Direct Capture Cross Research Articles

Measuring neutron capture cross sections of radioactive nuclei

Measuring neutron capture cross sections of radioactive nuclei is a crucial step towards a better understanding of the origin of the elements heavier than iron. For decades, the precise measurement of direct neutron capture cross sections in the “stellar” energy range (eV up to a few MeV) was limited to stable and longer-lived nuclei that could be provided as physical samples and then irradiated with neutrons. New experimental methods are now being developed to extend these direct measurements towards shorter-lived radioactive nuclei (t_{1/2}< 1 y). One project in this direction is a low-energy heavy-ion storage ring coupled to the ISAC facility at TRIUMF, Canada’s accelerator laboratory in Vancouver BC, which has a compact neutron source in the ring matrix. Such a pioneering facility could be built within the next 10 years and store a wide range of radioactive ions provided directly from the existing ISOL facility, allowing for the first time to carry out direct neutron capture measurements on short-lived isotopes in inverse kinematics.

Neutron capture on $$^{16}$$O within the framework of RMF + ACCC + BCS for astrophysical simulations

Neutron capture on $$^{16}$$ O may serve as a neutron poison in certain nucleosynthesis scenarios. We revisit this reaction at energy ranges of astrophysical interest, employing a novel theoretical approach that self-consistently treats capture through bound and resonant levels. Our covariant density functional theory is based on a relativistic mean field (RMF) theory with contributions from resonant orbitals included via the analytical continuation of the coupling constant (ACCC), and pairing correlations included via the resonant Bardeen–Cooper–Schrieffer (BCS) technique. We employ this RMF + ACCC + BCS approach to extract bound states, resonant states, and pairing correlations in $$^{17}$$ O in a self-consistent microscopic way. We calculate $$^{16}$$ O(n, $$\gamma $$ ) $$^{17}$$ O direct capture cross sections resulting from neutron E1 transitions from scattering states to bound states, resonant cross sections from a Breit–Wigner formalism, and Maxwellian-averaged cross sections and thermonuclear reaction rates for astrophysical applications. We use different effective interactions to determine the viability of our approach to determine the $$^{17}$$ O level structure and corresponding reaction rates. Comparisons to measurements and database values are given.

Radiative Cascade Repopulation of 1s2s2p 4P States Formed by Single Electron Capture in 2–18 MeV Collisions of C4+ (1s2s 3S) with He

This study focuses on the details of cascade repopulation of doubly excited triply open-shell C3+(1s2s2p)4P and 2P± states produced in 2–18 MeV collisions of C4+(1s2s3S) with He. Such cascade calculations are necessary for the correct determination of the ratio R of their cross sections, used as a measure of spin statistics [Madesis et al. PRL 124 (2020) 113401]. Here, we present the details of our cascade calculations within a new matrix formulation based on the well-known diagrammatic cascade approach [Curtis, Am. J. Phys. 36 (1968) 1123], extended to also include Auger depopulation. The initial populations of the 1s2snℓ4L and 1s2snℓ2L levels included in our analysis are obtained from the direct nℓ single electron capture (SEC) cross sections, calculated using the novel three-electron close-coupling (3eAOCC) approach. All relevant radiative branching ratios (RBR) for n≤4 were computed using the COWAN code. While doublet RBRs are found to be very small, quartet RBRs are found to be large, indicating cascade feeding to be important only for quartets, consistent with previous findings. Calculations including up to third order cascades, extended to n→∞ using an n−3 SEC model, showed a ∼60% increase of the 1s2s2p4P populations due to cascades, resulting, for the first time, in R values in good overall agreement with experiment.

