Transfer reactions induced by 17, 18O on 12, 13C at c.m. energies between 12.6 TO 14.0 MeV

Angular distributions for one-neutron and many-nucleon transfer reactions were measured in the systems ^{17, 18}O and ^{12, 13}C at c.m. energies between 12.6 to 14.0 MeV. All the cross sections were analyzed in terms of the full-recoil finite-range DWBA model. For multi-nucleon transfer processes an inert cluster transfer was assumed. The sensitivity of DWBA calculations to various parameter sets is discussed, and the effect of the no-recoil approximation on the phase and magnitude of the transfer amplitude is studied. For one-neutron transfer reactions the forward part of the angular distributions was reproduced reasonably well by the DWBA model, yielding satisfactory spectroscopic information. The rise of the cross section at the backward angles was not reproduced by the DWBA model. Possible contributions of cluster-exchange and compound-nucleus reactions are discussed. For multi-nucleon transfer reactions poorer fits were obtained, particularly in the ¹⁸O+¹²C system.     

Approximate recoil approach to heavy-ion induced one-nucleon transfer reactions

It is shown that a distorted wave Born approximation theory combining the Hankel function approach for the form factor with a linear recoil correction gives satisfactory results when compared to exact finite-range with recoil calculations for a large variety of heavy-ion induced one-nucleon transfer reactions. The test cases presented involve incident projectile energies in the vicinity of the Coulomb barrier as well as energies several MeV/nucleon above the barrier, strongly absorbing optical potentials as well as recently used more transparent potentials, and transfer with large recoil corrections. The exact calculations are generally reproduced with an accuracy of the order of 10%. Computing times are a factor 2 ± 0.5 larger than typical times needed for a no-recoil calculation. The limits of the method are discussed and the importance of the tails of bound states is stressed.     

Improved eikonal approach for charge exchange reactions at intermediate energies

In order to describe charge exchange reactions at intermediate energies,we implemented as a first step the formulation of the normal eikonal approach.The calculated differential cross-sections based on this approach deviated significantly from the conventional DWBA calculations for CE reactions at 140 MeV/nucleon.Thereafter,improvements were made in the application of the eikonal approximation so as to keep a strict three-dimensional form factor.The results obtained with the improved eikonal approach are in good agreement with the DWBA calculations and with the experimental data.Since the improved eikonal approach can be formulated in a microscopic way,it is easy to apply to CE reactions at higher energies,where the phenomenological DWBA is a priori difficult to use due to the lack,in most cases,of the required phenomenological potentials.     

Second-order breakup corrections to elastic deuteron-nickel scattering between 13 and 80 MeV

Breakup corrections to the elastic scattering matrix elements are calculated in the second-order distorted-wave Born approximation at deuteron incident energies of 45 and 85 MeV. The effects of spin are included. The size of the corrections are found to be generally as large as those obtained in a previous study at 13 and 21.6 MeV. The breakup cross section is calculated to first order in the breakup matrix elements by a distorted-wave Born treatment. Comparison with fully coupled calculations shows that the DWBA method overestimates the breakup cross section by a factor of about three.The continuum of breakup states up to a n-p relative momentum 1 fm^?1 is included in the calculations. This continuum is discretized by subdividing it first into two bins, and then into four bins. The finer discretization does not make a large difference in either the elastic cross section or the breakup cross sections. The higher bins give only a small contribution to either quantity.     

Calculation of the indirect contribution to the heavy-ion nucleon transfer reaction amplitude

The indirect contribution to the heavy-ion nucleon transfer reaction amplitude has been evaluated using the distorted-wave Born approximation neglecting recoil effects. This contribution is usually ignored. Two different formulations of the indirect interaction were tried. One of these formulations gives a completely negligible contribution to the nucleon transfer reaction amplitude. The other gives a negligible effect for the angular dependence of the differential cross section but nevertheless produces a considerable change in the magnitude of the cross section.     

25MeV/u 6He在9Be靶上的弹性转移反应研究

报告了25MeV/u ⁶He在⁹Be靶上的弹性散射和弹性转移的实验结果. 用光学模型和一阶DWBA的方法计算了弹性散射和³He集团转移的截面, 计算结果和实验测量基本一致. 计算表明³He在⁹Be中的谱幅度应该明显大于壳模型的理论计算值0.70.     

