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Deuteron-induced reactions at low and medium energies: Consistent direct and statistical model analyses

C. Project description

C3. Method and approach.

The complexity of the deuteron interaction with nuclei has triggered the need to consider carefully several distinct reaction types, for which various approximations have been still widely-used so far. They are briefly reviewed hereafter, to provide a sound motivation of the concluding work plan.

C3.1 Improved Optical Model Potentials for low energy deuterons

Since no global OMP describes reasonably well the elastic scattering data in the energy range up to 20 MeV4,5,6,9,10, so that particular analysis of differential elastic scattering cross sections and reaction cross sections should provide the appropriate OMP. First, in order to reduce the phenomenological character of such analyses the semi-microscopic optical potential based on a double-folding model (DF) real part10,11,12 and phenomenological imaginary and spin--orbits terms will be involved. The parameters of phenomenological imaginary and spin-orbits terms will be determined by a fit of experimental13 elastic-scattering differential and reaction cross sections of deuterons on, e.g., 54,56,58,natFe and 58,60,61,62,natNi nuclei, using a local modified version of the computer code SCAT214. It should be emphasized that no adjustable parameter or normalization constant are involved for the real (DF) potential, in order to couple the imaginary and spin-orbit part so that the predictive power of the semi-microscopic potential is preserved.

Next, the imaginary and spin-orbit potential parameters obtained by the semi-microscopic data analysis are kept fixed within a second step of the present analysis, while the microscopic real potential is changed with a phenomenological Woods-Saxon one in order to obtain a full phenomenological OMP requested by the codes devoted to the reactions cross section calculations. The real OMP parameters are obtained from the fit of the same data base used in the first step of analysis. The advantage of having well settled already at least half of the usual OMP parameters increases obviously the effectiveness of fitting the data, similarly to the α-particle case15.

C3.2 Deuteron breakup effects on activation cross sections

The deuteron breakup (BU) mechanism is responsible for the enhancement of many reactions along the whole incident-energy range, so that its contribution to the deuteron interaction overview has to be taken explicitly into account4-8. The physical picture of the deuteron-breakup in the Coulomb and nuclear fields of the target nucleus considers two distinct chains, namely the elastic-breakup (EB) in which the target nucleus remains in its ground state and none of the deuteron constituents interacts with it, and the inelastic-breakup or breakup fusion (BF), where one of these deuteron constituents interacts with the target nucleus while the remaining one is detected.

Concerning the energy dependence of the inelastic- and elastic-breakup components, the interest of the deuteron activation for incident energies up to 30 MeV has motivated an additional check of the elastic-breakup parameterization4-7 extension beyond the energies formerly considered for the derivation of its actual form. Actually, our parameterization has been obtained from the analysis of the proton-emission spectra and angular distributions from deuteron-induced reactions on nuclei from Al to Pb at incident energies from 15 to 80 MeV, while an energy range of only 15-30 MeV was available for the empirical elastic-breakup systematics. Thus, in the absence of available experimental deuteron elastic-breakup data at incident energies above 30 MeV, the correctness of an eventual extrapolation should be checked by comparison of the related predictions with results of an advanced theory as, e.g., the Continuum-Discretized Coupled-Channels (CDCC) method16.

The elastic-breakup component is treated within the CDCC formalism as an inelastic excitation of the projectile due to the nuclear and Coulomb interactions with the target nucleus. Consideration of this excitation is performed through the coupling of the projectile unbound excited states in the solution of the scattering problem by means of the coupled channels approach. The deuteron scattering is analyzed within a three-body model, comprising the two-body excited projectile and the inert target nucleus. We performed a CDCC analysis for elastic-breakup of deuterons on 63Cu and 93Nb nuclei17 and concluded that the extrapolation of the empirical parameterization beyond 30 MeV should be done with caution. The CDCC model provides an useful guidance for the assessment of these extrapolations accuracy, so that an extended CDCC analysis on more nuclei and various incident energies is highly requested within this project in order to improve the existing phenomenological approach of elastic-breakup component.

C3.3 Stripping and pick-up processes

An increased attention should be devoted to the direct interactions very poorly accounted so far in deuteron activation cross sections analysis. For deuteron energies below and around the Coulomb barrier the interaction of deuterons with target nuclei proceeds largely through direct reaction (DR) processes, while increasing the incident energy, processes like pre-equilibrium emission (PE) or evaporation from fully equilibrated compound nucleus (CN) become also important.