Nuclear Structures of 17O and Time-dependent Sensitivity of the Weak s-process to the 16O(n,γ)17O Rate

Abstract We revisit the radiative neutron capture reaction 16O(n,γ)17O of astrophysical interest, based on the new reevaluated cross-section data. Several potentials are proposed to predict direct capture cross sections. The contributions from single-particle resonances to total capture cross section are quantitatively considered in Breit–Wigner formalism, taking into account the interference term between direct capture and resonant cross sections, which is crucial for the description of the behavior around the resonance energies. A new cross section is achieved based upon χ 2-fittings for optimized resonance parameters using Minuit code, and it has a largely improved agreement with updated experimental data. Statistical errors are also evaluated for the total and Maxwellian-averaged cross sections. It is confirmed that the direct captures dominate the total cross sections; however, resonant contribution also becomes progressively more important as the energy increases to 100 keV. Resonance contribution can increase the reaction rates for energy region 50 keV &lt; E &lt; 100 keV by 5% ± 5%–25% ± 5%, and around 8% ± 5% in comparison with KADoNiS v0.3 rate and the latest data evaluations, respectively. We show a detailed propagation of the uncertainty in the 16O(n,γ) reaction rate to abundances of nuclei, including s-nuclei during the weak s-process with a multi-zone nuclear network calculation. Although an enhanced rate of 16O(n,γ) diminishes the s-process efficiency in the 25 M ☉ stellar model adopted from the Modules for Experiments in Stellar Astrophysics, it can lead to larger abundances of neutrons as well as 22Ne in the late epoch of C burning.

Direct capture cross section of Be9(n,γ)Be10

The cross section of the $^{9}$Be(n,$\gamma$)$^{10}$Be reaction was calculated in the direct capture model. All parameters of the calculations were adjusted to properties of the $^{9}$Be + n system at thermal energies. The calculated cross section at thermonuclear energies shows the expected $1/v$ behavior of $s$-wave capture at low energies, but increases towards higher energies as typical $p$-wave capture. Excellent agreement between new experimental data in the astrophysically relevant energy region and the present calculation is found.

Calculation of astrophysical S-factor and reaction rate in 12C(p, γ)13N reaction

The 12C(p, γ)13N reaction is the first process in the CNO cycle. Also it is a source of low-energy solar neutrinos in various neutrino experiments. Therefore, it is of high interest to gain data of the astrophysical S-factor in low energies. By applying Faddeev’s method, we calculated wave functions for the bound state of 13N. Then the cross sections for resonance and non-resonance were calculated through using Breit–Wigner and direct capture cross section formulae, respectively. After that, we calculated the total S-factor and compared it with previous experimental data, revealing a good agreement altogether. Then, we extrapolated the S-factor in zero energy and the result was 1.32 ± 0.19 (keV.b). In the end, we calculated reaction rate and compared it with NACRE data.

Cross section measurement of the astrophysically important O17(p,γ)F18 reaction in a wide energy range

The 17O(p,g)18F reaction plays an important role in hydrogen burning processes in different stages of stellar evolution. The rate of this reaction must therefore be known with high accuracy in order to provide the necessary input for astrophysical models. The cross section of 17O(p,g)18F is characterized by a complicated resonance structure at low energies. Experimental data, however, is scarce in a wide energy range which increases the uncertainty of the low energy extrapolations. The purpose of the present work is therefore to provide consistent and precise cross section values in a wide energy range. The cross section is measured using the activation method which provides directly the total cross section. With this technique some typical systematic uncertainties encountered in in-beam gamma-spectroscopy experiments can be avoided. The cross section was measured between 500 keV and 1.8 MeV proton energies with a total uncertainty of typically 10%. The results are compared with earlier measurements and it is found that the gross features of the 17O(p,g)18F excitation function is relatively well reproduced by the present data. Deviation of roughly a factor of 1.5 is found in the case of the total cross section when compared with the only one high energy dataset. At the lowest measured energy our result is in agreement with two recent datasets within one standard deviation and deviates by roughly two standard deviations from a third one. An R-matrix analysis of the present and previous data strengthen the reliability of the extrapolated zero energy astrophysical S-factor. Using an independent experimental technique, the literature cross section data of 17O(p,g)18F is confirmed in the energy region of the resonances while lower direct capture cross section is recommended at higher energies. The present dataset provides a constraint for the theoretical cross sections.

