氘核削裂反应理论研究及其进展

氘核削裂反应作为单核子转移反应的一种,在原子核的单粒子结构研究中一直起着重要的作用.同时,作为典型的三体核反应,它也是直接核反应理论研究的一个重要研究对象.本文简述了氘核削裂反应的研究历史,侧重介绍其反应理论的演进,以及平面波玻恩近似(Plane Wave Born Approximation,PWBA)、扭曲波玻恩近...     

The break-up of the deuteron and stripping to unbound states

We treat the break-up of the deuteron in the field of a heavy nucleaus. Our theory is based on the post formalism of the DWBA, which is discussed in detail. In particular we consider the case where the energy of the incoming deuteron is below the Coulomb barrier. This sub-Coulomb break-up permits a test of the DWBA by comparing experimental data with the theory. Small effects are investigated in this context, and other treatments of this process are reviewed critically. To give an intuitive picture of the break-up process we introduce a semiclassical model.In the second part the theory is extended to stripping reactions to unbound (resonant) states. We show that this reaction which interferes with the direct break-up process, can again be well described in the post-form of the DWBA. Using simple models we discuss the most important features of such reactions. Particular attention is paid to the “l-enhancement”, “parallelism” and the influence of the specific wave functions on resonance line shapes. A survey and comparison of various theories of stripping reactions to unbound states is given and finally we discuss possible future developments.     

Would the peak value of the electromagnetic quadrupole form factor of the deuteron determine the percentageD-state?

It is shown that short range unitary transformations on the deuteron wave function of the super-soft-core potential of de Tourreil and Sprung, which fix the percentageD state of the deuteronP _D, do not simultaneously fix the peak valueM of the electromagnetic quadrupole form factor of the deuteron within small error bars, even when the transformed wave functions are required to fit the quadrupole moment and the electric form factor of the deuteron within narrow limits. However there is a strong correlation betweenP _D andM ² for realistic interactions whose deuteron wave functions are suppressed at short distances.     

On the validity of dwba for deuteron stripping: (I). The Mitra three-body model

Previous work showing that there exists an exact formulation of the DWBA for stripping in the S-wave, separable potential, three-body model of Mitra is discussed and extended. The one-body equation obeyed by the c.m. wave function used in the reformulated DWBA is derived and compared with the equation obeyed by the wave function used in the standard formulation of DWBA, viz., the deuteron elastic scattering wave function. Results obtained by other workers on application of three-body methods to direct reactions are discussed in light of the fact that an exact DWBA exists for the separable potential model.     

The origin of the spin-dependence of low energy deuteron scattering

The spin-dependence of the interaction between a deuteron and a heavy target nucleus at low bombarding energies, resulting from coupling between the deuteron elastic and (d, p) transfer reaction channels, is studied quantitatively. By use of approximate two-step distorted wave Born approximation calculations, deuteron D-state effects are easily included. In the case of a ²⁰⁸Pb target, transfer channel coupling and not the folding model spin-dependent interactions, are shown to be primarily responsible for the experimentally observed spin-dependence of the deuteron elastic scattering at sub-Coulomb barrier energies.     

An approximate three-body theory of deuteron stripping

A treatment of deuteron stripping is developed in which the three-body effects associated with deuteron break-up in the nuclear field are included explicitly. The essence of the method is the choice of a convenient discrete set of n-p eigenfunctions as a representation of the three-body continuum effects. This approach leads to a distorted wave stripping matrix element similar to that of the DWBA, except that the elastic deuteron wave is replaced by a three-body wave function given as the solution of a set of coupled two-body Schrödinger equations. The adiabatic theory of Johnson and Soper appears as the solution in a suitable first approximation. This new formalism should prove useful in the evaluation of corrections to three-body models of the deuteron-nucleus system, in particular those models in which the nucleon-target interaction is represented by a complex local optical potential.     

