Elastic Breakup Cross Section Research Articles

Three-body description of C9 : Role of low-lying resonances in breakup reactions

The $^9$C nucleus and related capture reaction, ${^8\mathrm{B}}(p,\gamma){^9\mathrm{C}}$, have been intensively studied with an astrophysical interest. Due to the weakly-bound nature of $^9$C, its structure is likely to be described as the three-body (${^7\mathrm{Be}}+p+p$). Its continuum structure is also important to describe reaction processes of $^9$C, with which the reaction rate of the ${^8\mathrm{B}}(p,\gamma){^9\mathrm{C}}$ process have been extracted indirectly. We perform three-body calculations on $^9$C and discuss properties of its ground and low-lying states via breakup reactions. We employ the three-body model of $^9$C using the Gaussian-expansion method combined with the complex-scaling method. This model is implemented in the four-body version of the continuum-discretized coupled-channels method, by which breakup reactions of $^9$C are studied. The intrinsic spin of $^7$Be is disregarded. By tuning a three-body interaction in the Hamiltonian of $^9$C, we obtain the low-lying $2^+$ state with the resonant energy 0.781 MeV and the decay width 0.137 MeV, which is consistent with the available experimental information and a relatively high-lying second $2^+$ wider resonant state. Our calculation predicts also sole $0^+$ and three $1^-$ resonant states. We discuss the role of these resonances in the elastic breakup cross section of $^9$C on $^{208}$Pb at 65 and 160 MeV/A. The low-lying 2$^+$ state is probed as a sharp peak of the breakup cross section, while the 1$^-$ states enhance the cross section around 3 MeV. Our calculations will further support the future and ongoing experimental campaigns for extracting astrophysical information and evaluating the two-proton removal cross-sections.

Effect of the repulsive core in the proton-neutron potential on deuteron elastic breakup cross sections

The role of the short-range part (repulsive core) of the proton-neutron ($pn$) potential in deuteron elastic breakup processes is investigated. A simplified one-range Gaussian potential and the Argonne V4' (AV4') central potential are adopted in the continuum-discretized coupled-channels (CDCC) method. The deuteron breakup cross sections calculated with these two potentials are compared. The repulsive core is found not to affect the deuteron breakup cross sections at energies from 40 MeV to 1 GeV. To understand this result, an analysis of the peripherality of the elastic breakup processes concerning the $p$-$n$ relative coordinate is performed. It is found that for the breakup processes populating the $pn$ continua with orbital angular momentum $\ell$ different from 0, the reaction process is peripheral, whereas it is not for the breakup to the $\ell=0$ continua (the s-wave breakup). The result of the peripherality analysis indicates that the whole spatial region of deuteron contributes to the s-wave breakup.

Inclusive breakup of Borromean nuclei

We derive the inclusive breakup cross section of a three-fragment projectile nuclei, a = b + x1 +x2, in the spectator model. The resulting four-body cross section for observing b, is composed of the elastic breakup cross section which contains information about the correlation between the two participant fragments, and the inclusive non-elastic breakup cross section. This latter cross section is found to be a non-trivial four-body generalization of the Austern formula [1], which is proportional to a matrix element of the form, . The new feature here is the three-body absorption, represented by the imaginary potential, W3b. We analyze this type of absorption and supply ideas of how to calculate its contribution.

Inclusive breakup of three-fragment weakly bound nuclei

The inclusive breakup of three-fragment projectiles is discussed within a four-body spectator model. Both the elastic breakup and the non-elastic breakup are obtained in a unified framework. Originally developed in the 80's for two-fragment projectiles such as the deuteron, in this paper the theory is successfully generalized to three-fragment projectiles. The expression obtained for the inclusive cross section allows the extraction of the incomplete fusion cross section, and accordingly generalizes the surrogate method to cases such as (t,p) and (t,n) reactions. It is found that two-fragment correlations inside the projectile affect in a conspicuous way the elastic breakup cross section. The inclusive non-elastic breakup cross section is calculated and is found to contain the contribution of a three-body absorption term that is also strongly influenced by the two-fragment correlations. This latter cross section contains the so-called incomplete fusion where more than one compound nuclei are formed. Our theory describes both stable weakly bound three-fragment projectiles and unstable ones such as the Borromean nuclei.

Inclusive Breakup Theory of Three-Body Halos

We present a recently developed theory for the inclusive breakup of three-fragment projectiles within a four-body spectator model \cite{CarPLB2017}, for the treatment of the elastic and inclusive non-elastic break up reactions involving weakly bound three-cluster nuclei in $A\,(a,b)\,X$ / $a = x_1 + x_2 + b$ collisions. The four-body theory is an extension of the three-body approaches developed in the 80's by Ichimura, Autern and Vincent (IAV) \cite{IAV1985}, Udagawa and Tamura (UT) \cite{UT1981} and Hussein and McVoy (HM) \cite{HM1985}. We expect that experimentalists shall be encouraged to search for more information about the $x_{1} + x_{2}$ system in the elastic breakup cross section and that also further developments and extensions of the surrogate method will be pursued, based on the inclusive non-elastic breakup part of the $b$ spectrum.

