π Meson interaction on He at 120, 145 and 165 MeV

The total cross sections and the differential cross sections of π⁺-⁴He elastic and inelastic reactions at E_π=120, 145 and 165 MeV have been measured using a 38 cm diffusion cloud chamber in a magnetic field exposed to the Frascati Laboratories' pion beam. Total π⁺ track lengths of (2141 ± 10) × 10³ cm, (3435 ± 10) × 10³ cm and (2413 ± 10) × 10³ cm were measured at the three considered energies, respectively. The elastic cross-section data are in good agreement with the results of the Dubna-Torino collaboration. The total inelastic cross sections have been obtained taking into account the contributions from all the inelastic channels. The analysis of the various inelastic processes has allowed us to distinguish five main reaction mechanisms, which compare reasonably with the existing data and with the models for pion-light-nuclei interactions.     

12C+13C在库仑位垒以下能区的熔合截面测量

深垒下能区的12C+13C熔合截面测量对检验天体中熔合反应外推模型具有很重要的意义。目前在库仑位垒以下能区存在的各种测量结果,都利用了统计模型来修正得到熔合截面,但对于这些方法间的系统误差仍没有很好地研究。实验采用离线活度测量的方法,在E_c.m.=4.4～5.8 MeV能区内对12C+13C熔合截面进行测量。经Hauser-Feshbach统计模型对分支比的修正后,熔合总截面由24Na活度推导出。通过本实验数据与其它实验方法获得的数据进行比较,确定了统计模型的系统误差为14%。The study of fusion reactions of 12C+13C at the deep sub-barrier energies is very important for the test of predictive power of the extrapolation models for nuclear reactions for astrophysics. Until now, all the measurements below Coulomb barrier energies have to use the statistical model calculations to estimate the branching ratios to deduce the total fusion cross sections. However, the systematic uncertainty induced by the calculated corrections has not been studied well. In this experiment, the fusion cross sections of 12C+13C have been measured using an offline activity measurement in the range of E_c.m.=4.4 to 5.8 MeV. The total fusion cross sections have been deduced from the 24Na activities after correcting the branching ratios estimated with the Hauser-Feshbach statistical model. Through the comparison between our result and other data obtained with other methods, the systematic uncertainty of statistical model has been determined to be 14%.     

A Study of Intermediate Energy Proton-^16O Elastic Scattering Based on the α-Particle Model

In the framework of KMT multiple scattering theory, an optical potential for the intermediate energy proton-160 elastic scattering is presented based on the α particle model of 160. The differential cross sections, the analyzing powers, and the total cross sections of the intermediate energy proton-160 scattering have been calculated by using the obtained optical potential. The main features of the measured angular distributions of the cross section and the analyzing power can be well described. The calculated total cross sections are in good agreement with the experimental data at energies below 0.7 GeV and underestimate the data about 8% at higher energies.     

Analysis of Neutron Double-Differential Cross Section of n＋^14N at 14.2 MeV

Abstract By using a new reaction model for light nuclei, the double-differential cross section of n ^14N reactions at En=14.2 MeV has been analyzed. In the case of n ^14N reactions, the reaction mechanism is very complex, there are over one hundred opened partial reaction channels even at incident energy En=14.2 MeV. In this paper the opened reaction channels are listed in detail. With LUNF code the model calculation is performed to analyze the doubledifferential cross sections of total outgoing neutron. The calculated results agree fairly with the experimental data. The results indicate that the pre-equilibrium mechanism dominates the whole reaction processes, and the recoil egect in light nuclear reactions is essentially important. 5He emission has been considered, but it is only a small contribution to thedouble-differential cross section at incident energy En=14.2 MeV.     

THE STUDIES OF NON-RUTHERFORD BACKSCATTERING CROSS SECTIONS OF 4He FROM 16O

In this article, we report the 170° backscattering cross sections of ⁴He from ¹⁶O in the energy range of 2.0-9.0 MeV. Our measurements show that the alpha-oxygen scattering remains Rutherford scattering up to E_α=2.35 MeV, and there exist two energy regions, namely 5.55-5.85MeV and 8.50-8.80MeV, where the cross sections are enhanced and show a smooth variation. The measured laboratory cross sections are 9.50-9.97 and 35.0-33.0 times greater than the Rutherford values, respectively. In the 8.50-8.80MeV region, the cross sections at scattering angles of 160°, 165°, 170° and 175° were measured and found to be strongly angle-dependent. A most strong resonance occurred at 7.60 MeV, where the cross section is 200 times of its Rutherford value. This resonance has been used to measure the ¹⁶O concentration on a Cu surface, with a sensitivity of 1×10¹⁵ oxygen atoms/cm², Besides, we have studied the backscattering angle dependence of the threshold energy, i.e., the energy at which the elastic cross section begins to deviate from its Rutherford value. The experimental result seems not in agreement with the prediction made from the analytical formula developed by Bozoian et al.     

