine the energy of the neutrons detected in an array of two lithium glass scintillators and one NE-213 scintillator. The breakup cross section was determined as low as 225-keV neutron energy in the lithium glass detectors.

We review some aspects of R‐matrix theory and its application to the semi‐empirical analysis of nuclear reactions. Important applications for nuclear astrophysics and recent results for the 12C(α,γ)16O reaction are emphasized.

We discuss nuclear reactions which could play a role in Big Bang Nucleosynthesis (BBN). Most of these reactions involve lithium and beryllium isotopes and the rates for some of these have not previously been included in BBN calculations. Few of these reactions are well studied in the laboratory. We also discuss novel effects in these reactions, including thermal population of nuclear target states, resonant enhancement, and non-thermal neutron reaction products. We perform sensitivity studies which show that even given considerable nuclear physics uncertainties, most of these nuclear reactions have minimal leverage on the standard BBN abundance yields of 6Li and 7Li. Although a few have the potential to alter the yields significantly, we argue that this is unlikely., Comment: 13 pages, 6 figures

Neutron and proton evaporation spectra from the {sup 6}Li+{sup 55}Mn and d+{sup 59}Co reactions have been analyzed with the Hauser-Feshbach approach using different input models for nuclear level densities of {sup 60}Ni and {sup 60}Co nuclei. It has been found that models with a Fermi-gas like temperature dependence fail to reproduce particle spectra from both reactions simultaneously. We obtained the surprising result that the only way to describe our data is to assume the independence of the nuclear temperature on the excitation energy up to about the 20 MeV energy range.

We present new accurate measurements of the differential cross section $\ensuremath{\sigma}(\ensuremath{\theta})$ and the proton analyzing power ${A}_{y}$ for proton-$^{3}\mathrm{He}$ elastic scattering at various energies. A supersonic gas-jet target has been employed to obtain these low-energy cross-section measurements. The $\ensuremath{\sigma}(\ensuremath{\theta})$ distributions have been measured at ${E}_{p}=0.99$, 1.59, 2.24, 3.11, and 4.02 MeV. Full angular distributions of ${A}_{y}$ have been measured at ${E}_{p}=1.60$, 2.25, 3.13, and 4.05 MeV. This set of high-precision data is compared to four-body variational calculations employing realistic nucleon-nucleon ($\mathit{NN}$) and three-nucleon ($3N$) interactions. For the unpolarized cross section, the agreement between the theoretical calculation and data is good when a $3N$ potential is used. The comparison between the calculated and measured proton analyzing powers reveals discrepancies of approximately 50% at the maximum of each distribution. This is analogous to the existing ``${A}_{y}$ puzzle'' known for the past 20 years in nucleon-deuteron elastic scattering.

Nuclear physics has a long and productive history of application to astrophysics which continues today. Advances in the accuracy and breadth of astrophysical data and theory drive the need for better experimental and theoretical understanding of the underlying nuclear physics. This paper will review some of the scenarios where nuclear physics plays an important role, including Big Bang Nucleosynthesis, neutrino production by our sun, nucleosynthesis in novae, the creation of elements heavier than iron, and neutron stars. Big-bang nucleosynthesis is concerned with the formation of elements with A, To be published in the Proceedings of 19th Lake Louise Winter Institute (15-21 February 2004). 9 pages, 3 figures

An alternative parameterization of R-matrix theory is presented which is mathematically equivalent to the standard approach, but possesses features which simplify the fitting of experimental data. In particular there are no level shifts and no boundary-condition constants which allows the positions and partial widths of an arbitrary number levels to be easily fixed in an analysis. These alternative parameters can be converted to standard R-matrix parameters by a straightforward matrix diagonalization procedure. In addition it is possible to express the collision matrix directly in terms of the alternative parameters., Comment: 8 pages; accepted for publication in Phys. Rev. C; expanded Sec. IV, added Sec. VI, added Appendix, corrected typos

Angular distributions of sigma(theta), A_y, iT_11, T_20, T_21, and T_22 have been measured for d-p scattering at E_c.m.=667 keV. This set of high-precision data is compared to variational calculations with the nucleon-nucleon potential alone and also to calculations including a three-nucleon (3N) potential. Agreement with cross-section and tensor analyzing power data is excellent when a 3N potential is used. However, a comparison between the vector analyzing powers reveals differences of approximately 40% in the maxima of the angular distributions which is larger than reported at higher energies for both p-d and n-d scattering. Single-energy phase-shift analyses were performed on this data set and a similar data set at E_c.m.=431.3 keV. The role of the different phase-shift parameters in fitting these data is discussed., Comment: 18 pages, 6 figures

We present measurements of differential cross sections and the analyzing powers A_y, iT11, T20, T21, and T22 at E_c.m.=431.3 keV. In addition, an excitation function of iT11(theta_c.m.=87.8 degrees) for 431.3, 13 pages, 11 figures

Tensor analyzing powers for {sup 2}H(d(vector sign),d){sup 2}H elastic scattering were measured at deuteron energies of 3.0, 4.75, and 6.0 MeV. The measured values are below 0.02 and increase with increasing energy. The data were compared to the results of an R-matrix parametrization and microscopic four-body calculations. The calculations indicate that the nucleon-nucleon p waves have a strong effect on the observables. (c) 2000 The American Physical Society.

