Study of form factors for single-proton transfer reactions on152Sm,154Gd and156Gd

The (³He,d) and (α,t) single-proton transfer reactions on targets of¹⁵²Sm,¹⁵⁴Gd and¹⁵⁶Gd were studied at 35MeV incident energy. Differential cross sections of rotational states built upon various single-proton configurations are compared with results of DWBA calculations which employed various radial form factors. The agreement between calculated and measured reaction cross sections is found to improve significantly when the commonly used spherical bound-state potentials are replaced by deformed ones, including deformed Coulomb and spin-orbit wells, and projected form factors are used to calculate DWBA cross sections. Discrepancies in the differential cross sections so large that they cannot be attributed to band mixing phenomena are readily explained by form factor effects.     

Hyperon-Neutron Elastic Scattering

It is shown that the Chou-Yang model can be extended to hyperon-neutron elastic reactions at high energies by assuming that the hadronic form factor of neutron is proportional to its magnetic form factor. It is also predicted that the scaling of magnetic form factor of neutron with charge as well as magnetic form factors of proton implies that the differential cross sections of corresponding hyperon-proton and hyperon-neutron reactions should be equal.     

Role of the nuclear surface in the formation of total cross sections for heavy-ion reactions

Within the Glauber-Sitenko approach, a procedure for calculating cross sections for intermediate-energy heavy-ion reactions is developed by using the analytic form of the eikonal phase for the symmetrized Woods-Saxon potential. The differential and total cross sections obtained on this basis comply well with the results derived by numerically solving the wave equation. A clear and instructive model of the phase is constructed, which makes it possible to separate, in total reaction cross sections, the contributions of the internal and the peripheral region of interaction. It is found that the nuclear surface plays an important role in the formation of reaction cross sections, and the effect of the Coulomb field on these cross sections is investigated. The origin of a continuous ambiguity in optical potentials is revealed in interpreting total cross sections.     

Exact finite range calculations of light-ion induced two-neutron transfer reactions

Exact finite-range (EFR) distorted-wave Born approximation calculations were performed for light-ion induced two-neutron transfer reactions, by using a technique to calculate the form factors rather fast. The use of this method made it possible to carry out calculations even when realistic light-ion wave functions and multi-configurational two-neutron wave functions were used and large transferred angular momenta were considered. It was found that, at lower bombarding energies, the predictions of the EFR and zero-range calculations agree very closely both in angular distributions and relative magnitudes of the cross sections, though they differ significantly in absolute magnitude. As the bombarding energy increases, the discrepancy between the predicted absolute magnitude becomes still larger, and noticeable differences are seen even in relative cross sections. For all the energies considered, the EFR calculations predicted the absolute magnitudes of the experimental cross sections to within a factor of several units.     

Cross sections for charmonia dissociation in collisions with pions, rhos and kaons

We calculate the unpolarized cross sections for dissociation reactions of charmonia in collisions with π,ρ and K in a potential that is derived from QCD.The reactions are governed by the quark-interchange processes.The mesonic quark-antiquark relative-motion wave functions are determined by the central spinindependent terms of the potential.The numerical wave functions and cross sections are parametrized.The difference of transition amplitudes in the prior form and in the post form is explored by deriving and examining the transition amplitudes of the one-gluon-exchange spin-spin term of the potential in the two forms.We find that the post-prior discrepancy in meson-meson elastic scattering that is governed by quark-interchange processes depends on the difierence of quark or antiquark masses and of quark-antiquark spatial distributions ofthe two mesons.     

Microscopic form factor for DWBA analysis of light-ion induced three-nucleon transfer reactions

A modified zero-range distorted-wave Born approximation calculation was performed for the (p, α) reactions. The form factor is calculated by a first method, which is an extension of the Bayman and Kallio method to extract the relative l = 0 part of two-nucleon shell-model wave functions. The method includes some of the range effects so that one can predict the absolute magnitudes of the cross sections. A second method in finite range involves the ³He cluster expansion of the α-particle where the known (³He, α) transfer normalization may be used to estimate the absolute cross sections. The ¹¹⁸Sn(p, α)¹¹⁵In reactions are analyzed using the hole-vibration coupling model for ¹¹⁵In. The shapes of the experimental cross sections and the analyzing powers can be fitted by the calculations but the magnitudes of the cross sections are predicted to be too small.     

What kind of optical model potentials should be used for deuteron stripping reactions?