Folding Model Analysis of Elastic Scattering of 11B from Light,Medium, and Heavy Nuclei

The elastic scattering angular distributions of ¹¹B projectile on light, medium, and heavy target nuclei including ⁷Li, ⁹Be, ¹²C, ¹⁶O, ^24,25,26Mg, ²⁷Al, ²⁸Si, ⁴⁰Ca, ⁵⁸Ni, ⁵⁹Co, ⁶⁰Ni, ¹⁹⁷Au, ²⁰⁸Pb, and ²⁰⁹Bi have been analyzed at various incident energies. The theoretical results have been obtained by using two different nuclear potentials within the framework of the optical model (OM). Firstly, the double folding potential for real part and the Wood-Saxon (WS) potential for imaginary part have been applied. Secondly, the calculations with double folding potential for both real and imaginary part have been performed and compared with the experimental data. It has been seen that the results are in very good agreement with the experimental data. Also, the volume integrals and cross-sections for each reaction have been obtained. Finally, a new and simple formula for the imaginary potential depth has been derived to clarify the nuclear interactions of ¹¹B nucleus at low energy reactions.     

Improved isospin dependent quantum molecular dynamics model and its application to fusion reactions near Coulomb barrier

The isospin dependent quantum molecular dynamics model is developed by introducing switch function method which deals with correctly the surface interaction and shell effect in the process of projectile and target approaching. The fusion excitation functions for ⁴⁰Ca + ⁴⁰Ca, ⁴⁰Ca + ⁴⁸Ca and ⁴⁸Ca + ⁴⁸Ca at energies in the vicinity of the Coulomb barrier are studied. The experimental data of the fusion cross sections for these three systems can be regenerated very well. It is found that the fusion cross sections for neutron-rich system increase obviously. The static and dynamical Coulomb barriers are studied in order to clarify the phenomena. The neutron to proton ratio (N/Z ratio) at neck region is also studied, which apparently presents isospin effects of projectile-target combinations.     

The elastic and inelastic scattering of intermediate energy protons on deuterium at small momentum transfer

The differential cross sections for the elastic and inelastic scattering of protons on deuterium have been measured for scattering angles less than 14° at 198.5, 297.6 and 456.6 MeV. These quantities were determined relative to dσ / dΩ for pp elastic scattering with a precision of typically 2%. The range of excitation energies for the (p, p') reaction was chosen to emphasize the region near the np threshold dominated by the final-state interaction in the ¹S₀ channel. Particular attention was given to the dependence on excitation energy of the spectra at 198.5 MeV to examine the sensitivity to the ¹S₀ scattering length, a_np In this paper all data are compared with a new, detailed formulation of a simple model of the reaction mechanism based on the impulse approximation. The experimental results differ from the predictions by typically 10% and the differential cross sections exhibit a sensitivity to the intermediate-energy nucleon-nucleon amplitudes. If the impulse approximation is used to estimate a_np from the data at 198.5 MeV a value of − 24.7 ± 0.4 fm is obtained.     

A comparison of the He(p, 2p)d and He(p, pd)p reactions

The ³He(p, 2p)d and ³He(p, pd)p reactions have been compared at three bombarding energies from 65 to 100 MeV. A comparison of plane wave impulse approximation calculations to the experimental data indicates that multiple scattering effects are large and energy dependent but that they primarily produce a uniform reduction in cross section. Although multiple scattering effects are large the ratio of the cross sections for the two reactions is in agreement with that predicted by the impulse approximation.     

Coulomb and photo cross sections for nucleon emission from relativistic O projectiles

Coulomb cross sections for nucleon emission out of ¹⁶O projectiles scattered with laboratory energies of 2.1, 60 and 200 GeV/nucleon on various target nuclei are calculated in first-order perturbation theory by using the corresponding photo cross sections. The photo cross sections are obtained with an 1-particle-1-hole basis in the giant resonance region and with the quasi-deuteron model up to photon energies of 140 MeV. Whereas the 2.1 GeV/nucleon results agree well with the experimental data points, the 60 and 200 GeV/nucleon cross sections are roughly one quarter lower than the measured ones, because also photons with energies higher than 140 MeV contribute at these incident energies.     

Nuclear reactions between oxygen isotopes

Elastic and inelastic cross sections have been measured for the system ¹⁶O + ¹⁷O at c.m. energies from 12.5 to 15.5 MeV, and for ¹⁶O + ¹⁸O at c.m. energies from 12 to 20 MeV, at angles between 60° and 125°. Position-sensitive detectors were employed, using the kinematic coincidence technique. The data have been analyzed with particular attention to the contributions of multiple-exchange processes.     

