Asymptotic Normalization Coefficient Method 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.

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

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.

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 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.

Indirect determination of the astrophysical S factor for the Li6 ( p,γ)Be7 reaction using the asymptotic normalization coefficient method

Background: The Li 6 ( p , γ ) Be 7 cross section influences a variety of astrophysical scenarios, including big-bang and stellar nucleosynthesis. In recent years, conflicting results of direct measurements have been published, reporting contradictory low-energy trends. Purpose: To shed light on the contradiction between the existing data sets, the reaction was studied using the asymptotic normalization coefficient (ANC) technique which was up-to-now never used for this reaction. Methods: To derive the ANC, the Li 6 ( He 3 , d ) Be 7 transfer reaction, studied at the Department of Physics and Astronomy of the University of Catania and at the John. D. Fox Superconducting Accelerator Laboratory at Florida State University, was re-analyzed, focusing on the proton transfer mechanism [the α transfer process is discussed by Kiss et al. [Phys. Lett. B 807, 135606 (2020)]. The energy of the He 3 beam impinging on a Li 6 target was E lab = 3 MeV and E lab = 5 MeV. The yield of the emitted deuterons was measured with high precision by using silicon Δ E - E telescopes. Results: From the DWBA analysis of the angular distributions of the emitted deuterons populating the ground ( E * = 0.0 MeV; 3 2 − ) and the first excited ( E * = 0.429 MeV ; 1 2 − ) states of Be 7 , the ANCs for the Li 6 + p → Be 7 system were deduced. Furthermore, the recently measured Li 6 ( p , γ ) Be 7 reaction cross sections [Piatti , Phys. Rev. C 102, 052802 (2020)] were also analyzed within this theoretical framework. Excellent agreement was found between ANC values derived indirectly and those determined from the direct data, which strengthens the conclusion of the present work. The astrophysical S factor—at energies characterizing the Sun—for the Li 6 ( p , γ ) Be 7 reaction was calculated using the weighted mean of the experimentally derived ANC values. Conclusions: The result of the present comprehensive study supports the extrapolation of Piatti [Phys. Rev. C 102, 052802 (2020)], Dong [J. Phys. G Nucl. Partic. 44, 045201 (2017)], and Gnech and Marcucci [Nucl. Phys. A 987, 1 (2019)], and thus disfavors the conclusions drawn by He [Phys. Lett. B 725, 287 (2013)] and Xu [Nucl. Phys. A 918, 61 (2013)].

Isospin triplet A=14: search for states with enhanced radii

This article is devoted to study of isobar-analogue states 1− in triplet A=14: 14C-14N-14O. Previously signs of neutron halo in the 1−, 6.09 MeV state of 14C were obtained by two independent groups. In this article we propose to study neighbouring nuclei 14N and 14O using the Modified diffraction model (MDM) method and the method of Asymptotic normalization coefficients (ANC). Methods were applied to experimental differential cross sections of 14C(α,α)14C scattering and reactions 13C(3He,d)14N and 14N(3He,t)14O. MDM and ANC gave practically similar within errors radii for the studied 1− states: the 6.09 MeV state in 14C – 2.7±0.1 fm, the 8.06 MeV state in 14N – 2.7 ± 0.1 fm, the 5.17 MeV state in 14O – 2.6 ± 0.2 fm. Moreover, the signs of proton halo in the 1− state of 14N were obtained for the first time.

ANC From Experimental Perspective

We give a review of activities of the application of the method of Asymptotic Normalization Coefficients (ANC) for the determination of the cross-sections and astrophysical S-factors of the radiative (p, γ) captures on stable and radioactive nuclei. Number of experiments was done in the Nuclear Physics Institute of the Czech Academy of Sciences in cooperation with Texas A&M University and Istituto Nazionale di Fisica Nucleare -Laboratori Nazionali del Sud (Catania, Italy). The method was introduced in the last decade of the 20th century and was for the first time used to contribute to the intensively studied topic of solar neutrinos. Later its use was extended from Li, Be and B element region to the CNO cycle and above. The obtained results were found (where other measurements were available) compatible with other indirect methods and even with direct measurements. The method was tested in measurements performed using solid state detectors and a magnetic spectrometer. While the direct measurements increasingly reach higher Z isotopes, the advantage of the ANC and other indirect methods in general is still crucial to determine the astrophysical S-factors where short living isotopes participate e.g. in 11 C(p, γ) 12 N, 12 N(p, γ) 13 O and 13 N(p, γ) 14 O. The ANC method can also provide predictions for reactions with mirror nuclei. Other uses of ANCs are also discussed.