A study of the proton momentum spectrum from deuteron fragmentation at 8.9 GeV/c and an estimate of admixture parameters for the six-quark state in the deuteron

The momentum spectrum of protons emitted at small angles in the stripping reaction d + ¹²C → p + X has been measured at a deuteron momentum of 8.9 GeV/c. The data are described in the framework of the Glauber-Sitenko theory using the hybrid model of the deuteron wave function which includes a six-quark state. The parameters of this state are determined. A shoulder in the spectrum has been observed in the proton momenta region which kinematically corresponds to the production of a dibaryon resonance with a mass from 2.0 to 2.2 GeV.     

Deuteron form factors for the Nijmegen potentials

The deuteron form factors and tensor polarizations in elastic ed scattering are considered for four versions of the Nijmegen nucleon-nucleon potentials. The numerical deuteron wave functions in these potentials are approximated by a series of Gaussian functions with the result that it can be used in any computations of integrated characteristics. The quality of this approximation of the wave function is exemplified by comparing the results that it produces for the momentum distributions, the quadrupole moment, the D-state probability, and the deuteron radius with the results of the corresponding precise calculations.     

Deuteron size effects on its elastic scattering from1H and4He

The effect of change in deuteron size on its elastic scattering from protons and alphas is investigated by varying the Hulthen parameters of the deuteron wave function in the scattering process. The cross sections forp-d scattering, calculated in the Born approximation, are found to increase substantially at backward angles even when the deuteron size is reduced by a small amount, whereas the shape of the angular distribution does not change significantly. For theα-d elastic scattering, interaction potential is obtained by folding the deuteron wave function and the optical potential for nucleon-scattering. The cross sections calculated atE _d = 13·7 MeV, shows that the first minimum around Θ_cm = 60° is deepend as the deuteron size is reduced, while at 52 MeV bombarding energy, the size effects are not very distinct. These observations are useful in the interpretation of deuteron cluster knockout reactions.     

Polarization transfer in deuteron stripping reactions

Polarization phenomena involving the spins of a and b in the A(a, b)B reaction are discussed using a complete set of irreducible tensors carrying definite spin transfer. The linear model independent equations relating the cross section and the polarization observables with these tensors are shown to be particularly appropriate for the study of spin dependent interactions, preferentially associated with particular values of spin transfer. The DWBA theory of polarization transfer in deuteron stripping reactions is thoroughly discussed and among the 17 polarization observables we distinguish those likely to be more sensitive to spin dependent distortion, to have stronger deuteron D-state effects, to exhibit the sign-rule j-dependence and other forms of j-dependence. For certain deuteron polarizations, when the spin transfer is pure $\text{s =}\text{1}\text{2}$, it is shown that deuteron stripping reactions are transparent to vector polarization transfer and the outgoing nucléon polarization independent of scattering angle and deuteron energy. DWBA calculations including contributions from spin transfer $\text{3}\text{2}$ through the deuteron D-state and spin-orbit distortion show that polarization transfer in such deuteron polarizations can be explored as a method of producing fast polarized neutrons with known polarization.     

The 13C(p̄, d)12C reaction at 119 MeV

Differential cross sections and analysing powers for transitions to many residual states of ¹²C below 20 MeV excitation energy have been measured for the (p̄, d) reaction on ¹³C at 119 MeV. Distorted wave Born approximation calculations using either adiabatic or conventional deuteron elastic scattering potentials were unable to adequately reproduce the cross-section and analysing power data for the strongest observed transitions. In order to improve the fits to both these sets of data it was necessary to include an imaginary spin-orbit term in the deuteron potential. The spectroscopic factors deduced in this analysis are, however, smaller than theoretical predictions. The mechanisms for the population of the observed weak residual states are discussed semi- quantitatively, and for the higher excitation energy region, a comparison to the known level structure of ¹²C is made.     

Three-Dimensional Low-Momentum Interaction in Two-Body Bound State Calculations

The deuteron binding energy and wave function are calculated by using the recently developed three-dimensional form of low-momentum nucleon–nucleon (NN) interaction. The homogeneous Lippmann–Schwinger equation is solved in momentum space by using the low-momentum two-body interaction, which is constructed from Malfliet–Tjon potential. The results for both, deuteron binding energy and wave function, obtained with low-momentum interaction, are compared with the corresponding results obtained with bare potential.     