Studies of X-ray burst reactions with radioactive ion beams from RESOLUT

Reactions on certain proton-rich, radioactive nuclei have been shown to have a significant influence on X-ray bursts. We provide an overview of two recent measurements of important X-ray burst reactions using in-flight radioactive ion beams from the RESOLUT facility at the J. D. Fox Superconducting Accelerator Laboratory at Florida State University. The 17 F(d,n) 18 Ne reaction was measured, and Asymptotic Normalization Coefficients were extracted for bound states in 18 Ne that determine the direct-capture cross section dominating the 17 F(p, γ ) 18 Ne reaction rate for T≲ 0.45 GK. Unbound resonant states were also studied, and the single-particle strength for the 4.523-MeV (3 + ) state was found to be consistent with previous results. The 19 Ne(d,n) 20 Na proton transfer reaction was used to study resonances in the 19 Ne(p, γ ) 20 Na reaction. The most important 2.65-MeV state in 20 Na was observed to decay by proton emission to both the ground and first-excited states in 19 Ne, providing strong evidence for a 3 + spin assignment and indicating that proton capture on the thermally-populated first-excited state in 19 Ne is an important contributor to the 19 Ne(p, γ ) 20 Na reaction rate.

Exploration of direct neutron capture with covariant density functional theory inputs

Predictions of direct neutron capture are of vital importance for simulations of nucleosynthesis in supernovae, merging neutron stars, and other astrophysical environments. We calculated direct capture cross sections using nuclear structure information obtained from a covariant density functional theory as input for the fresco coupled reaction channels code. We investigated the impact of pairing, spectroscopic factors, and optical potentials on our results to determine a robust method to calculate cross sections of direct neutron capture on exotic nuclei. Our predictions agree reasonably well with experimental cross section data for the closed shell nuclei $^{16}\mathrm{O}$ and $^{48}\mathrm{Ca},$ and for the exotic nucleus $^{36}\mathrm{S}$. We then used this approach to calculate the direct neutron capture cross section on the doubly magic unstable nucleus $^{132}\mathrm{Sn}$ which is of interest for the astrophysical r-process.

Continuum dipole response near the threshold and the direct neutron capture cross section at astrophysical energies

We apply the continuum quasiparticle random phase approximation to calculate the direct neutron capture cross section relevant to the r-process nucleo-synthesis. The electric dipole strength function in an even-even n-rich nucleus is decomposed with respect to the channels of direct neutron decays. Using the detailed balance relation, the partial dipole strengths are converted to obtain the direct neutron-capture cross sections. Numerical examples are given for 142Sn.

Direct capture in the130Sn(n,γ)131Sn and132Sn(n,γ)133Sn reactions underr-process conditions

The cross sections of the ${}^{130}$Sn($n,\phantom{\rule{-0.16em}{0ex}}\ensuremath{\gamma}$)${}^{131}$Sn and ${}^{132}$Sn($n,\phantom{\rule{-0.16em}{0ex}}\ensuremath{\gamma}$)${}^{133}$Sn reactions are calculated in the direct capture model at low energies below 1.5 MeV. Using recent data from ($d\phantom{\rule{-0.16em}{0ex}},\phantom{\rule{-0.16em}{0ex}}p$) transfer experiments on ${}^{130}$Sn and ${}^{132}$Sn, it is possible to avoid global input parameters with their inherent uncertainties and to determine all inputs to the direct capture model by local adjustments. The calculated direct capture cross sections of ${}^{130}$Sn and ${}^{132}$Sn are almost identical and have uncertainties of less than a factor of 2. The stellar reaction rates ${N}_{A}\ensuremath{\langle}\ensuremath{\sigma}v\ensuremath{\rangle}$ show a slight increase with temperature. Finally, an estimate for the influence of low-lying resonances to the stellar reaction rates is given.

Determination of the Astrophysically Relevant 6Li(n, γ)7Li Cross Sections from the 7Li(6Li, 7Li)6Li Elastic-Transfer Reaction

Angular distributions for the 7Li(6Li, 7Li)6Li elastic-transfer reaction have been measured with the Q3D magnetic spectrograph at the HI-13 tandem accelerator of Beijing, China. The neutron spectroscopic factors of 7Li are derived by comparing the calculated differential cross sections, which are obtained through the distorted-wave Born approximation (DWBA) calculation, to the experimental data. And these spectroscopic factors are then used to deduce the direct capture cross sections in 6Li(n, γ)7Li at energies of astrophysical relevance.

