Asymptotic Normalization Coefficients Research Articles

Analysis of astrophysical 26Mg(n,γ)27Mg reaction via the asymptotic normalization coefficient method

The [Formula: see text] reaction plays a crucial role in the process of nucleosynthesis in stars. It occurs primarily in massive stars during their late evolutionary stages or during explosive events like supernovae. This paper focuses on investigating discrepancies in the ANC values of the [Formula: see text] reaction by analyzing experimental angular distributions of [Formula: see text] using the DWBA, ADWA and CDCC methods for both ground and first excited states. We then use a mirror nucleus procedure to extract information on the ANCs of the ground state [Formula: see text] reaction. The Hauser–Feshbach formalism of the statistical Compound Nucleus (CN) model was applied in this study to perform a compound-nucleus analysis of the [Formula: see text] reaction. The [Formula: see text] reaction has almost fulfilled the condition of peripherality, which is necessary for understanding the magnitude of the direct reaction contribution. ANCs for the [Formula: see text] virtual decay system were obtained. Moreover, according to charge symmetry of mirror nuclei, the square of proton ANC for a [Formula: see text] is determined and comparison between the values of the presented ANCs.

Asymptotic normalization coefficient for 6He+p→7Li from the proton transfer d(6He,7Li)n reaction

The main purpose of this work is to determine values of the asymptotic normalization coefficients for the virtual decays 6He+p[Formula: see text]Li(g.s.) and 6He+p[Formula: see text]Li(0.48[Formula: see text]MeV). For this purpose, the recently measured experimental differential cross-section of the proton transfer reaction d(6He,7Li)n has been analyzed. The modified distorted wave born approximation is used to determine the values of the asymptotic normalization coefficients. The peripheral character of this reaction has been tested. It has been shown that this reaction is peripheral. New values of the asymptotic normalization coefficients for the virtual decays 6He+p[Formula: see text]Li(g.s.) and 6He+p[Formula: see text]Li(0.48[Formula: see text]MeV) with their uncertainties have been obtained.

Determination of the astrophysical factor of the 3He(α,γ)7Be down to zero energy using the asymptotic normalization coefficient method

The observation of neutrinos emitted in the p − p chain and in the CNO cycle can be employed to test the Standard Solar Model. The 3He(α,γ)7Be reaction is the first reaction of the 2nd and 3rd branch of the p − p chain, so the indetermination of its cross section significantly affects the predicted 7Be and 8B neutrino fluxes. Notwithstanding its relevance and the great deal of experimental and theoretical papers, information of the reaction cross section at energies of the core of the Sun (15 keV - 30 keV) is sparse and additional experimental work is necessary to attain the target (~ 3%) accuracy. The precise understanding of the external capture component to the 3He(α,γ)7Be reaction cross section is pivotal for the theoretical assessment of the reaction mechanism. In this work, the indirect measurement of this external capture component using the Asymptotic Normalization Coefficient (ANC) technique is discussed. To extract the ANC, the angular distributions of deuterons yielded in the 6Li(3He,d)7Be α-transfer reaction were detected with high precision at E3He =3.0 MeV and 5.0 MeV. The ANCs were then deduced from the juxtaposition of DWBA and CC calculations with the experimental angular distributions and the zero energy astrophysical S-factor for 3He(α,γ)7Be reaction was calculated to equal 0.534 ± 0.025 keVb. Both our experimental and theoretical approaches were tested through the analysis of the 6Li(p,γ)7Be astrophysical factor, with further interesting astrophysical implications.

NUCLEAR ASYMPTOTIC NORMALIZATION COEFFICIENT FOR 27Al →26Mg+p REACTION

The 26Mg(p,ɣ)27Al reaction is important in nuclear astrophysics as it play a crucial role in understanding the nucleosynthesis processes in red giants and Wolf-Rayet stars. The 26Mg(p,ɣ)27Al reaction is responsible for the production of 27Al in these stars, while the 26Mg(3He,d)27Al reaction provides information on the asymptotic normalization coefficient for the ground state of 27Al.The asymptotic normalization coefficient (ANC) method is an indirect method that provides information on the normalization of the overlap functions for a given reaction. This information is crucial for nuclear astrophysics as it allows for the calculation of the direct component of the reaction rate at astrophysical relevant energies.In this work, the angular distribution of the 26Mg(3He,d)27Al reaction have been analyzed using separate sets of optical potentials via the Distorted Wave Born Approximation which allows for a better understanding of the reaction mechanism and the determination of the ANC. Consequently,thecross section and Astrophysical S factor for 27Al→26Mg + p have been calculated for the direct capture

Hyperspherical Cluster Model for Bosons: Application to Sub-threshold Halo States in Helium Drops

