Inclusive Breakup Reactions Research Articles

Comparison of Ichimura-Austern-Vincent and Glauber models for the deuteron-induced inclusive breakup reaction in light and medium-mass nuclei

Comparison of Ichimura-Austern-Vincent and Glauber models for the deuteron-induced inclusive breakup reaction in light and medium-mass nuclei

Coulomb breakup reaction of loosely bound F17 with dynamic polarization potentials

We investigate the elastic scattering, inelastic scattering, breakup reaction, and total fusion reactions of the $^{17}\mathrm{F}+^{208}\mathrm{Pb}$ system using an optical model approach by including the dynamical polarization potential. In particular, we focus on the breakup reaction channels, whose effects on other reactions have been argued to be small. By exploiting two different potentials composed of a surface-type Woods-Saxon potential, which were obtained by a fitting analysis, and a Love-type optical potential, the breakup reaction cross sections are explained with other elastic and quasielastic scattering cross sections. For the breakup reaction at ${E}_{\text{lab}}=170$ MeV in the forward angle region, where only exclusive reaction data are known, inclusive breakup reaction data are deduced from available theoretical and experimental $E1$ strength values. We discuss the breakup reaction effects on the other nuclear reactions related to the $^{17}\mathrm{F}$ projectile in detail.

Lagrange-mesh R -matrix method for inhomogeneous equations

The Lagrange-mesh $R$-matrix method is generalized to inhomogeneous equations. This method is numerically stable and efficient. It can be directly used for transfer reactions with the formalism discussed by Ascuitto and Glendenning [Phys. Rev. 181,1396 (1969)] and for inclusive breakup reactions modeled by Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)]. We first present a simple example to assess the method. Then the application to the $^{93}$Nb($d$,$pX$) non-elastic breakup is discussed.

The neutron within the deuteron as a surrogate for neutron-induced reactions

We propose the use of neutron poisons in reactions induced by radioactive beams as a test of theoretical models aiming to relate neutron capture in nuclei with neutron surrogate reactions such as ([Formula: see text]) reactions. We exploit the approximations necessary to obtain a direct relation between the two reactions: surrogate versus neutron capture. We also show how this is intimately related to the momentum distribution of the neutron within the deuteron. The models we use are based on the theory of inclusive breakup reactions commonly employed in the treatment of incomplete fusion and surrogate method. Such theories were developed in the 1980s by Ichimura, Austern and Vincent [Phys. Rev. C 32 (1985) 431], Udagawa and Tamura [Phys. Rev. C 24 (1981) 1348] and Hussein and McVoy [Nucl. Phys. A 445 (1985) 124]. We use these theories to derive an expression for the proton yield in the reaction [Formula: see text]. The capture reaction [Formula: see text] is then extracted using reasonable approximations. By recalling an old method proposed by Serber [Phys. Rev. 80 (1950) 1098; Proc. Roy. Soc. A 208 (1951) 559] we explain how the momentum distribution of neutrons within the deuteron will depend on the short-range dependence of the nucleon–nucleon force. The relevance of our work to nucleosynthesis in the rapid neutron capture process is emphasized.

Comprehensive analysis of large α yields observed in Li6 -induced reactions

Background: Large $\ensuremath{\alpha}$ yields have been reported over the years in reactions with $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ projectiles. Previous theoretical analyses have shown that the elastic breakup (EBU) mechanism (i.e., projectile breakup leaving the target in its ground state) is able to account only for a small fraction of the total $\ensuremath{\alpha}$-inclusive breakup cross sections, pointing toward the dominance of nonelastic breakup (NEB) mechanisms.Purpose: We aim to provide a systematic study of the $\ensuremath{\alpha}$-inclusive cross sections observed in nuclear reactions induced by $^{6}\mathrm{Li}$ projectiles. In addition to estimating the total $\ensuremath{\alpha}$ singles' cross sections, it is our goal to evaluate angular and energy distributions of these $\ensuremath{\alpha}$ particles and compare them with experimental data, when available.Method: We compute separately the EBU and NEB components of the inclusive breakup cross sections. For the former, we use the continuum-discretized coupled-channels (CDCC) method, which treats this mechanism to all orders. For the NEB part, we employ the model proposed by Ichimura et al. [Phys. Rev. C 32, 431 (1985)], within the distorted-wave Born approximation (DWBA).Results: Overall, the sum of the computed EBU and NEB cross sections is found to reproduce very well the measured singles' cross sections. In all cases analyzed, we find that the inclusive breakup cross section is largely dominated by the NEB component.Conclusions: The presented method provides a global and systematic description of inclusive breakup reactions induced by $^{6}\mathrm{Li}$ projectiles. It provides also a natural explanation of the previously observed underestimation of the measured $\ensuremath{\alpha}$ yields by CDCC calculations. The method used here can be extended to other weakly bound projectiles, including halo nuclei.

