Asymptotic Normalization Coefficients Research Articles

Analytic continuation of differential cross-sections as a way to determine asymptotic normalization coefficients. Application to the 16O(d,p)17O reaction

Asymptotic normalization coefficients (ANC) are important nuclear characteristics. This paper discusses a method for determining ANC values from experimental data on differential cross-sections of nuclear transfer reactions. The method is based on the use of the analytic continuation of these cross-sections to the pole point of the reaction amplitude with respect to the variable [Formula: see text], where [Formula: see text] is the center-of-mass scattering angle. The method under consideration is used to determine the ANC for the channel [Formula: see text]O(1/2[Formula: see text]; 0.871[Formula: see text]MeV) [Formula: see text]O(0[Formula: see text]; 0[Formula: see text]MeV) [Formula: see text] from the data on the [Formula: see text]O(0[Formula: see text]; 0[Formula: see text]MeV)[Formula: see text]O (1/2[Formula: see text]; 0.871[Formula: see text]MeV) reaction. 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 have a great impact on the extracted ANC value.

Asymptotic Normalization Coefficient Investigation of the 17O(d, p) Transfer for Astrophysical Application to the 17O(n, α)14C Reaction at Low Energies

Indirect methods have proven to be a complementary approach for extending our knowledge of nuclear structure and low-energy cross sections. Among these, the neutron-induced reaction cross sections appear to be of particular interest since 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 8038, 8125, 8213, and 8282 keV resonances in 18O are studied, and their Γ n are derived. A comparison with recent 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 investigations, and shows new frontiers for neutron-induced reactions with radioactive ion beams. Moreover, we examined the impact of adopting the newly recommended 17O(n, α)14C reaction rate on asymptotic giant branch stars' nucleosynthesis. Our findings reveal significant variations (≳10%) in the production of the neutron-rich heavy isotopes sensitive to neutron density, underlining the neutron-poisoning effect of 17O on the s-process.

ANC and SF of bound states in 15N→14C+p, 16O→15N+p, 19F→18O+p, 32S→31P+p

Asymptotic normalization coefficients (ANCs) and spectroscopic factors (SFs) for proton binding in the ground states of the [Formula: see text]N, [Formula: see text]O, [Formula: see text]F and [Formula: see text]S nuclei were extracted from an analysis of available literature data on the (3He[Formula: see text]) and ([Formula: see text]) reactions. Modified DWBA and ADWA analyses showed that the proton transfer process is more peripheral in (3He,d) reactions and therefore more reliable for determining the ANCs. As a result of the comparative analysis of peripheral (3He,d) and nonperipheral ([Formula: see text]) reactions, the uncertainties in the extracted values of SFs were reduced. The data obtained are to be used in calculating astrophysical S-factors for radiative proton capture.

Determination of Asymptotic Normalization Coefficients by Analytic Continuation of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}$$\\end{document}-Matrix

The method of finding the values of asymptotic normalization coefficients (ANC) is proposed based on the analytic continuation of the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R$$\\end{document}-matrix that describes the elastic nuclear scattering into the unphysical region of the negative energy of collision (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E<0$$\\end{document}). The formula is derived, expressing the partial-wave scattering amplitude through the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R$$\\end{document}-matrix and modified Coulomb functions. This formula allows, when continuing the amplitude to the region \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E<0$$\\end{document}, to overcome difficulties associated with irregular behavior of the scattering amplitude near \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E=0$$\\end{document} if the Coulomb interaction is present. The proposed method is used to determine the ANC for the channel \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{16}\ extrm{O}\ o\\alpha+{}^{12}$$\\end{document}C.

Calculation of the Cross Sections for Neutron Scattering on the 9Be Nucleus Using Ab Initio Calculated Asymptotic Normalization Coefficients and Decay Widths

Calculation of the Cross Sections for Neutron Scattering on the 9Be Nucleus Using Ab Initio Calculated Asymptotic Normalization Coefficients and Decay Widths

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 the study of the mirror nuclei 7Li and 7Be

We present a theoretical study of the nuclear structure of the mirror nuclei 7Li and 7Be by using the asymptotic normalization coefficient (ANC) method through the transfer reactions 6Li(d,p)7Li and 6Li(3He,d)7Be. For these reactions, the elastic scattering and the transfer angular distributions were calculated considering cluster structures for the residual nucleus and the transfer particle. With the use of the Fresco code, we found the optical model parameters which reproduce the experimental data for the elastic and the transfer angular distributions and we got the ANC for the single particle model and the spectroscopic factor on the ground and the first excited states of each nuclei. This methodology allows to calculate the nuclear ANC which describes the peripheral behavior of both nuclei on their bound states.

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

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

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

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.

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$^{-1/2}$.