Normalization Coefficients Research Articles

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

Automatic classification method of power user’s requirements text based on parallel naive Bayesian algorithm

In order to ensure the efficiency of power user’s requirements processing, an automatic classification method for demand test of power users based on parallel naive Bayesian algorithm is proposed. Polynomial naive Bayes is selected to build Hadoop cluster, and the feature words of power user’s requirements are selected through chi square test. The weight of each feature item is calculated by word frequency-inverse text frequency index method, and the weight sum of each category is calculated. The weight sum is input into naive Bayes algorithm to output the text classification results of power user’s requirements. At the same time, The naive Bayes classification algorithm is parallelized and encapsulated to reduce the cost of data movement and exchange in the classification process, and improve the operation efficiency of demand text classification of power user. The experimental results show that this method can accurately extract the feature words of power user’s requirements, effectively realize the automatic classification of power user’s requirements text, and have a more accurate classification effect. The average fitness value of the proposed method tends to be stable after more than 20 training times, and the number of network convergence steps is 7. When the ratio of energy function is about 0.4 and 0.6, the average IU value is the highest. When the required number of texts ranges from 500 to 1500, the delay time of text classification is 0.02 s, and the peak signal-to-noise ratio is more than 33, among which the highest peak signal-to-noise ratio is 42.52, and the normalization coefficient is 1.

Influence of online E-commerce interaction on consumer satisfaction based on big data algorithm

With the rapid development of the times, people have entered the era of intelligence, and the application of big data algorithms is becoming increasingly widespread. The satisfaction of consumers in online shopping is closely related to communication and interaction during shopping. Based on this, this article studies the impact of online e-commerce interaction on consumer satisfaction based on big data algorithms. This article introduces the mediating variable of consumer satisfaction from the perspective of interaction, constructs a model between interaction and trust, and studies the internal impact mechanism of online interaction on consumer satisfaction in online shopping. This article takes the JD interactive shopping platform as the research object, and analyzes and explores the target consumer satisfaction of the women's clothing interactive shopping platform. Analyzed the impact of interaction on merchant qualifications and service satisfaction evaluations, store size, and logistics of purchased goods. The research results indicate that the normalization coefficients of the H1a and H1b pathways are 0.131 and 0.118, respectively, which are slightly smaller, indicating that the impact of perceived risk on consumer satisfaction is not significant. Meanwhile, the CR in H1 is a positive number and the direction of influence is positive, which is contrary to the assumption. Therefore, it is necessary to calibrate the initial model. After correction, the GFI value is 0.816, AGFI value is 0.825, RMSEA value is 0.042, TFI value is 0.930, CFI value is 0.955, PGFI value is 0.718, and PNFI value is 0.810. The degree is within an acceptable range. Therefore, when implementing interactive shopping, e-commerce companies need to create a good shopping environment for the implementation of interactive activities between sellers and customers. The impact of online e-commerce interaction based on big data algorithms on consumer satisfaction is a hot topic. Personalized recommendations can improve consumer satisfaction and loyalty, but data privacy and security issues are also receiving increasing attention. In addition, it is also necessary to consider the fairness and bias issues of the algorithm, as well as the transparency issues of data analysis and decision-making. On the premise of ensuring data privacy and security, it is necessary to improve the fairness and transparency of algorithms to improve consumer satisfaction and trust, and achieve sustainable development.

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

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.

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.

Application of Zero-Watermarking for Medical Image in Intelligent Sensor Network Security

The field of healthcare is considered to be the most promising application of intelligent sensor networks. However, the security and privacy protection of medical images collected by intelligent sensor networks is a hot problem that has attracted more and more attention. Fortunately, digital watermarking provides an effective method to solve this problem. In order to improve the robustness of the medical image watermarking scheme, in this paper, we propose a novel zero-watermarking algorithm with the integer wavelet transform (IWT), Schur decomposition and image block energy. Specifically, we first use IWT to extract low-frequency information and divide them into non-overlapping blocks, then we decompose the sub-blocks by Schur decomposition. After that, the feature matrix is constructed according to the relationship between the image block energy and the whole image energy. At the same time, we encrypt watermarking with the logistic chaotic position scrambling. Finally, the zero-watermarking is obtained by XOR operation with the encrypted watermarking. Three indexes of peak signal-to-noise ratio, normalization coefficient (NC) and the bit error rate (BER) are used to evaluate the robustness of the algorithm. According to the experimental results, most of the NC values are around 0.9 under various attacks, while the BER values are very close to 0. These experimental results show that the proposed algorithm is more robust than the existing zero-watermarking methods, which indicates it is more suitable for medical image privacy and security protection.

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 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.

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$^{-1/2}$.

Runoff prediction of urban stream based on the discharge of pump stations using improved multi-layer perceptron applying new optimizers combined with a harmony search

Prediction using neural networks is applied in various fields, including hydrology and water resource management. In the learning process, an optimizer is used to determine the relationship (weights and biases) between the input and output data to lower the value of the loss function. Existing optimizers rely absolutely on the relationship that are initially generated and have the probability to converge to a local optimum. Additionally, since there is no structure for storing information about the previously generated correlation, there is a probability that the optimal weights and biases could not be found even when learning proceeds. It is necessary to apply a meta-heuristic optimization algorithm that can consider both global/local search and has a structure that can store the previously generated solution. In this study, a new optimizer was combined with a harmony search (HS), to improve existing optimizers. To test the performance of the improved multi-layer perceptron using the new optimizer (IMLP), the runoff of the Dorim stream in Seoul was predicted. The rainfall and the discharge of pump stations were constructed as input data, and data preprocessing was performed by normalization and correlation coefficients. The IMLP showed improved accuracy and could be used to manage urban streams.

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.

Development of the Normalization Method for the Jagiellonian PET Scanner

This work aims at applying the theory of the component-based normalization for the Jagiellonian PET scanner, currently under development at the Jagiellonian University. In any Positron Emission Tomography acquisition, efficiency along a line-of-response can vary due to several physical and geometrical effects, leading to severe artifacts in the reconstructed image. To mitigate these effects, a normalization coefficient is applied to each line-of-response, defined as the product of several components. Specificity of the Jagiellonian PET scanner geometry is taken into account. Results obtained from GATE simulations are compared with preliminary results obtained from experimental data.

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.