Asymptotic normalization coefficient method for two-proton radiative capture

The method of asymptotic normalization coefficients is a standard approach for studies of two-body non-resonant radiative capture processes in nuclear astrophysics. This method suggests a fully analytical description of the radiative capture cross section in the low-energy region of the astrophysical interest. We demonstrate how this method can be generalized to the case of three-body 2p radiative captures. It was found that an essential feature of this process is the highly correlated nature of the capture. This reflects the complexity of three-body Coulomb continuum problem. Radiative capture 15O+p+p→17Ne+γ is considered as an illustration.

Search for Signs of Neutron and Proton Halos in the Excited Isobaric Analog States of A = 14 Nuclei

The isobaric analog states with isospin T = 1 in triplet of the A = 14 nuclei: 14C, 14N, and 14O, are studied. Signs of neutron halo in the 1− (6.09 MeV) state of 14C have been revealed earlier by two groups. We confirm this result and study isobaric analog 1− states of neighboring 14N and 14O nuclei. The differential cross sections of the 14C(α, α)14C* (6.09 MeV, 1−) inelastic scattering, the 13C(3He, d)14N* (8.06 MeV, 1−), and the 14N(3He, t)14O* (5.17 MeV, 1−) reactions are analyzed by two methods: the modified diffraction method and the method of asymptotic normalization coefficients. The rms radii for all three mirror nuclei in the studied 1− states are found almost the same: 2.7 ± 0.1 fm for 14C, 2.67± 0.07 fm for 14N, and 2.6 ± 0.2 fm for 14O. The signs of proton halo in the 1− state of 14N are identified for the first time.

Astrophysical S-factor for the 3He(α,γ)7Be reaction via the asymptotic normalization coefficient (ANC) method

The detection of the neutrinos produced in the p−p chain and in the CNO cycle can be used 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, therefore, the uncertainty of its cross section sensitively influences the prediction of the 7Be and 8B neutrino fluxes. Despite its importance and the large number of experimental and theoretical works devoted to this reaction, the knowledge on the reaction cross section at energies characterizing the core of the Sun (15 keV - 30 keV) is limited and further experimental efforts are needed to reach the desired (≈ 3%) accuracy. The precise knowledge on the external capture contribution to the 3He(α,γ)7Be reaction cross section is crucial for the theoretical description of the reaction mechanism. In the present work the indirect measurement of this external capture contribution using the Asymptotic Normalization Coefficient (ANC) technique is reported. To extract the ANC, the angular distributions of deuterons emitted in the 6Li(3He,d)7Be α-transfer reaction were measured with high precision at EH3e = 3.0 MeV and EH3e = 5.0 MeV. The ANCs were then extracted from comparison of DWBA calculations to the measured data and the zero energy astrophysical S-factor for 3He(α,γ)7Be reaction was found to be 0.534 ± 0.025 keVb.

Transfer reactions as an Indirect Method in Nuclear Astrophysics

In my presentation, I will discuss the use of transfer reactions as an indirect method of determining information important for nuclear astrophysics. Specifically, I will focus on peripheral reactions and their analysis with the Asymptotic Normalization Coefficients (ANC) method. I will present results from related experiments that have been conducted at the Cyclotron Institute, Texas A&M University with focus on the 0ptical Model Parameters obtained and the need for reliable calculations. Additionally, I will describe the im- provements in the measured data that we obtained after upgrading the detection system used.