核子-核子碰撞截面的参数化公式

核子-核子碰撞截面(σ_NN)是描述原子核反应模型中的重要物理量。 核子-核子碰撞截面包括质子-质子碰撞截面（σ_pp）、中子-中子碰撞截面（σ_NN）和中子 质子碰撞截面（σ_np）, 它们随着核子能量与核物质密度的改变而变化。人们在目前研究中提出了多种核子-核子碰撞截面关于能量和核物质密度的参数化公式,通过计算12C+12C的完全反应截面,比较了不同入射能量下使用各种核子-核子碰撞截面参数化公式对12C完全反应截面的影响。 The nucleus-nucleus cross sections(σ_NN) include the proton-proton cross section, neutron-neutron cross section, and neutron-proton cross section. σ_NN change with the variations of the incident energies and the densities. Some parameterizations of σ_NNas a function of incident energy and density have been proposed in the theoretical and experimental study of nuclear reactions. Through the calculation of reaction cross sections of 12C+12C at different energies, the effect of different σ_NN parameterizations in the reaction cross sections of 12 are studied.      

Cross sections for several (n, 2n) reactions at 14 Mev

Precision measurements of the cross sections of the (n, 2n) reactions to produce ^44mSc, ⁸⁸Y, ⁸⁹Zr, ⁹²Nb, ¹⁵⁰Eu(35y), ¹⁶⁸Tm, ^174m+gLu and ¹⁹⁶Au were made for a range of neutron energies from 13.7 to 15.0 MeV. The samples were irradiated at various positions on the surface of a 20 cm radius sphere centered at the ²H–³H neutron source. This allowed a range of neutron energies to be obtained with good energy resolution. The ²⁷Al(n, )²⁴Na reaction was used to monitor the neutron fluence in the target samples. Particular attention was given to the accurate measurement of the (n, 2n) products, using calibrated Ge(Li) and NaI(Tl) detectors. An uncertainty of about ±5% is assigned to the results, except those for ¹⁵⁰Eu and ¹⁷⁴Lu, which have an additional uncertainty in their decay schemes.     

Photoproduction of positive pions from hydrogen with PHOENICS at ELSA

The differential cross section of the reaction γp→π⁺n has been measured with the PHOENICS detector at ELSA in Bonn. For the first time this cross section has been determined simultaneously over a large range of photon energies (E_γ = 220−900 MeV) and pion angles (Θ^c.m._pi = 35°−135°) with a tagged photon facility. The experimental set-up allowed a considerable kinematic overdetermination of the investigated reaction. Accordingly, the background contributions have been suppressed to below 1%. The measured differential cross section is in good agreement with existing data. The comparison with different model calculations is presented.     

p+56Fe散裂反应中同位素产生截面的规律现象

提出一个经验公式,预测散裂反应中同位素产生的截面值,并且利用现有GSI-FRS实验测量的300,500,750,1 000和1 500 MeV/u能量下p+56Fe散裂反应产物的实验结果进行验证。发现此经验公式预测的同位素截面值与实验值的符合度比较好,但随着质量数与能量的改变,同位素产生截面的计算值与实验值的差距也在变大。通过引入质量与能量修正可使此经验公式计算出的同位素截面值的精确度更高,与实验值的符合程度更好。An empirical formula is proposed to predict the isotopic cross section in spallation reactions. The measured fragments in the 300, 500, 750, 1 000 and 1 500 MeV/u p+56Fe spallation reactions have been adopted to perform the analysis. The cross sections of isotopes predicted by the proposed empirical formula have been compared to the experimental results, which shows that the empirical formula can predict the results well. But with the change of the mass and incident energy, the difference between the calculated results and experimental data is larger. The proposed empirical formula is found to predict the isotopic cross sections better, by incorporating the incident energy and mass dependents of fragments.     

The two-neutron transfer reactions (O, O) with O, C and Mg targets

Excitation functions, angular distributions and differential ranges were measured for the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction at ¹⁸O beam energies of 20–45 MeV. Excitation functions only were measured for the reactions ¹⁴C(¹⁸O, ¹⁹O)¹³C, ¹⁴C(¹⁸O, ¹⁶O)¹⁶C, ¹⁴C(¹⁸O, ²⁰O)¹²C, ¹⁴C(¹⁸O, ¹⁵N)¹⁷N and ¹⁸O(¹⁸O, ¹⁹O)¹⁷O, ¹⁸O(¹⁸O, ¹⁶O)²⁰O, ¹⁸O(¹⁸O, ¹⁵N)²¹F at ¹⁸O beam energies of 13–41 MeV. We have identified these as direct reactions in which a single neutron, a two-neutron cluster, a deuteron and a triton are transferred between projectile and target.