Applicability of the continuum-discretized coupled-channels method to the deuteron breakup at low energies

We re-examine the deuteron elastic breakup cross sections on 12C and 10Be at low incident energies, for which a serious discrepancy between the continuum-discretized coupled-channels method (CDCC) and the Faddeev-Alt-Grassberger-Sandhas theory (FAGS) was pointed out. We show the closed-channels neglected in the preceding study affect significantly the breakup cross section calculated with CDCC, resulting in good agreement with the result of FAGS.

Inclusive Proton Emission Spectra from Deuteron Breakup Reactions

We present calculations of deuteron elastic and nonelastic breakup cross sections and angular distributions at deuteron energies below 100 MeV obtained using the post-form DWBA approximation. The elastic breakup cross section was extensively studied in the past. Very few calculations of nonelastic breakup have been performed, however. We compare two forms of the elastic DWBA breakup amplitude but conclude that neither provides a correct description of the inclusive proton emission cross section.

Elastic breakup cross sections of well-bound nucleons

The 9Be(28Mg,27Na) one-proton removal reaction with a large proton separation energy of Sp(28Mg)=16.79 MeV is studied at intermediate beam energy. Coincidences of the bound 27Na residues with protons and other light charged particles are measured. These data are analyzed to determine the percentage contributions to the proton removal cross section from the elastic and inelastic nucleon removal mechanisms. These deduced contributions are compared with the eikonal reaction model predictions and with the previously measured data for reactions involving the re- moval of more weakly-bound protons from lighter nuclei. The role of transitions of the proton between different bound single-particle configurations upon the elastic breakup cross section is also quantified in this well-bound case. The measured and calculated elastic breakup fractions are found to be in good agreement.

Extracting the electric dipole breakup cross section of one-neutron halo nuclei from inclusive breakup observables

How to extract an electric dipole (E1) breakup cross section \sigma(E1) from one- neutron removal cross sections measured by using 12C and 208Pb targets, \sigma_(-1n)^C and \sigma_(-1n)^Pb, respectively, is discussed. It is shown that within about 5% error, \sigma(E1) can be obtained by subtracting \Gamma \sigma_(-1n)^C from \sigma_(- 1n)^Pb, as assumed in preceding studies. However, for the reaction of weakly-bound projectiles, the scaling factor \Gamma is found to be two times as large as that usually adopted. As a result, we obtain 13-20% smaller \sigma(E1) of 31Ne at 250 MeV/nucleon than extracted in a previous analysis of experimental data. By compiling the values of \Gamma obtained for several projectiles, \Gamma=(2.30 +/- 0.41)\exp(- S_n)+(2.43 +/- 0.21) is obtained, where S_n is the neutron separation energy. The target mass number dependence of the nuclear parts of the one-neutron removal cross section and the elastic breakup cross section is also investigated.

Improved deuteron elastic breakup energy dependence via the continuum-discretized coupled-channels method

Experimental elastic-scattering angular distributions for deuteron interaction with $^{63}\mathrm{Cu}$ and $^{93}\mathrm{Nb}$ targets are compared with calculations performed within the continuum-discretized coupled-channels (CDCC) method, in which coupling to breakup channels is explicitly taken into account. The calculated elastic breakup cross sections are compared with the predictions of an empirical parametrization for a wide range of deuteron incident energies. The good agreement between the calculations and the systematics at the energies where data are available indicates that the CDCC method permits a useful assessment of empirical parametrizations and provides useful guidance for the extrapolation of these parametrizations beyond the energies formerly considered.

Fusion, break-up and elastic scattering of weakly bound nuclei

We describe the behaviour of the fusion, break-up, reaction cross sections and elastic scattering of weakly bound nuclei, at near and above barrier energies. The total fusion cross sections are not affected by the break-up process at this energy regime. The elastic break-up cross sections are important at energies close and above the Coulomb barrier, even in systems with light targets, and increase the reaction cross sections. We also show that the break-up process at near and sub-barrier energies is responsible for the vanishing of the usual threshold anomaly of the optical potential and gives rise to a new type of anomaly, named by us as break-up threshold anomaly.

Proton-neutron correlation in the deuteron breakup at 56 MeV and prior-form DWBA analysis

Abstract Proton-neutron angular correlations in the 12 C, 51 V and 118 Sn(d, pn) reactions have been measured at 56 MeV to investigate the deuteron breakup process. The elastic breakup which leaves the target nucleus in its ground state dominates the coincident spectra. The elastic breakup cross sections are estimated to be 36–48% of the inclusive breakup yields at 15° or 17.5°. In the angular correlations the protons are emitted predominantly on the side of the beam opposite to the neutrons. The experimental data have been analyzed using the prior-form DWBA. For both nuclear and Coulomb breakup, sufficient convergence of the calculations is obtained by including the pn angular momenta up to l = 2. For the nuclear breakup calculations, the l = 0 and 2 contributions dominate the cross sections. For the Coulomb breakup the l = 1 contribution is predominant. In the calculations the effect of the Coulomb breakup is seen at forward angles of the angular correlation. The DWBA calculations reproduce fairly well the coincident energy spectra and the angular correlations in the angular region where the protons are emitted on the side of the beam opposite to the neutrons. On the other hand the calculations overestimate the break-up cross sections by a factor of 2 to 10 in the angular region where the protons are emitted on the same side of the beam as the neutrons. The distributions of deuteron c.m. angular momenta that contribute to the breakup amplitude are examined to obtain information on the region of space in which the breakup reactions takes place.