Continuum-discretized Coupled-channels Method Research Articles

Investigation of the unbound21C nucleus via transfer reaction

The cross section of the transfer reaction 20 C(d,p) 21 C at 30.0 MeV is investi- gated. The continuum-discretized coupled-channels method (CDCC) is used in order to obtain the final state wave function. The smoothing procedure of the transition matrix and the channel-coupling effect on the cross section are discussed.

Two neutron decay from the21+state of6He

Decay mode of the $2_1^+$ resonant state of $^6$He populated by the $^6$He breakup reaction by $^{12}$C at 240 MeV/nucleon is investigated. The continuum-discretized coupled-channels method is adopted to describe the formation of the $2_1^+$ state, whereas its decay is described by the complex-scaled solutions of the Lippmann-Schwinger equation. From analysis of invariant mass spectra with respect to the $\alpha$-$n$ and $n$-$n$ subsystems, coexistence of two decay modes is found. One is the simultaneous decay of two neutrons correlating with each other and the other is the emission of two neutrons to the opposite directions. The latter is found to be free from the final state interaction and suggests existence of a di-neutron in the $2_1^+$ state of $^6$He.

Interplay between the02+resonance and the nonresonant continuum of the drip-line two-neutron halo nucleus22C

The breakup cross section (BUX) of 22C by 12C at 250 MeV/nucleon is evaluated by the continuum-discretized coupled-channels method incorporating the cluster-orbital shell model (COSM) wave functions. Contributions of the low-lying 0+_2 and 2+_1 resonances predicted by COSM to the BUX are investigated. The 2+_1 resonance gives a narrow peak in the BUX, as in usual resonant reactions, whereas the 0+_2 resonant cross section has a peculiar shape due to the coupling to the nonresonant continuum, i.e., the Fano effect. By changing the scattering angle of 22C after the breakup, a variety of shapes of the 0+_2 resonant cross sections is obtained. Mechanism of the appearance of the sizable Fano effect in the breakup of 22C is discussed.

Non-resonant Triple-α Reaction Rate at Low Temperature

The triple α reaction rate in stars is quite important in many astrophysical scenarios including the stellar evolution and carbon synthesis in stars. Recently the non-resonant triple α reaction rate has been reevaluated using a calculation with the continuum-discretized coupled-channels (CDCC) method, which dramatically increased the rate at low temperature compared to the widely-used NACRE compilation. Since the enhancement influences strongly on astrophysical model simulations, we have planned an experiment for drawing conclusion on the non-resonant triple α reaction rate at low temperature by measuring the three-α continuum state in 12C. We report the present situation of the experiment.

Four-Body CDCC Analysis for Breakup Reactions of Three-Body Projectiles

We present a new method of smoothing discrete breakup cross sections calculated by the continuum-discretized coupled-channels method based on the complex-scaling method. One of the advantages of this approach is to be applicable to many-body breakup reaction systems. In this work, we apply the new smoothing method to analyses of 12C(6He, nn4He) and 208Pb(6He, nn4He) reactions at 240 MeV/A.

Determination of 8B(p, γ )9C Reaction Rate From 9C Breakup

The astrophysical factor of the 8B(p, γ )9C reaction at zero energy, S18(0), is determined from three-body model analysis of 9C breakup processes. The elastic breakup 208Pb(9C,p8B)208Pb at 65 MeV/nucleon and the one-proton removal reaction of 9C at 285 MeV/nucleon on C and Al targets are calculated with the continuum-discretized coupled-channels method (CDCC) and the eikonal reaction theory (ERT), respectively. As a result of the present analysis, S18(0) extracted from the two reactions shows good consistency, in contrast to in the previous studies.

Analysis of7Li(n,n′)7Li*reactions using the continuum-discretized coupled-channels method

We study ${}^{7}$Li${(n,{n}^{\ensuremath{'}})}^{7}$Li${}^{*}$ reactions by using the continuum-discretized coupled-channels (CDCC) method with the complex Jeukenne-Lejeune-Mahaux effective nucleon-nucleon interaction. In this study, the ${}^{7}$Li nucleus is described by an $\ensuremath{\alpha}+t$ cluster model. The calculated elastic cross sections for incident energies between 11.5 and 24.0 MeV show good agreements with experimental data. Furthermore, we calculate the neutron spectra of ${}^{7}$Li ground and excited breakup states measured at selected angular points for incident energies of 11.5 and 18.0 MeV. The results reproduce the observed data systematically.