A new measurement of the p-d differential cross section at Ep= 1 MeV has been performed. These new data and older data sets at energies below the deuteron breakup are compared to calculations using the two-nucleon Argonne v18 and the three-nucleon Urbana IX potentials. A quantitative estimate of the capability of these interactions to describe the data is given in terms of a chi^2 analysis. The chi^2 per datum drastically improves when the three-nucleon interaction is included in the Hamiltonian., Comment: 13 pages, 5 figures, to be published in Phys. Rev. C

The total cross section for p-d breakup is studied in terms of the elastic S-matrix through the unitary condition. Calculations using the complex Kohn variational method along with the Pair Correlated Hyperspherical Harmonic basis are presented. The results have been restricted to energies below Ep=30 MeV where Coulomb effects are expected to be sizable and are compared to the existing data. Two different measurements have been found in the literature: 40 years ago, Gibbons and Macklin (1959); and 26 years ago, Carlosn et al. (1973). The calculations are found to be in reasonable agreement with these old data, though a discrepancy is observed near the deuteron breakup threshold. Moreover, a detailed analysis of the contributions to the observable from different partial waves has been presented. Unexpectedly, the main contribution for a wide range of energies has been detected in the J=3/2- state., Comment: 12 pages, 5 figures, to be published in Physics Letters B

Scientists at the National Ignition Facility plan to generate fusion energy and study fusion in nuclear weapons. But the starlike conditions that NIF creates will also enable them to study astrophysically important nuclear reactions.

We present measurements of the analyzing powers Ay and iT11 for proton-deuteron scattering at Ecm=432 keV. Calculations using a realistic nucleon-nucleon potential (Argonne V18) are found to underpredict both analyzing powers by 40. The inclusion of the Urbana three-nucleon interaction does not significantly modify the calculated analyzing powers. Due to its short range, it is difficult for this three-nucleon interaction to affect Ay and iT11 at this low energy. The origin of the discrepancy remains an open question., 12 pages, Revtex, one figure, to be published in Phys. Lett. B

The three-nucleon system is studied at energies a few hundred keV above the N-d threshold. Measurements of the tensor analyzing powers $T_{20}$ and $T_{21}$ for p-d elastic scattering at $E_{c.m.}=432$ keV are presented together with the corresponding theoretical predictions. The calculations are extended to very low energies since they are useful for extracting the p-d scattering lengths from the experimental data. The interaction considered here is the Argonne V18 potential plus the Urbana three-nucleon potential. The calculation of the asymptotic D- to S-state ratio for $^3$H and $^3$He, for which recent experimental results are available, is also presented., Comment: Latex, 11 pages, 2 figures, to be published in Phy.Lett.B

A leading order determination of the gluon density in the proton has been performed in the fractional momentum range $1.9 \cdot 10^{-3} < x_{g/p} < 0.18$ by measuring multi-jet events from boson-gluon fusion in deep-inelastic scattering with the H1 detector at the electron-proton collider HERA. This direct determination of the gluon density was performed in a kinematic region previously not accessible. The data show a considerable increase of the gluon density with decreasing fractional momenta of the gluons., 19 pages, latex, 5 figures appended as uuencoded file

The cross sections for the charged current processes ${e^{-}p}\rightarrow{\nu_e+hadrons}$ and, for the first time, ${e^{+}p}\rightarrow{\overline{\nu}_e+hadrons}$ are measured at HERA for transverse momenta larger than 25 GeV., Comment: 21 pages, latex, 10 figures appended as uuencoded file

Proton evaporation spectra from 6,7 Li induced reactions on 54,56,58 Fe nuclei have been measured and analyzed with Hauser-Feshbach compound reaction calculations with a Gilbert and Cameron input level density model. Level densities of residual 59 64 Ni nuclei have been extracted from proton spectra. Both level density and level density pa- rameter a have been compared against the respective values obtained from neutron res- onance spacing data. The discrepancy has been found in systematics behavior of level densities against the mass number of Ni isotopes.