The cross sections for two-neutron transfer reactions were found to be relatively high and those for the ¹⁸O+¹⁸O and the ¹⁴C+¹⁸O reactions were higher than the ones of single-neutron transfers over most of the energy range.

Attempts were made to apply the theory of Buttle and Goldfarb for single-neutron transfer to the case of two-neutron transfer in the ²⁶Mg(¹⁸O, ¹⁶O)²⁸Mg reaction below the Coulomb barrier. It is shown that for those reactions for which the assumptions, implicit in the model, are valid, good agreement is obtained with experiment. We also tried to apply the diffraction model of Dar and Kozlovsky to the calculation of the angular distribution of these reactions. A good fit to the experimental results could be obtained if quite different sets of parameters were used in the calculations for the two bombarding energies.     

Optical potential approach for positron scattering by metastable 2~3S state of helium

The momentum space coupled channels optical(CCO) method for positron scattering has been extended to study the scattering of positrons by metastable helium for impact energies in the range from the positronium threshold up to high energies. Both the positronium formation and ionization continuum channels are included in the calculations via a complex equivalent local potential. The positronium formation, ionization, elastic and 2~3S–2~3P excitation, and total scattering cross sections are all presented and compared with the available information.     

Double-Differential Cross Section of 5He Emission

The probability of ⁵He particle emission has been affirmed theoretically [J.S. Zhang, Science in China G47 (2004) 137]. In order to describe the ⁵He emission, the theoretical formula of the double-differential cross section of emitted ⁵He is to be established. Based on the pick-up mechanism, used for calculating the formula of d, t, ³He, α emissions, the theoretical formula of double-differential cross section of ⁵He is obtained, which is expressed in the form of Legendre coefficients. In the case of low incident energies, the configuration [J.S. Zhang, Science in China G47 (2004) 137; J.S. Zhang, Commun. Theor. Phys. (Beijing, China) 39 (2003) 83] is the dominant part in the reaction processes. The calculated result indicates that the forward peaked angular distribution of the composite particle emission is weaker than that of the emitted single nucleon due to pick-up nucleon from the Fermi sea. As an example, the reactions of n+¹⁴N have been calculated, and the Legendre coefficients of d, t, ³He, α, ⁵He emissions are obtained respectively. The results show that the forward tendency is decided by the average momentum per nucleon in the emitted composite particles. The larger the average momentum is, the stronger the forward tendency is.     

轻奇特核结构中的核心激发--以11Be为例

近年来,越来越多的实验表明,很多轻奇特核结构中都有核心激发成分。本研究以丰中子晕核11Be为例,介绍核心激发成分的实验和理论研究进展,重点阐述核心激发成分对直接核反应微分截面的影响。实验上,1n移除反应及11Be（p,d）和10Be（d,p）转移反应是测量11Be核心激发成分比例的典型实验类型。理论上,发展了能够包括11Be核心激发成分的Faddeev AGS方法,XDWBA方法以及XCDCC方法。加入核心激发成分后,这些模型的计算结果可以更加合理地描述11Be在各种靶上的弹性散射和碎裂微分截面。通过对比是否包含核心激发成分的计算结果,发现其影响主要体现在弹散微分截面的大质心系角度,以及（p,d）转移反应角分布的小质心系角度。另外,对E_x=0:5s3 MeV的激发能区的碎裂反应,核心激发的影响不可忽略;对E_x=3s5:5 MeV的碎裂反应,核心激发的贡献非常重要。It was found that many light exotic nuclei have the core-excitation components. In this paper, taking one-neutron halo nucleus 11Be for example, the experimental and theoretical research progress, as well as the influences on the direct nuclear reaction differential cross sections of this exotic component were reviewed. The 1n removal, 11Be(p, d) and 10Be(d, p) transfer reactions are typical experimental methods to investigate this component. The Faddeev AGS, the XDWBA, and the XCDCC methods are developed to include this constituent in various theoretical models. With the core-excitation component, the calculated results can more reasonably describe the elastic scattering and breakup differential cross sections of 11Be impinging on various targets. Comparing the full XCDCC calculation with that omitting core-excitation effect, we found that this component mainly affects the elastic scattering differential cross sections at large center-of-mass angles, and the (p, d) transfer reaction angular distributions at small center-of-mass angles. In addition, its effect is non-negligible for the breakup reaction within the excitation energy interval of E_x = 0:5~3 MeV, and is remarkable for E_x =3 5:5 MeV.