To describe long-range behaviour of one particle removed from a few- or a many-body system, a hyperspherical cluster model has been developed. It has been applied to the ground and first excited states of helium drops with five, six, eight and ten atoms interacting via a two-body soft gaussian potential. Convergence of the hyperspherical cluster harmonics expansion is studied for binding energies, root-mean-squared radii and overlaps of the wave functions of two helium drops differing by one atom. It was shown that with increasing model space the functional form of such overlaps at large distances converges to the correct asymptotic behaviour. The asymptotic normalization coefficients that quantify the overlaps’ amplitudes in this region are calculated. It was also shown that in the first excited state one helium atom stays far apart from the rest forming a two-body molecule, or a halo. The probability of finding the halo atom in the classically-forbidden region of space depends on the definition of the latter and on the valence atom binding energy. The total norm of the overlap integrals, the spectroscopic factor, represents the number of partitions of a many-body state into a chosen state of the system with one particle removed. The spectroscopic factors have been calculated and their sum rules are discussed giving a further insight into the structure of helium drops.

Resonances in low-energy nuclear processes and nuclear astrophysics and asymptotic normalization coefficients: a review

Resonances in low-energy nuclear processes and nuclear astrophysics and asymptotic normalization coefficients: a review

New Determination of the 12C(α, γ)16O Reaction Rate and Its Impact on the Black-hole Mass Gap

We present a precise measurement of the asymptotic normalization coefficient (ANC) for the 16O ground state (GS) through the 12C(11B, 7Li)16O transfer reaction using the Quadrupole‐3‐Dipole (Q3D) magnetic spectrograph. The present work sheds light on the existing discrepancy of more than 2 orders of magnitude between the previously reported GS ANC values. This ANC is believed to have a strong effect on the 12C(α, γ)16O reaction rate by constraining the external capture to the 16O ground state, which can interfere with the high-energy tail of the 2+ subthreshold state. Based on the new ANC, we determine the astrophysical S-factor and the stellar rate of the 12C(α, γ)16O reaction. An increase of up to 21% in the total reaction rate is found within the temperature range of astrophysical relevance compared with the previous recommendation of a recent review. Finally, we evaluate the impact of our new rate on the pair-instability mass gap for black holes (BH) by evolving massive helium core stars using the MESA stellar evolution code. The updated 12C(α, γ)16O reaction rate decreases the lower and upper edges of the BH gap about 12% and 5%, respectively.

Ab initio symmetry-adapted emulator for studying emergent collectivity and clustering in nuclei

We discuss emulators from the ab initio symmetry-adapted no-core shell-model framework for studying the formation of alpha clustering and collective properties without effective charges. We present a new type of an emulator, one that utilizes the eigenvector continuation technique but is based on the use of symplectic symmetry considerations. This is achieved by using physically relevant degrees of freedom, namely, the symmetry-adapted basis, which exploits the almost perfect symplectic symmetry in nuclei. Specifically, we study excitation energies, point-proton root-mean-square radii, along with electric quadrupole moments and transitions for 6Li and 12C. We show that the set of parameterizations of the chiral potential used to train the emulators has no significant effect on predictions of dominant nuclear features, such as shape and the associated symplectic symmetry, along with cluster formation, but slightly varies details that affect collective quadrupole moments, asymptotic normalization coefficients, and alpha partial widths up to a factor of two. This makes these types of emulators important for further constraining the nuclear force for high-precision nuclear structure and reaction observables.

ANC experiments for nuclear astrophysics: The 26Si(p, γ)27P case

The Asymptotic Normalization Coefficient (ANC) method has proven to be useful in retrieving the direct part of the radiative capture cross section for a number of reactions of astrophysical interest. In this work, the study of the 26Si(p, γ)27P reaction, studied via the ANC in its extension for mirror nuclei will be discussed.

Determination of the 3He(α, γ)7Be and 6Li(p, γ)7Be astrophysical factors down to zero energy using the asymptotic normalization coefficients

The p - p-chain reaction 3He(α, γ)7Be can sensitively influence the prediction of the 7Be and 8B neutrino fluxes. Despite its importance, the knowledge of its reaction cross section at energies of the core of the Sun (15 keV 30 keV) is limited and the accuracy far from the desired 3% level. In the present paper the indirect measurement of the external capture contribution using the asymptotic normalization coefficient (ANC) technique is reported. The angular distributions of deuterons emitted in the 6Li(3He,d)7Be α-transfer reactions were measured and the ANCs extracted from the scaling of distorted-wave Born approximation (DWBA) and coupled-channel (CC) calculations. Then, the astrophysical S-factor for the 3He(α, γ)7Be reaction was calculated assuming E1 direct capture and the zero energy value turned out to be 0.534 0.025 keVb. Both our experimental and theoretical approaches were benchmarked through the analysis of the 6Li(p,γ)7Be astrophysical factor, with interesting astrophysical applications to the understanding of the primordial lithium problem. In particular, the present work disfavors the occurrence of a claimed 200 keV resonance in the astrophysical factor.