The determination of the astrophysical S-factor of the direct 18O(p,$\gamma$)19F capture by the ANC method

The depletion of 18O via the $(\mathrm{p},\gamma)$ capture competes with the $(\mathrm{p}, \alpha)$ capture during the CNO cycles in AGB stars. Despite the fact that the $(\mathrm{p}, \alpha)$ capture is dominant, the $ (\mathrm{p}, \gamma)$ can play an important role in mixing stages of the AGB star evolution. Here, we attempt to determine the astrophysical S-factor of the direct part of the 18O(p,$\gamma$)19F capture by the indirect method of asymptotic normalization coefficients (ANC). We measure the differential cross section of the transfer reaction 18O(3He, d)19F at a 3He energy of 24.6 MeV. The measurement was performed on the cyclotron of the CANAM infrastructure of NPI in Řež, Czech Republic, with the gas target consisting of the high-purity 18O (99.9%). The reaction products were measured by eight $ \Delta E$-E telescopes composed of thin and thick silicon surface-barrier detectors. The parameters of the optical model for the input channel were deduced by means of the code ECIS and the analysis of transfer reactions to 12 levels of the 19F nucleus up to 8.014 MeV was made by the code FRESCO. The deduced ANCs were then used to specify the direct contribution to the 18O(p,$\gamma$)19F capture process and were compared with the mutually different results of two works.

Neutron Halos in Excited States of 12B

An experiment was done to search for states with a neutron halo in 12B. The measurements were carried out at the cyclotron of the University of Jyvaskyla (Finland) using Large Scattering Chamber (LSC). The idea of the work was to search for two states with the expected neutron halo, 1 ̄ and 2 ̄. Differential cross sections with excitation of 12B states, including abovementioned states, were observed. The preliminary calculations on halo radii by the method of asymptotic normalization coefficients for the 2 ̄ and 1 ̄ states which are in a discrete spectrum gave following values: 5.6 fm and 7.4 fm, which is much larger than the radius of the valence neutron in the ground state. But strictly the presence of a neutron halo can be confirmed only for 1 ̄ state. The 2 ̄ state can be considered only as candidate for halo. An unexpected result was obtained for the 3 ̄, 3.39 MeV state, which is in continuum 19 keV above the decay threshold 12B → 11B + n, preliminary estimation for its halo radius is ∼ 6.5 fm. This indicates that the halo can be present in this state as well. But strict conditions for neutron halo are not fulfilled in the same way as for 2 ̄ state. Until now, the neutron halo in unbound states has been observed only for the members of the rotational bands.

ANC experiments for nuclear astrophysics in NPI CAS

Asymptotic Normalization Coefficients method is one of the indirect methods used in nuclear astrophysics. The method allows to deduce a direct part of a radiative capture cross section from the measurement of a two body reaction under specific conditions. The experimental works started in collaboration of NPI CAS, TAMU and INFN LNS from 90-ties and continue till the present. The introduction to this method is presented and experimental experiences from NPI CAS and the collaboration are shared.

The astrophysical S-factor of the direct 18O(p, γ)19F capture by the ANC method

We attempted to determine the astrophysical S-factor of the direct part of the 18 O(p, γ )19 F capture by the indirect method of asymptotic normalization coefficients (ANC). We measured the differential cross section of the transfer reaction 18 O(3 He, d)19 F at a 3 He energy of 24.6 MeV. The measurement was realized on the cyclotron of the NPI in Řež, Czech Republic, with the gas target consisting of the high purity 18 O (99.9 %). The reaction products were measured by eight ∆E-E telescopes composed from thin and thick silicon surface-barrier detectors. The parameters of the optical model for the input channel were deduced by means of the code ECIS and the analysis of transfer reactions to 12 levels of the 19 F nucleus up to 8.014 MeV was made by the code FRESCO. The deduced ANCs were then used to specify the direct contribution to the 18 O(p, γ )19 F capture process and were compared with the mutually different results of two works.

Determination of neutron halo radii in the first excited states ofC13andBe11with the asymptotic normalization coefficients method