Elastic and inelastic scattering of 185 MeV protons from 12C

The polarization of 185 MeV protons in elastic scattering and in the excitation of the 2⁺ state at 4.44 MeV and the 0⁺ state at 7.65 MeV in ¹²C has been measured in the angular region 2°–60°. Optical model calculations are performed for the elastic scattering. Angular distributions for the inelastic scattering from the 2⁺ state at 4.44 MeV and the 3^? state at 9.64 MeV are calculated in the distorted-wave impulse approximation (DWIA) as well as in the distorted-wave Born approximation (DWBA).     

A generator coordinate theory of nuclear reactions

The generator coordinate formalism is generalized to incorporate optical potentials, coupled waves, and a distorted-wave approximation. An estimate of the importance of recoil is proposed. An analytical illustrative example related to the generator coordinate DWBA is given.     

Transfer of nucleons at high relative velocities

We discuss nucleon transfer between bound states of nuclei at high relative velocities. It is shown that the tails of the internal momentum distributions of the nuclear states participating in the transition strongly influence the transfer probabilities at energies between 30–90 MeV/u. Data and DWBA calculations show an exponential decrease of the cross sections in this energy regime and we dub it TGV (Transfer à Grande Vitesse).     

Full finite-range calculation for heavy ion two nucleon transfer reactions

Finite-range full-recoil DWBA calculations have been performed for the reaction ¹²C(¹⁸O, ¹⁶O)¹⁴C. The form factor is calculated by expanding the two-nucleon overlap as a multipole series of the relaive angular momentum of the transferred nucleon pair, which turns out to converge rapidly. In this case the recoil effect does not affect the magnitudes of the cross section and the shape of the angular distribution, except for the forward angles.     

The (d, 6Li) reaction on 24Mg, 26Mg and 28Si at 35 MeV

Data for the (d, ⁶Li) reaction on targets of ²⁴Mg, ²⁶Mg and ²⁸Si have been obtained at 35 MeV bombarding energy. Angular distributions were measured for low-lying states in the residual nuclei. Zero-range distorted-wave Born approximation (DWBA) calculations have been used to analyze the data. The DWBA calculations account for the shapes of the experimental distributions reasonably well. The observation of significant population of unnatural parity states implies, however, that other transfer mechanisms may be important. The experimental spectroscopic factors are in qualitative agreement with those obtained from SU(3) theory.     

Single-nucleon transfer reactions induced by16O on14C

Angular distributions of the proton and neutron transfer reactions¹⁴C(¹⁶O,¹⁵N)¹⁵N and¹⁴C(¹⁶O,¹⁷O)¹³C leading to the ground states of the final nuclei were measured atE _lab=20, 25 and 30 MeV. A DWBA analysis was performed using the no-recoil approximation of Buttle and Goldfarb. All angular distributions, including the pronounced structures of the proton transfer arising from the fact that the final nuclei are identical, are well reproduced. The spectroscopic factor for the neutron transfer is in agreement with shell model calculations whereas the proton transfer into aj _<-state yields a value which is too high. Exact finite-range calculations do not show this discrepancy, indicating that recoil effects are important even for light targets and lower energies. Contributions of the nonnormall-transfer, however, are small.     

The (p,t) reaction on 12C, 54Fe and 208Pb at 80 MeV

Angular distributions have been measured for the low-lying levels of the residual nuclei for the ¹²C, ⁵⁴Fe and ²⁰⁸Pb(p, t) reactions at E_p = 80 MeV. The shapes of these angular distributions are generally well reproduced by the zero-range distorted-wave Born approximation (DWBA). Enhancement factors extracted from the data show that the DWBA predicts relative strengths consistent with those observed at lower bombarding energies. However, the overall empirical DWBA normalization at E_p = 80 MeV is observed to be $\text{1}\text{12}$ ($\text{1}\text{4}$) of that required at 40 MeV for ²⁰⁸Pb (⁵⁴Fe).     