This paper presents the results of a study that compares CTOM, a microscopic optical model potential(OMP), which is an optical model co-created by the China Nuclear Data Center & Tuebingen University, to CH89, which is a typical phenomenological OMP.The respective OMPs were tested by applying them to the modelling of nucleon elastic scattering and(d,p) transfer reactions involving14C,36S, and58Ni targets at both low and relatively high energies. The results demonstrated that although both potentials successfully accounted for the angular distributions of both the elastic scattering and transfer cross sections, the absolute values of the transfer cross sections calculated using CTOM were approximately 25% larger than those calculated using CH89. This increased transfer cross sections allowed CTOM to produce single particle strength reduction factors for the three reactions that were consistent with those extracted from(e,e′p) reactions as well as with more recent(p,2p) and(p,pn) reactions. Notch tests suggested that nucleon elastic scattering and transfer reactions are sensitive to different regions of the OMP;accordingly,phenomenological OMPs, which are constrained only by elastic scattering cross sections, may not be sufficient for nucleon transfer reactions. Therefore, we suggest that microscopic OMPs, which reflect more theoretical considerations, should be preferred over phenomenological ones in calculations of direct nuclear reactions.     

Fusion and transfer reactions in beams of light loosely bound nuclei at energies in the vicinity of the Coulomb barrier

Experiments devoted to studying cross sections for fusion and transfer reactions induced by the interaction of beams of halo-like (⁶He), cluster (⁶Li and ⁷Li), and loosely bound (³He) nuclei with nuclei of light and heavy elements are described. The cross sections obtained experimentally for such reactions are analyzed. Special features in the behavior of the cross sections for the formation of evaporation residues and products of transfer reactions at energies in the vicinity of the Coulomb barrier are revealed. In particular, an increase in the cross sections for fusion and transfer reactions involving halo-like nuclei and proceeding at energies in the subbarrier region is observed. The cross sections for neutron-transfer and light-cluster-transfer reactions reachmaximum values at an energy in the vicinity of the Coulomb barrier for the reaction being considered.     

A comparison of absolute cross sections for electro- and photo-induced reactions

Absolute cross sections for electron and positron induced reactions on¹²C,⁶³Cu and¹⁰⁷Ag are compared with cross sections for the corresponding photo-induced reactions in order to test DWBA calculations of the virtual photon spectra. A good agreement is found between the experimental cross sections for the electrodisintegration and those calculated with DWBA spectra and photonuclear cross sections.     

The analysis of proton- and deuteron-induced-reaction cross sections on tin isotopes at the beam energy of 3.65 GeV/nucleon

The total inelastic cross sections of the reactions of protons and deuterons on nuclear targets of enriched tin isotopes are compared. The factorization of cross sections of reactions is discussed. Furthermore, the comparison of theoretical estimations on total inelastic cross sections with corresponding experimental ones is made.     

Near-barrier transfer and fusion of the systems33S +90,91,92Zr

Double differential cross sections of all prominent transfer channels have been measured in the systems³³S +^99,91,92Zr at two energies close to the nominal Coulomb barrier. In addition the fusion excitation functions of these systems have been measured below and around the barrier. The angular- andQ-distributions of the most important transfer reactions have been analysed in the framework of a simple semiclassical formalism. Particularly the two-nucleon transfer angular distributions exhibit strong multi step coupling effects which manifest themselves in reduced cross sections at large angles corresponding to close distances. From the angular distributions at forward angles, where a single step character of the transfer reaction can be assumed, approximate form factors have been extracted employing a first order perturbation theory. Within the uncertainties of a schematic coupled channels calculation the isotopic differences of the sub-barrier fusion enhancement can be understood on the basis of the isotopic differences of the transfer form factors andQ-values.     

Neutron inelastic scattering from 40Ca at 21.7 and 25.5 MeV

Differential cross sections for the scattering of neutrons from ⁴⁰Ca for states up to 5 MeV excitation energy have been measured at 21.7 and 25.5 MeV. The analysis is done using a coupled channel formalism in terms of a vibration collective model. The results using a usual standard Woods-Saxon form factor for the transitions are compared with those obtained using form factors derived from a model-independent analysis to the elastic cross sections.     