Shedding light on 17O(n,α)14C reaction at astrophysical energies with Trojan Horse Method and Asymptotic Normalization Coefficient

Indirect methods have been established in the past as a complementary way of increasing our knowledge about nuclear structure and low-energy cross section measurements. Among these, the neutron induced reaction cross sections appear to be of particular interest because of their role both for unstable and stable beams. In view of this, we report here the combined study of the 17O(n,α)14C reaction accomplished by the Trojan Horse Method (THM) and the Asymptotic Normalization Coefficient (ANC) method. The low lying resonances 8038, 8125, 8213, and 8282 keV in 18O are studied and Γn are derived. A comparison with direct data and recent THM experimental data is presented. The independent ANC investigation corroborates our previous THM results, confirms the consistence of the two indirect investigation and shows new frontiers also in view of neutron induced reactions with RIB’s.

ANC method: Experimental approach and recent results

The Asymptotic Normalization Coefficient (ANC) method, has proven to be useful in retrieving the direct part of the radiative capture cross section for a number of reactions of astrophysical interest. In this work, some of the latest results obtained by the AsFin2 group of the LSN-INFN (Catania) and the OJR of the NPI (Řež) will be briefly discussed.

Determination of asymptotic normalization coefficients for the channel $$^{16}$$O$$\rightarrow \alpha +^{12}$$C: excited state $$^{16}$$O($$0^+; 6.05$$ MeV)

Asymptotic normalization coefficients (ANC) determine the overall normalization of cross sections of peripheral radiative capture reactions. In the present paper, we treat the ANC $C$ for the virtual decay $^{16}$O$(0^+; 6.05$ MeV)$\to \alpha+^{12}$C(g.s.), the known values of which are characterized by a large spread $(0.29-1.65)\times 10^3$ fm$^{-1/2}$. The ANC $C$ is found by analytic continuation in the energy of the $\alpha^{12}$C $s$-wave scattering amplitude, known from the phase-shift analysis of experimental data, to the pole corresponding to the $^{16}$O bound state and lying in the unphysical region of negative energies. To determine $C$, two different methods of analytic continuation are used. In the first method, the scattering data are approximated by the sum of polynomials in energy in the physical region and then extrapolated to the pole. The best way of extrapolation is chosen on the basis of the exactly solvable model. Within the second approach, the ANC $C$ is found by solving the Schr\"odinger equation for the two-body $\alpha^{12}$C potential, the parameters of which are selected from the requirement of the best description of the phase-shift analysis data at a fixed experimental binding energy of $^{16}$O$(0^+; 6.05$ MeV) in the $\alpha+^{12}$C channel. The values of the ANC $C$ obtained within these two methods lie in the interval (886--1139) fm$^{-1/2}$.

Bayesian estimation of theSfactor and thermonuclear reaction rate forO16(p,γ)F17

The $^{16}$O(p,$\gamma$)$^{17}$F reaction is the slowest hydrogen-burning process in the CNO mass region. Its thermonuclear rate sensitively impacts predictions of oxygen isotopic ratios in a number of astrophysical sites, including AGB stars. The reaction has been measured several times at low bombarding energies using a variety of techniques. The most recent evaluated experimental rates have a reported uncertainty of about 7.5\% below $1$~GK. However, the previous rate estimate represents a best guess only and was not based on rigorous statistical methods. We apply a Bayesian model to fit all reliable $^{16}$O(p,$\gamma$)$^{17}$F cross section data, and take into account independent contributions of statistical and systematic uncertainties. The nuclear reaction model employed is a single-particle potential model involving a Woods-Saxon potential for generating the radial bound state wave function. The model has three physical parameters, the radius and diffuseness of the Woods-Saxon potential, and the asymptotic normalization coefficients (ANCs) of the final bound state in $^{17}$F. We find that performing the Bayesian $S$ factor fit using ANCs as scaling parameters has a distinct advantage over adopting spectroscopic factors instead. Based on these results, we present the first statistically rigorous estimation of experimental $^{16}$O(p,$\gamma$)$^{17}$F reaction rates, with uncertainties ($\pm 4.2$\%) of about half the previously reported values.