Apart from the breakup contributions to deuteron interactions, the DR mechanisms like stripping and pick-up have to be properly considered in order to describe the low energy side of the (d,p), (d,n) and (d,t) excitation functions4-8. The DR contribution to the (d,p), (d,n) and (d,t) reaction cross sections, through population of the low-lying discrete levels of residual nuclei, will be calculated using the code FRESCO18, based on the Coupled-Reaction Channels (CRC) method, and post form distorted-wave transition amplitude with finite-range interaction. The n–p interaction in deuteron is described with a Gaussian potential interaction while the neutron respectively proton bound states are generated in a Woods-Saxon real potential. However, qualitative improvements can be possible in the description of d-n interaction in triton involving so far a Woods-Saxon potential19.

Actually, the (d,p) reaction has been of critical importance for the nuclear structure studies, with reference to the weaker (d,n) stripping or (d,t) pick-up reactions. Thus, the spectroscopic factors extracted from the analysis of experimental angular distributions of the corresponding emitted protons/neutrons did contribute to the validation of the nuclear shell model, taking into account that the nucleon from the deuteron is transferred to a single-particle state of the residual nucleus. Consequently, the rich systematics of the achieved experimental spectroscopic factors makes possible the calculation of almost total stripping and pick-up cross-section contribution to the deuteron activation.

A particular note should concern the (d,t) pick-up mechanism contribution to the total (d,t) activation cross section, usually neglected in spite of its unique contribution at low energies, between its threshold and the (d,dn) and (d,p2n) thresholds leading to the same residual nucleus.

C3.4 Statistical particle emission

The PE+CN reaction mechanisms less fast, completing the deuteron interaction analysis, will be considered using the related computer code STAPRE-H20. A consistent set of statistical model parameters21 should and will be validated using independent experimental data for, e.g., neutron total cross sections, proton reaction cross sections, level densities and resonance data, and gamma- ray strength functions based on neutron-capture data22. On the other hand, no free parameter is involved for the PE description within the corresponding generalized Geometry Dependent Hybrid model. However a particular comment concerns the initial configuration of excited particles (p) and holes (h) for deuteron-induced reactions. Our previous analysis5 pointed out 2p-1h initial configuration instead of the more usual 3p-1h. This point should be completely settled by further analysis of the measured and calculated cross sections obtained using various (p,h) configurations23. The comparison of various calculations, including their sensitivity to model approaches and parameters, should and will concern all activation channels for which there are measured data. Finally, the proper description of all reaction channels of deuteron incident on a specific target nucleus will be looked for in order to validate the consistent account of all reaction mechanisms involved in the deuteron interaction with nuclei.

C3.5 Particular innovative approach

Beyond other various novel items, the complexity of deuteron-breakup process and its effects on the various deuteron reaction cross sections will be additionally concerned within this project since there are so far notable deuteron-induced reaction studies24 that took into account only the statistical emission and eventually a 'reduction factor' of the compound nucleus cross section due to 'direct processes'. However, this reduction factor does not allow the distinction between processes such as the breakup and stripping mechanisms that lead to quite different energy ranges of the consequently emitted particles. On the other hand, considering only the 'reduction factor', the inelastic BU enhancement of the activation cross section is totally ignored by these studies. Thus it results the importance of detailed theoretical treatment of the breakup contribution in order to obtain a reliable understanding of the interaction process as well as accurate deuteron activation cross sections.

C3.5 Work plan and milestones/year [senior researcher (SR) / postdoctoral (PD) time commitments]

  1. Consistent analysis of deuteron interaction with medium-mass nuclei at low energies, triggered by the direct reaction consideration.

  2. [3 man-months SR, on stripping and pick-up reaction microscopic description and outlook]

  3. Breakup cross sections components calculations corresponding to deuteron interactions with medium-mass nuclei at incident energy E<60 MeV.

  4. [12 man-months SR, on improved BU and model parameter sets; 12 man-months PD, on systematic analysis of BU data in broad mass- and energy ranges, using the CDCC method]

  5. Consistent analysis of deuteron interaction with the 54,56,58,natFe nuclei at low energies.

  6. [12 man-months SR, on DR, PE, and CN consistent account; 12 man-months PD, on inclusive neutron/proton emission-spectra analysis for settling the contributing mechanisms]

  7. Consistent analysis of deuteron interaction with the 58,60,61,62,natNi nuclei at low energies.

  8. [12 man-months SR, on DR, PE, and CN consistent account and model parameter sets; 12 man-months PD, on BU improved description and systematic BU component studies]

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