An analysis of the differential cross sections of the $^{12}\mathrm{C}(d,p)^{13}\mathrm{C}$ (ground state, or g.s., $1/{2}_{1}^{+}$) and $^{10}\mathrm{Be}(d,p)^{11}\mathrm{Be}$ (g.s., $1/{2}_{1}^{\ensuremath{-}}$) reactions at the incident deuteron energies of 11.8, 25.9, and 30 MeV for the first system, and 12.0 and 25.0 MeV for the second system has been performed by applying the coupled-reaction-channels method. The spectroscopic factors ${S}_{\text{expt}}$, asymptotic normalization coefficients (ANCs), and rms radii of the last neutron in the ground states and the first excited states of the stable $^{13}\mathrm{C}$ and the radioactive $^{11}\mathrm{Be}$ nuclei were extracted. The existence of neutron halos in the first excited state of $^{13}\mathrm{C}$ and the ground state of $^{11}\mathrm{Be}$ is confirmed. The rms radii of halos in these states were found to be $5.72\ifmmode\pm\else\textpm\fi{}0.16$ and $8.0\ifmmode\pm\else\textpm\fi{}0.2$ fm, respectively, in agreement with experimental results. We showed that a halo is also formed in the 0.32 MeV $1/{2}_{1}^{\ensuremath{-}}$ excited state of $^{11}\mathrm{Be}$. The halo radius in this state was determined for the first time and was found to be ${R}_{h}=4.65\ifmmode\pm\else\textpm\fi{}0.20$ fm.

Peripheral elastic and inelastic scattering ofO17,18on light targets at 12 MeV/nucleon

A study of interaction of neutron-rich oxygen isotopes $^{17,18}\mathrm{O}$ with light targets has been undertaken in order to determine the optical potentials needed for the transfer reaction $^{13}\mathrm{C}(^{17}\mathrm{O},^{18}\mathrm{O})^{12}\mathrm{C}$. Optical potentials in both incoming and outgoing channels have been determined in a single experiment. This transfer reaction was used to infer the direct capture rate to the $^{17}\mathrm{F}(p,\ensuremath{\gamma})^{18}\mathrm{Ne}$ which is essential to estimate the production of $^{18}\mathrm{F}$ at stellar energies in ONe novae. The success of the asymptotic normalization coefficient (ANC) as indirect method for astrophysics is guaranteed if the reaction mechanism is peripheral and the distorted wave Born approximation cross-section calculations are warranted and stable against the optical model potential (OMP) used. We demonstrate the stability of the ANC method and the OMP results by using good-quality elastic and inelastic-scattering data with stable beams before extending the procedures to rare-ion beams. The peripherality of our reaction is inferred from a semiclassical decomposition of the total-scattering amplitude into barrier and internal barrier components. Comparison between elastic scattering of $^{17}\mathrm{O}$, $^{18}\mathrm{O}$, and $^{16}\mathrm{O}$ projectiles is made.

A quantification model of Traditional Chinese Medicine syndromes in children with idiopathic precocious puberty and early puberty

ObjectiveTo establish a quantification model of Traditional Chinese Medicine (TCM) syndromes by sampling patients undergoing idiopathic precocious puberty (IPP) and early puberty. MethodsA questionnaire for classifying and quantifying TCM syndromes was designed and administered. All the results were analyzed; the relationship between 3 types of syndrome and 47 symptoms were summated. Meanwhile, the frequency distribution of each symptom or sign was aggregated. Fuzzy mathematics was used to develop a quantification model of TCM syndromes. ResultsWe found that precocious puberty had 3 types of syndrome, including hyperactivity of fire due to Yin deficiency (Syndrome I), depressed liver Qi transforming into fire (Syndrome II), and end retention of damp heat (Syndrome III). In the IPP group, Syndrome I was the most common principal syndrome (100%). Forty-six patients (43.81%) were diagnosed with Syndrome I accompanied by Syndrome II and 11 (10.48%) were diagnosed with Syndrome I accompanied by Syndrome III. In the early puberty group, Syndrome I was also the main syndrome (98.39%). The degrees of most symptoms were mild to moderate. Reddened tongue was the most common tongue manifestation (62.86% prevalence) in the IPP group. The most common pulse manifestations were slippery pulse, thread pulse, and taut pulse. The Asymptotic Normalization Coefficient (ANC) method was used to quantify the TCM syndromes in 167 cases. Diagnostic accuracy rate reached 91%, comparable to expert diagnosis. ConclusionWe find that there are 3 types of syndrome in the IPP group and in the early puberty group. Syndrome I (hyperactivity of fire due to Yin deficiency) is the main syndrome in the two groups. ANC may be an appropriate for quantification model of TCM syndromes.