Astrophysical reaction rates forNi58,60(n,γ) from new neutron capture cross section measurements

New neutron capture cross sections of $^{58,60}\mathrm{Ni}$ were measured in the energy range from 100 eV to 600 keV using the Oak Ridge Electron Linear Accelerator. The combination of these new neutron capture data with previous transmission data allowed a resonance analysis up to 900 keV using $\mathcal{R}$-matrix theory. The theoretically determined direct capture cross sections were included in the analyses. From these resonance parameters and the direct capture contribution, new ($n$,$\ensuremath{\gamma}$) astrophysical reaction rates were determined over the entire energy range needed by the latest stellar models describing the so-called weak $s$ process.

Calculation of astrophysical reaction rate of 82Ge(n,γ)83Ge

The neutron capture reaction on a neutron-rich near closed-shell nucleus 82Ge may play an important role in the r-process following the fallout from nuclear statistical equilibrium in core-collapse supernovae. By carrying out a DWBA analysis for the experimental angular distribution of 82Ge(d, p)83Ge reaction we obtain the single particle spectroscopic factors, S2,5/2 and S0,1/2 for the ground and first excited states of 83Ge = 82Ge⊗n, respectively. And then these spectroscopic factors are used to calculate the direct capture cross sections for the 82Ge(n, γ)83Ge reaction at energies of astrophysical interest. The optical potential for neutron scattering on unstable nucleus 82Ge is not known experimentally. We employed a real folding potential which was calculated by using the proper 82Ge density distribution and an effective nucleon-nucleon force DDM3Y. The neutron capture reactions on neutron-rich closed-shell nuclei are expected to be dominated by the direct capture to bound states. We will show that the direct capture rates on these nuclei are sensitive to the structure of the low-lying states.

Erratum: Extracting (n,γ) direct capture cross sections from Coulomb dissociation: Application toC14(n,γ)C15[Phys. Rev. C78, 011601 (2008)

A methodology for extracting neutron direct capture rates from Coulomb dissociation data is developed and applied to the Coulomb dissociation of 15C on 208Pb at 68 MeV/nucleon. Full Continuum Discretized Coupled Channel calculations are performed and an asymptotic normalization coefficient is determined from a fit to the breakup data. Direct neutron capture calculations using the extracted asymptotic normalization coefficient provide $(n,\gamma)$ cross sections consistent with direct measurements. Our results show that the Coulomb Dissociation data can be reliably used for extracting the cross section for 14C(n,g)15C if the appropriate reaction theory is used. The resulting error bars are of comparable magnitude to those from the direct measurement. This procedure can be used more generally to extract capture cross sections from breakup reactions whenever the desired capture process is fully peripheral.

New measurements of the astrophysicalSfactor for12C(p,γ)13Nreaction at low energies and the asymptotic normalization coefficient (nuclear vertex constant) for thep+12C→13Nreaction

New measurements of differential and total cross sections for the {sup 12}C(p,{gamma}){sup 13}N reaction have been made at beam energies of E{sub p}=354,390,460,463,565,750, and 1061 keV. Analysis of the astrophysical S factor S(E) for the {sup 12}C(p,{gamma}){sup 13}N reaction at low energies and of the reaction rates has been carried out within the R-matrix approach by using the previously measured nuclear vertex constant (or the respective asymptotic normalization coefficient) for the virtual decay {sup 13}N{yields}p+{sup 12}C to fix the direct capture part of the amplitude in S(E). It is demonstrated that the R-matrix approach, using the measured asymptotic normalization coefficient, can be employed as an ideal tool, minimizing the uncertainties associated with a calculation of the direct capture cross section of the {sup 12}C(p,{gamma}){sup 13}N reaction at extremely low energies. New information on the proton and {gamma} width for the first excited state of {sup 13}N is obtained.