Analysis of <Emphasis Type="Italic">p</Emphasis><Superscript>10</Superscript>B scattering within Glauber theory

The differential cross sections for p ¹⁰B scattering are calculated at the energies of 197, 600, and 1000 MeV within Glauber theory. The contributions of single and double collisions are taken into account in the multiple-scattering operator. The contributions of proton collisions with nucleons belonging to various (1s, 1p) shells are estimated in the single-scattering cross sections. A comparison with experimental data and with the result of calculations in the distorted-wave Born approximation (DWBA) at 197 MeV showed that the differential cross sections for p ¹⁰B scattering are adequately described in the region forward scattering angles.     

Energy dependence of the zero-range DWBA normalization of the 58Ni(3He, α) 58Ni reaction

Strong transitions in the ⁵⁸Ni(³He, α)⁵⁷Ni reaction were analyzed using both the zero-range and exact finite-range DWBA. Data considered covered a range of bombarding energies from 15 to 205 MeV. The zero-range DWBA described all data well when finite-range and non-locality corrections were included in the local energy approximation. Comparison of zero-range and exact finite-range calculations showed the local energy approximation correction to be very accurate over the entire energy region. Empirically determined D₀ values showed no energy dependence. A theoretical D₀ value calculated using an α wave function which reproduced the measured α rms charge radius and the elastic electron scattering form factor agreed well with the empirical values. Comparison was made between these values and D₀ values quoted previously in the literature.     

Square graphs in direct nuclear reactions at moderate energies

The present work contains the analysis of various reactions proceeding at relatively small projectile energies (～ 10 MeV) for which a mechanism described by the square diagram may be regarded as a dominant one. It is shown that such a mechanism may be realized both in reactions in which one or several nucleons are transferred and in reactions of nucleon or deutron inelastic scattering. Also, such an interesting property of the above diagrams is discussed as the extremely well pronounced forwardness of the angular distributions for the processes of inelastic scattering. Various variants of the theory are examined (DWBA, oscillator approximation, etc.). Formal properties of the square diagrams are also studied such as the dependence of differential cross section shape on the value of total orbital momentum transferred and the approximation on an energy surface for its calculation.     

Angular Distribution of the 12C(6He, 7Li)11B Reaction

Angular distribution of the ¹²C(⁶He,⁷Li)¹¹B transfer reaction is measured with a secondary ⁶He beam of 36.4MeV for the first time. The experimental angular distribution is well reproduced by the distorted-wave Born approximation (DWBA) calculation. The success of the present experiment shows that it is feasible to measure one-nucleon transfer reaction on a light nucleus target with the secondary beam facility of the HI-13 tandem accelerator at China Institute of Atomic Energy (CIAE), Beijing.     

Post-collision interactions and the polarization effect in （e, 2e） collisions of helium

A modified distorted-wave Born approximation (DWBA) method is used to calculate the triple differential cross sections (TDCSs) in a coplanar asymmetric geometry for the electron impact single ionization of a He (1s2) atom at intermediate and lower energies. The post-collision interaction and the polarization effect in (e, 2e) collisions of helium are considered in the calculations. The polarization potentials from the damping method and density functional theory (DFT) are compared. Theoretical results are compared with the recent experimental data.     

Analysis of the normal optical,Michel and molecular potentials on the <Superscript>40</Superscript>Ca(<Superscript>6</Superscript>Li,d)<Superscript>44</Superscript> Ti reaction

Full finite-range (FFR) distorted-wave Born approximation (DWBA) method has been applied to analyse the angular distributions of cross-sections of the ⁴⁰Ca(⁶Li, d) ⁴⁴Ti reaction at 28 MeV incident energy for the 22 transitions involving both the bound and unbound states of ⁴⁴Ti by using the normal optical, Michel and molecular potentials. The extracted spectroscopic factors for the three optical potentials are compared with those of some previous studies of zero-range (ZR) calculations of the ⁴⁰Ca(⁶Li, d) ⁴⁴Ti reaction using the normal optical potential. The χ² values of all the levels are obtained for the three optical potentials to estimate the quality of the fits. Molecular and Michel potentials have been used for the first time to analyse the four-nucleon transfer reaction and it seems that the molecular potential fits the experimental data more satisfactorily for some of the states than the normal optical and Michel potentials.