Scattering of deuterons by nuclei with breakup effects

The deuteron direct-breakup reaction is explicitly incorporated into the d + nucleus formulation of model K which is a simplified version of the microscopic resonating-group method. By employing the same nucleon-nucleon potential as that used in the corresponding nucleon + nucleus system and by adopting an imaginary potential with a single adjustable parameter to crudely represent other reactions not explicitly included in the formulation, it is shown that a good agreement between calculated and experimental differential cross sections can be obtained for deuteron scattering by a wide variety of target nuclei, ranging from ²⁸Si to ²⁰⁸Pb. In addition, the results also indicate that the deuteron breakup reaction is a significant, but not dominant, reaction in the d + nucleus system. To make model K into a truly microscopic model without any phenomenological imaginary potential, one must further explicitly include the (d, p) and (d, n) one-nucleon-transfer or stripping reactions into the model-K formulation.     

Medium energy cluster knock-out reactions on 6Li and their interpretation in terms of distorted waves

The ⁶Li(d, 2d)⁴He and ⁶Li(d, dα)²H reactions were performed at 27 MeV. Analyses of these and the 42.8 and 55 MeV ⁶Li(α, 2α)²H reactions were performed using distorted wave and plane wave impulse approximations. The kinematic and potential coupling approximations to final state three-body Schrödinger equation and the post and prior form approximations to off-shell scattering cross section were studied for the three reactions. It was found that only the kinematic coupling and post form approximations could be used for the consistent analyses of the three reactions. The effects of distortions and localization of the reactions were investigated. Manifestations of deuteron cluster deformation were noticed in the analyses of the three reactions.     

Possible interpretation of the „anomalous“ behaviour of the proton spectrum at 0° from the deuteron fragmentation at 9 GeV/c

The momentum spectra of protons, produced at 0° as a result of fragmentation of relativistic deuterons on nuclei, are analyzed. Possible causes of the existing discrepancy of the data on the 0° proton spectrum from the¹ H(d,p)X reaction at 9.1 GeV/c with results of the impulse approximation calculations are considered. It is shown that taking into account the finite angular resolution of the experimental setup and the corresponding renormalization of the experimental data, on the one hand, and also the inclusion of the additional (to stripping) contribution of protons from the scattering of deuteron nucleons by target protons, on the other, make it possible to match these data with the results of calculations within the framework of the relativistic impulse approximation using the deuteron wave function for the Paris potential.     

Continuum-discretized coupled-channels calculations for three-body models of deuteron-nucleus reactions

The formalism and results of truncated coupled channels evaluations of three-body models of deutron-induced nuclear reactions are reviewed. Emphasis is placed on breakup, elastic scattering and stripping. The relations of the coupled channels method to the Faddeev method, the adiabatic approximation and the distorted wave Born approximation are discussed extensively. Although the adiabatic approximation is seen to be excellent for the wavefunction in the elastic channel, it significantly underestimates the contributions of breakup states in stripping. Significant effects are associated with coupling to relative l = 2 breakup states.     

On the variable-charge Coulomb-projected Born approximation

Total cross-sections for electron impact excitation of 1¹ S – 2³ S transition in helium have been calculated using variable-charge Coulomb-projected Born approximation and also using a distorted wave model in which the prior form of theT-matrix is used. The comparison of the two sets of results enables us to make certain observations about the suitability of the variable-charge Coulomb-projected Born approximation.     

在巴黎势的波函数中氘核的形状因子A(Q~2)(英文)

在非相对论的框架内和应用描述了高动量过程的巴黎势所产生的氘核的波函数,计算了氘核的电磁形状因子A(Q~2)。A(Q~2)因子化为氘核的结构函数Z(t)和偶极形状G_D(t)之积。结构函数Z(t)是用巴黎势的波函数做数值计算而得到的。对A(Q~2)的预言跟实验数据的分析非常一致,这一对实验结果的成功描述说明:氘核形状因子A(Q~2)这一简单的理论描述是非常成功的,并且可以用到氘核的其他静态性质的研究。