Extracting (n,γ) direct capture cross sections from Coulomb dissociation: Application toC14(n,γ)C15

A methodology for extracting neutron direct capture rates from Coulomb dissociation data is developed and applied to the Coulomb dissociation of $^{15}\mathrm{C}$ on $^{208}\mathrm{Pb}$ at 68 MeV/nucleon. Full continuum discretized coupled channel calculations are performed and an asymptotic normalization coefficient is determined from a fit to the breakup data. Direct neutron capture calculations using the extracted asymptotic normalization coefficient provide $(n,\ensuremath{\gamma})$ cross sections consistent with direct measurements. Our results show that the Coulomb dissociation data can be reliably used for extracting the cross section for $^{14}\mathrm{C}$($n,\ensuremath{\gamma}$)$^{15}\mathrm{C}$ if the appropriate reaction theory is used. The resulting error bars are of magnitude comparable to those from the direct measurement. This procedure can be used more generally to extract capture cross sections from breakup reactions whenever the desired capture process is fully peripheral.

Asymptotic normalization coefficients for mirror virtual nucleon decays in a microscopic cluster model

It has been suggested recently (Phys. Rev. Lett. 91, 232501 (2003)) that charge symmetry of nucleon-nucleon interactions relates the Asymptotic Normalization Coefficients (ANCs) of proton and neutron virtual decays of mirror nuclei. This relation is given by a simple analytical formula which involves proton and neutron separation energies, charges of residual nuclei and the range of their strong interaction with the last nucleon. Relation between mirror ANCs, if understood properly, can be used to predict astrophysically relevant direct proton capture cross sections using neutron ANCs measured with stable beams. In this work, we calculate one-nucleon ANCs for several light mirror pairs, using microscopic two-, three- and four-cluster models, and compare the ratio of mirror ANCs to the predictions of the simple analytic formula. We also investigate mirror symmetry between other characteristics of mirror one-nucleon overlap integrals, namely, spectroscopic factors and single-particle ANCs.

TheLi8(d,p)Li9reaction and the astrophysicalLi8(n,γ)Li9reaction rate

The $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}$ reaction plays an important role in both the r-process nucleosynthesis and the inhomogeneous big bang models. Its direct capture rates can be extracted from the $^{8}\mathrm{Li}(d,p)^{9}\mathrm{Li}$ reaction, indirectly. We have measured the angular distribution of the $^{8}\mathrm{Li}(d,p)^{9}\mathrm{Li}{}_{g.s.}$ reaction at ${E}_{c.m.} = 7.8$ in inverse kinematics using coincidence detection of $^{9}\mathrm{Li}$ and the recoil proton, for the first time. Based on distorted wave Born approximation (DWBA) analysis, the $^{8}\mathrm{Li}(d,p)^{9}\mathrm{Li}{}_{g.s.}$ cross section was determined to be 7.9 \ifmmode\pm\else\textpm\fi{} 2.0 mb. The single particle spectroscopic factor ${S}_{1,3/2}$ for the ground state of $^{9}\mathrm{Li}=^{8}\mathrm{Li}\ensuremath{\bigotimes}n$ was derived to be $0.68\ifmmode\pm\else\textpm\fi{}0.14$, and then used to calculate the direct capture cross sections for the $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}{}_{g.s.}$ reaction at energies of astrophysical interest. The astrophysical $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}{}_{g.s.}$ reaction rate for the direct capture was found to be $3970\ifmmode\pm\else\textpm\fi{}950\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.3em}{0ex}}{\mathrm{mole}}^{\ensuremath{-}1}\phantom{\rule{0.3em}{0ex}}{s}^{\ensuremath{-}1}$ at ${T}_{9}=1.$ This presents the first experimental constraint for the $^{8}\mathrm{Li}(n,\ensuremath{\gamma})^{9}\mathrm{Li}$ reaction rates of astrophysical relevance.

Spectroscopic factors from direct proton capture

Spectroscopic factors derived from direct capture studies are systematically compared to those obtained from transfer reaction experiments and from shell model calculations for the $\mathrm{A}=16--32$ target mass region. The direct proton capture and proton transfer spectroscopic factors are obtained in the present work from a reanalysis of literature data by using the same bound state potential parameters. Our direct capture spectroscopic factors differ significantly from the values originally reported in the literature. The sensitivity of the direct capture cross section to different choices for the scattering potential is explored. We find evidence that spectroscopic factors obtained from direct capture studies are as reliable as those extracted from transfer measurements if the (direct capture) radial scattering wave function is calculated with a zero nuclear scattering potential instead of the common choice of a hard-sphere potential.