Compatibility of the asymptotic normalization coefficient for the C14→B13+p overlap extracted from the C14(B11,C12)B13 reaction with C14(d,He3)B13 data

When the asymptotic normalization coefficient (ANC) for the ${}^{\mathrm{A}+1}(Z+1)\ensuremath{\rightarrow}{\phantom{\rule{0.16em}{0ex}}}^{\mathrm{A}}Z+p$ overlap is extracted from data for proton pickup from the ${}^{\mathrm{A}+1}(Z+1)$ nucleus, the value obtained may strongly depend on the degree of completeness of the modeling of the reaction mechanism, particularly when heavy-ion probes are employed. Taking the specific case of the ANC for the $^{14}\mathrm{C}\ensuremath{\rightarrow}^{13}\mathrm{B}+p$ overlap, an analysis of data for the heavy-ion $^{14}\mathrm{C}(^{11}\mathrm{B},^{12}\mathrm{C})^{13}\mathrm{B}$ reaction showed that the distorted wave Born approximation (DWBA) yields a significantly larger ANC than the coupled reaction channel (CRC) technique, incorporating multistep reaction paths. In this paper we present an analysis of data from the literature for the light-ion $^{14}\mathrm{C}(d,^{3}\mathrm{He})^{13}\mathrm{B}$ pickup reaction and show that the ANC extracted from the heavy-ion data using the CRC technique is entirely compatible with the light-ion data when used in either DWBA or more complete coupled discretized continuum channel plus CRC calculations. The present results also show that the ANC extracted from the light-ion reaction is essentially unaffected by multistep reaction paths, in contrast with the heavy-ion case.

Elastic α−C12 scattering at low energies with the resonant 22+ and 23+ states of O16

The elastic $\alpha$-$^{12}$C scattering for $l=2$ at low energies is studied in an effective Lagrangian approach. We explicitly include two resonant $2_2^+$ and $2_3^+$ states of $^{16}$O in the scattering amplitudes and construct an $S$ matrix assuming that three amplitudes, the non-resonant part of the amplitude which has the sub-threshold $2_1^+$ state of $^{16}$O and those of the two resonant states, are represented by the summation of corresponding parts of the phase shift. Then, we fit the parameters in the $S$ matrix to the phase shift data by imposing three conditions at very low energies where the phase shift data are not available. By using the fitted parameters, we calculate the asymptotic normalization coefficients (ANC) of the $2_1^+$ state of $^{16}$O and find that the previously reported small and large values of the ANC can be reproduced depending on the imposed conditions, but we obtain large error bars for the large ANC values which are reported from the $\alpha$ transfer reactions.

Performing Bayesian Analyses With AZURE2 Using BRICK: An Application to the 7Be System

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.

Erratum to: Determination of Asymptotic Normalization Coefficients by Analytic Continuation of Differential Cross Sections

An Erratum to this paper has been published: https://doi.org/10.1134/S106377882233002X

Determination of Asymptotic Normalization Coefficients by Analytic Continuation of Differential Cross Sections

A method is discussed for determining the asymptotic normalization coefficients (ANC) using the analytic continuation of experimental differential cross sections for nuclear transfer reactions to the pole point of the reaction amplitude with respect to the variable costheta, where theta is the scattering angle. Within the framework of this method, using experimental data on the differential cross section for the reaction {}^{12}textrm{C}(0^{+};0textrm{ MeV})(d,p){}^{13}textrm{C}(1/2^{+};3.09textrm{ MeV}) the ANC for the channel {}^{13}textrm{C}(1/2^{+};3.09textrm{ MeV})to{}^{12}textrm{C}(0^{+};0textrm{ MeV})+n was determined. When determining the ANC, the corrections caused by the Coulomb interaction in the initial, final and intermediate states of the reaction were taken into account. It is shown that these corrections significantly affect the extracted ANC value.

Extracting the asymptotic normalization coefficient for the C14→B13+p overlap from the C14(B11,C12)B13 reaction

The availability of a comparatively complete data set for the elastic and inelastic scattering of a 45-MeV beam of $^{11}\mathrm{B}$ ions from a $^{14}\mathrm{C}$ target, together with an angular distribution for the $^{14}\mathrm{C}(^{11}\mathrm{B},^{12}\mathrm{C})^{13}\mathrm{B}$ proton pickup reaction enables a determination of the $\ensuremath{\langle}^{14}\mathrm{C}\ensuremath{\mid}^{13}\mathrm{B}+p\ensuremath{\rangle}$ asymptotic normalization coefficient (ANC) using the coupled reaction channel (CRC) technique. The complete nature of the data set allows two-step contributions to the reaction mechanism to be controlled while a set of $\ensuremath{\langle}^{12}\mathrm{C}\ensuremath{\mid}^{11}\mathrm{B}+p\ensuremath{\rangle}$ overlaps obtained from a consistent analysis of ($d,^{3}\mathrm{He}$) and ($e,{e}^{\ensuremath{'}}p$) data fixes the projectile overlaps. We find that the level of completeness of the modeling of the reaction mechanism has a significant effect on the value obtained for the ANC, with a distorted wave Born approximation analysis yielding a significantly larger ANC than the full CRC calculation. The final result obtained, when compared with the theoretical value calculated within the source term approach, is in accord with trends for proton removal from similar $p$-shell nuclei.