Effects of four-body breakup on6Li elastic scattering near the Coulomb barrier

We investigate projectile breakup effects on 6Li+209Bi elastic scattering near the Coulomb barrier with the four-body version of the continuum-discretized coupled-channel method (four-body CDCC). This is the first application of four-body CDCC to 6Li elastic scattering. The elastic scattering is well described by the p+n+4He+209Bi four-body model. We propose a reasonable three-body model for describing the four-body scattering, clarifying four-body dynamics of the elastic scattering.

Exclusive breakup of17F on58Ni and208Pb within the continuum-discretized coupled-channels method

An analysis of the elastic and exclusive breakup of ${}^{17}$F on ${}^{58}$Ni and ${}^{208}$Pb targets is presented. The study is undertaken using the continuum-discretized coupled-channels (CDCC) method, assuming a core+valence model for the ${}^{17}$F projectile. The results are compared with recent data published for these reactions [Phys. Lett. B 681, 22 (2009)]. The calculations show that the exclusive breakup cross sections contain contributions from high multipoles, as well as a complicated interplay between Coulomb and nuclear couplings. This makes it difficult to extract radiative capture cross sections or structure information from the analyzed data.

Determination of the8B(p,γ)9C reaction rate from9C breakup

The astrophysical factor of ${}^{8}$B($p$,$\ensuremath{\gamma}$)${}^{9}$C at zero energy, ${S}_{18}(0)$, is determined from three-body model analysis of ${}^{9}$C breakup processes. The elastic breakup reaction ${}^{208}$Pb(${}^{9}$C,$p{}^{8}$B)${}^{208}$Pb at 65 MeV/nucleon and the one-proton removal reaction of ${}^{9}$C at 285 MeV/nucleon on C and Al targets are calculated with the continuum-discretized coupled-channels method (CDCC) and the eikonal reaction theory (ERT), respectively. The asymptotic normalization coefficient (ANC) of ${}^{9}$C in the $p$-${}^{8}$B configuration, ${C}_{p{}^{8}\text{B}}^{{}^{9}\text{C}}$, extracted from the two reactions shows good consistency, unlike in previous studies. As a result of the present analysis, ${S}_{18}(0)=66\ifmmode\pm\else\textpm\fi{}10\phantom{\rule{0.28em}{0ex}}\mathrm{eVb}$ is obtained.

Testing the continuum-discretized coupled channels method for deuteron-induced reactions

The continuum-discretized coupled channels (CDCC) method is a well established theory for direct nuclear reactions which includes breakup to all orders. Alternatively, the three-body problem can be solved exactly within the Faddeev formalism which explicitly includes breakup and transfer channels to all orders. With the aim to understand how CDCC compares with the exact three-body Faddeev formulation, we study deuteron-induced reactions on (i) ${}^{10}$Be at ${E}_{\mathrm{d}}=21.4,40.9\phantom{\rule{0.28em}{0ex}}\mathrm{and}\phantom{\rule{0.28em}{0ex}}71$ MeV; (ii) ${}^{12}$C at ${E}_{\mathrm{d}}=12\phantom{\rule{0.28em}{0ex}}\mathrm{and}\phantom{\rule{0.28em}{0ex}}56$ MeV; and (iii) ${}^{48}$Ca at ${E}_{\mathrm{d}}=56$ MeV. We calculate elastic, transfer, and breakup cross sections. Overall, the discrepancies found for elastic scattering are small with the exception of very backward angles. For transfer cross sections at low energy, $\ensuremath{\sim}$10 MeV/u, CDCC is in good agreement with the Faddeev-type results and the discrepancy increases with beam energy. In contrast, breakup observables obtained with CDCC are in good agreement with Faddeev-type results for all but the lower energies considered here.

Recent Development of CDCC and Future

Recent development of the continuum-discretized coupled-channels method (CDCC) is reviewed. The following three topics are covered: i) four-body CDCC with the clusterorbital shell-model (COSM) wave functions, COSM-CDCC, and its application to the study of nuclear breakup of C, ii) the eikonal reaction theory (ERT) that accurately describes inclusive breakup processes within the framework of CDCC, and iii) some applications of CDCC to nuclearastrophysics.

Three-Body Model Calculation of Spin Distribution in Two-Nucleon Transfer Reaction for the System of 238U(18O,16O)240U Reaction

The differential cross sections of two-nucleon transfer reactions 238U(18O,16O)240U around 180 MeV are calculated by one-step Born approximation with a 16O+2 n+238U three-body model. The wave function in the initial channel is obtained by the continuum-discretized coupled-channels method, and that in the final channel is evaluated by adiabatic approximation. The cross sections have a peak around the grazing angle, and the spin distribution, i.e., the cross section at the peak as a function of the transferred spin, is investigated. The shape of the spin distribution is found to be not sensitive to the incident energies, optical potentials, and treatment of the breakup channels, whereas it depends on the excitation energy of the residual nucleus 240U. To fulfill the condition that the peak position should not exceeds 10ħ, which is necessary for the surrogate ratio method to work, it is concluded that the excitation energy must be less than 10 MeV.