Evaluation of inclusive breakup cross sections in reactions induced by weakly-bound nuclei within a three-body model

In 1980s Ichimura, Austern and Vincent [Phys.Rev.C 32, 431 (1985)] proposed a quantum mechanical theory to study the problem of inclusive breakup cross sections in the nuclear reactions. Using the DWBA version of this model, applications to deuteron and 6 Li inclusive breakup reactions are presented and compared with some available data.

Reaction theory: Status and perspectives

The current status of the reaction theory of nuclear collisions involving weakly-bound exotic nuclei is presented. The problem is addressed within the Continuum Discretized Coupled Channel (CDCC) framework, recalling its foundations and applications, as well as its connection with the Faddeev formalism. Recent developments and improvements of the method, such as core and target excitations and the extension to three-body projectiles, are presented. The use of the CDCC wave function in the calculation of inclusive breakup reactions is also introduced.

Numerical assessment of post-prior equivalence for inclusive breakup reactions

We address the problem of the post-prior equivalence in inclusive breakup reactions induced by weakly-bound nuclei. The problem is studied within the DWBA model of Ichimura, Austern, Vincent [Phys. Rev. C32, 431 (1985)]. The post and prior formulas obtained in this model are briefly recalled, and applied to several breakup reactions induced by deuterons and $^6$Li projectiles, to test their actual numerical equivalence. The different contributions of the prior-form formula are also discussed. A critical comparison with the prior-form distorted-wave Born approximation (DWBA) model of Udagawa and Tamura [Phys. Rev. C24, 1348 (1981)] is also provided.

Measurement of the 2H(p, n) Breakup Reaction at 170 MeV and the Three-Nucleon Force Effects

The effects of three nucleon force (3NF) have been actively studied via the nucleon–deuteron (Nd) scattering states. The differential cross sections and the vector analyzing powers A y of the 2H(p, n) inclusive breakup reaction at 170 MeV were measured for the study of 3NF effects in the intermediate energy region. The polarized proton beam of 170 MeV was injected to the deuterated polyethylene (CD2) target and the energy of scattered neutrons were measured by using TOF method. The data were compared with the Faddeev calculations based on modern nucleon–nucleon (NN) forces with and without the 3NF. Concerning the differential cross sections, we can see large discrepancies between the data and the calculations in the region of scattered neutron energies are low, which is similar to the results of the 2H(p, p) inclusive breakup reaction at 250 MeV.

Study of the Three-Nucleon Force Effects in the 2H(p, n) Breakup Reaction at 170 MeV

For the study of three nucleon force (3NF) effects in the intermediate energy region, the differential cross sections and the vector analyzing power Ay were measured for the 2H(p, n) inclusive breakup reaction at 170 MeV. The polarized proton beam of 170 MeV was injected to the deuterated polyethylene (CD2) target and the energy of scattered neutrons were deduce by TOF method. The data was compared with the results of the Faddeev calculations with and without 3NFs. Concerning about the differential cross sections, we can see large discrepancies between the data and the calculations in the region where the energies of scattered neutrons are low, which are similar to the results of the 2H(p, p) inclusive breakup reaction at 250 MeV.

Measurements of the Cross Sections and A y for D(p, n) Inclusive Breakup Reaction at 170 MeV

The effects of three-nucleon force (3NF) has been actively studied by using the nucleon–deuteron (Nd) scattering states. The differential cross sections of the elastic Nd scattering at the energy below 150 MeV can be well reproduced by incorporating 3NF in the Faddeev calculation based on modern nucleon–nucleon (NN) interactions. On the other hand, the differential cross sections of Nd elastic and inelastic scatterings at 250 MeV show large discrepancies between the data and the Faddeev calculations with 3NF. It indicates the presence of the missing features of the three nucleon system at this energy region. For the systematic study about the energy dependence of this large discrepancies, we measured the differential cross sections and the vector analyzing power Ay for the 2H(p, n) inclusive breakup reaction at 170 MeV. The experiment was carried out at RCNP by detecting scattered neutrons by using the neutron detector NPOL3. The data was compared with the results of the Faddeev calculations with and without the 3NF.