Stripping cross sections in collisions of light nuclei

By evaluating all the contributions of the intermediate states of the multiple scattering theory diagrams, we compute the integrated stripping cross sections of collisions among light nuclei. The resulting expressions have the simple form of a combination of total inelastic cross sections of nuclear reactions with projectile nuclei differing in the atomic mass number. We also check the accuracy of some widely used relations in heavy ion collisions. Received: 18 March 1998     

中子与52Cr反应截面的理论分析

根据中子与天然核Cr及其同位素反应的总截面,去弹性散射截面和弹性散射角分布的实验数据,获得了入射中子能量从1MeV—250MeV的一组普适中子与Cr及其同位素反应的光学模型势参数.应用光学模型,扭曲波玻恩近似理论,宽度涨落修正的Hauser-Feshbach理论,和预平衡反应的激子模型,计算和分析了中子与⁵²Cr反应的所有截面、角分布、能谱和双微分截面.理论计算与实验数据进行了分析比较.     

Dipole resonances in the electroexcitation of the <Superscript>24</Superscript>Mg nucleus

The wave functions and form factors of E1 excited states of the deformed nucleus ²⁴Mg are obtained within the particle-core coupling version of the shell model by using spectroscopic data on direct nucleon-pickup reactions. A comparison of the calculated E1-strength distributions with experimental cross sections shows the validity of the theoretical approach used, which is based on connections between direct and resonance nuclear reactions.     

Direct reactions and Hauser-Feshbach theory

In the presence of direct reactions, the calculation of energy-averaged cross sections, polarizations, analyzing powers etc. in terms of the energy-averaged S-matrix is possible with the help of a unitary transformation U, defined as the matrix which diagonalizes Satchler's transmission matrix. For a fixed number of channels and in the limit of a very large number N of compound nucleus resonances, we show analytically that the transition from the origially given statistical scattering matrix S to the matrix reduces the Hauser-Feshbach problem with direct reactions to the one without. The analytical proof is supported by numerical calculations which show that the results are valid on the 2 to 3% level of statistical accuracy of the numerical calculations for values of N as small as 100. We also show analytically that in the absence of direct reactions, energy-averaged cross sections depend only upon the transmission coefficients. The form of this dependence as well as the dependence on the transmission coefficients of other quantities needed for the evaluation of cross sections in the presence of direct reactions, is parametrized by simple fit formulas which, while lacking theoretical support, give a very satisfactory overall representation of our numerical results.     

COMPARISON OF RAYLEIGH AND COMPTON SCATTERING IN THE PHOTON-MOMENTUM TRANSFER REGION OF 2.219 × 3.814 Å−1

Rayleigh and Compton scattering differential cross sections for Mo, Ag and Sn have been measured from 55° and 105° at 59.5 keV using an Hp Ge detector. The ratios of measured cross sections are compared with ratios of theoretical scattering cross section values calculated using nonrelativistic form factors.     

Isomeric ratios of the cross sections for Sn(p, xpyn)X reactions

In proton-nucleus reactions, the ratios of the cross sections for 18 isomeric pairs were measured by the induced-activity method as functions of the initial-proton energy and of the number of emitted nucleons. The isotopic effect and the cross sections for charge-exchange reactions are discussed. The experimental values of the cross sections for disintegration reactions like (p, xpyn) are compared with the theoretical values calculated on the basis of the cascade-evaporation model.     

Recent developments in the theory of stripping to unbound states

A comparative analysis is carried out of different approaches to the calculation of DWBA cross sections for stripping to unbound states including single-particle resonances, compound resonances and the smooth background. A relationship is derived between unbound stripping and scattering cross sections on the same target. The reliability of spectroscopic factor concepts is discussed. Numerical checks are performed with the aid of stripping form factors obtained from the solution of a coupled channels equation system.     

A scaling phenomenon for the cross section of fragment produced in projectile fragmentation reactions

A scaling phenomenon has been found for the cross section of a fragment, which is defined as a "square" cross section(SCS).This phenomenon can unify the cross sections of fragments in projectile fragmentation(PF) reactions. An empirical formula is proposed to calculate SCSfor a fragment with parameters determined by an extensive investigation of measured reactions ranging from Fermi energies to relativistic energies. The scaling phenomenon of SCShas been verified using different techniques,showing that the scaling of SCSgenerally exists in PF reactions. The concept of SCS, which can be assumed as a standard value for a fragment, is shown to accurately predict the cross sections of isotopes in PF reactions with incident energies ranging from tens of A MeV to approximately 1000 A MeV.