Status of breakup reaction theory

Recent studies on breakup reactions with the continuum-discretized coupled-channels method are reviewed. The topics covered are: four-body breakup processes for 6He induced reaction, dynamical relativistic effects on Coulomb breakup, microscopic description of projectile breakup processes, description of ternary processes (new triple-α reaction rate) and new approach to inclusive breakup processes.

Systematic description of theLi6(n,n′)6Li*→d+αreactions with the microscopic coupled-channels method

We investigate $^6$Li($n$, $n'$)$^6$Li$^*$ $\to$ $d$ + $\alpha$ reactions by using the continuum-discretized coupled-channels method with the complex Jeukenne-Lejeune-Mahaux effective nucleon-nucleon interaction. In this study, the $^6$Li nucleus is described as a $d$ + $\alpha$ cluster model. The calculated elastic cross sections for incident energies between 7.47 and 24.0 MeV are good agreement with experimental data. Furthermore, we show the neutron spectra to $^6$Li breakup states measured at selected angular points and incident energies can be also reproduced systematically.

Effective radii of deuteron-induced reactions

The continuum-discretized coupled-channels method (CDCC) for exclusive reactions and the eikonal reaction theory (ERT) as an extension of CDCC to inclusive reactions are applied to deuteron induced reactions. The CDCC result reproduces experimental data on the reaction cross section for $d+^{58}$Ni scattering at 200 MeV/nucleon and ERT does data on the neutron-stripping cross section for inclusive $^7$Li$(d,n)$ reaction at 40 MeV. For deuteron induced reactions at 200 MeV/nucleon, target-dependence of the reaction, elastic-breakup, nucleon-stripping, nucleon-removal, complete- and incomplete-fusion cross sections is clearly explained by simple formulae. Accuracy of the Glauber model is also investigated.

Three-Body Model Calculation of Spin Distribution in Two-Nucleon Transfer Reaction for the System of 238U(18O,16O)240U Reaction

The differential cross sections of two-nucleon transfer reactions 238U(18O,16O)240U around 180 MeV are calculated by one-step Born approximation with a 16O+2 n+238U three-body model. The wave function in the initial channel is obtained by the continuum-discretized coupled-channels method, and that in the final channel is evaluated by adiabatic approximation. The cross sections have a peak around the grazing angle, and the spin distribution, i.e., the cross section at the peak as a function of the transferred spin, is investigated. The shape of the spin distribution is found to be not sensitive to the incident energies, optical potentials, and treatment of the breakup channels, whereas it depends on the excitation energy of the residual nucleus 240U. To fulfill the condition that the peak position should not exceeds 10ħ, which is necessary for the surrogate ratio method to work, it is concluded that the excitation energy must be less than 10 MeV.

Simultaneous analysis of elastic, breakup, and fusion channels for6He induced reactions at energies near the Coulomb barrier

We present some recent applications of the Continuum-Discretized Coupled-Channels (CDCC) and Coupled-Reaction-Channels (CRC) methods to the study of reactions induced by weakly-bound nuclei on stable targets. The methods are applied to the scattering of the Borromean nucleus 6 He at energies around the Coulomb barrier. Elastic scattering data are very well described by four-body CDCC calculations (based on a three-body description of the 6 He nucleus) but also by simpler three-body CDCC calculations, using a suitable two-body model for 6 He. By contrast, inclusivedata are better described using the CRC approach, which treats the breakup within the transfer to the continuum picture and, unlike the CDCC method, allows the inclusion of transfer to bound states of the target. We explore also the possibility of calculating the fusion cross sections using the CRC framework.

New description of the four-body breakup reaction

We present a novel method of smoothing discrete breakup cross sections calculated by the method of continuum-discretized coupled-channels. The method based on the complex scaling method is tested with success for $^{58}$Ni($d$, $pn$) reaction at 80 MeV as an example of a three-body breakup reaction, and applied to $^{12}$C($^6$He, $nn^4$He) reaction at 229.8 MeV as a typical example of a four-body breakup reaction. The new method does not need to derive continuum states of the projectile in order to evaluate the breakup cross section as a smooth factor of the excitation energy of the projectile. Fast convergence of the breakup cross section with respect to extending the modelspace is confirmed. For the $^6$He breakup cross section, the resonant component is separated from the non-resonant one.

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.