Three-body approaches for inclusive breakup reactions

The formal problem of three-body breakup in nuclear reactions is addressed. Two alternative treatments, namely, the direct breakup and transfer to the continuum approaches, are discussed and compared. Calculations for the reactions 8B+ 58Ni at 26 MeV and 6He + 208Pb at 22 MeV are presented and compared with existing data.

Reaction mechanisms with loosely bound nucleiLi7+Li6at forward angles in the incident energy range 14–20 MeV

Emission of charged particles from the $^{7}\mathrm{Li}$+$^{6}\mathrm{Li}$ reaction at $E$($^{7}\mathrm{Li}$$)=14\text{\ensuremath{-}}20$ MeV is studied at forward angles. Analysis of the inclusive spectra are performed in terms of the statistical model for compound nuclear process and Serber model for inclusive breakup reactions. Compound nuclear calculations better reproduce the experimental data in comparison to the projectile breakup calculations even at extreme forward angles and above barrier energies.

Nuclear breakup of8Bin a direct fragmentation model

We calculate the cross sections of the elastic and inelastic breakup modes for the inclusive breakup reaction ${}^{28}\mathrm{Si}{(}^{8}\mathrm{B}{,}^{7}\mathrm{Be})$ at beam energies between 10 and 40 MeV/nucleon within a direct fragmentation model formulated in the framework of the post-form distorted-wave Born approximation. In contrast to the case of the stable isotopes, the inelastic breakup mode is found to contribute only up to $30%$ to the total breakup cross section, which is in agreement with the recently measured experimental data. However, the high energy tail of the energy spectra of ${}^{7}\mathrm{Be}$ fragments is dominated by the inelastic breakup mode. The breakup amplitude is found to be dominated by contributions from distances well beyond the nuclear surface.

Polarization transfer in [formula omitted] at 2.1 GeV

The polarization of the proton from the inclusive breakup reaction 1H( d, p)X at 2.1 GeV was measured at 0°. The results are expressed as the ratio of the proton polarization, P p , to the deuteron beam polarization, P d , κ 0= P p / P d . The measured values of κ 0 range from +0.983 to -0.305 and are in general agreement with the expected behavior arising from the D state in the deuteron wave function.

Faddeev and DWBA description of inclusive break-up and incomplete fusion reactions

Abstract Three-body contributions to the inclusive break-up cross section are derived and discussed. The Faddeev equations are used for this purpose. A new sum rule, which is similar in structure as the Ichimura, Austern and Vincent sum rule, but it contains the full three-body corrections at the DWBA level, is derived and analysed.

Relation among theories of inclusive breakup reactions.

The relation among various recently proposed theories for inclusive breakup reactions is clarified from a unified viewpoint. Udagawa and Tamura's prior form formalism, Ichimura, Austern, and Vincent's post form formalism, and Hussein and McVoy's formalism are understood on a common basis by referring to a three-body model of Austern et al.

Approximate sum rules for inclusive breakup reactions.

We show the inadequacy of the Udagawa-Tamura-Mastroleo discussion of the distorted-wave Born approximation sum rule.

Exact and approximate sum rules for inclusive breakup reactions.

The sum rule formalism of Ichimura, Austern, and Vincent, constructed for inclusive breakup reactions based on the distorted-wave Born approximation, is compared critically with the exact sum rule formalism. This presents a possible explanation of why the former formalism overpredicts cross sections.

Comparison of approximate formalisms for inclusive breakup reactions.

A coupled-channels Born approximation formalism for breakup reactions recently proposed by Udagawa and Tamura is compared with the distorted-wave Born approximation formalism discussed by Ichimura, Austern, and Vincent. Udagawa and Tamura claimed that the distorted-wave Born approximation method erroneously includes pure inelastic scatterings. We show that their argument is invalid and that there is no asymptotically observable inelastic scattering in the distorted-wave Born approximation breakup formalism.