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Register a new userPractical method for decomposing discretized breakup cross sections into components of each channel
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Background: In the continuum-discretized coupled-channel method, a breakup cross section (BUX) is obtained as an admixture of several components of different channels in multi-channel scattering. Purpose: Our goal is to propose an approximate way of decomposing the discretized BUX into components of each channel. This approximation is referred to as the probability separation (P-separation). Method: As an example, we consider $^{11}$Be scattering by using the three-body model with core excitation ($^{10}mathrm{Be}+n+mathrm{T}$, where T is a target). The structural part is constructed by the particle-rotor model and the reaction part is described by the distorted wave Born approximation (DWBA). Results: The validity of the P-separation is tested by comparing with the exact calculation. The approximate way reproduces the exact BUXs well regardless of the configurations and/or the resonance positions of $^{11}$Be. Conclusion: The method proposed here can be an alternative approach for decomposing discretized BUXs into components in four- or five-body scattering where the strict decomposition is hard to perform.
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The Continuum Discretized Coupled Channels (CDCC) method is a well established theory for direct nuclear reactions which includes breakup to all orders. Alternatively, the 3-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 3-body Faddeev formulation, we study deuteron induced reactions on: i) $^{10}$Be at $E_{rm d}= 21.4, 40.9 ; {rm and} ; 71$ MeV; ii) $^{12}$C at $E_{rm d} = 12 ; {rm and} ; 56$ MeV; and iii) $^{48}$Ca at $E_{rm d} = 56$ 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 $sim$10 MeV/u, CDCC is in good agreement with the Faddeev-type results and the discrepancy increases with beam energy. On the contrary, breakup observables obtained with CDCC are in good agreement with Faddeev-type results for all but the lower energies considered here.
We present a method for smoothing discrete breakup $S$-matrix elements calculated by the method of continuum-discretized coupled-channels (CDCC). This smoothing method makes it possible to apply CDCC to four-body breakup reactions. The reliability of the smoothing method is confirmed for two cases, $^{58}$Ni($d$, $p n$) at 80 MeV and the $E1$ transition of $^6$He. We apply CDCC with the smoothing method to $^6$He breakup reaction at 22.5 MeV. Multi-step breakup processes are found to be important.
We use a three-body Continuum Discretized Coupled Channel (CDCC) model to investigate Coulomb and nuclear effects in breakup and reaction cross sections. The breakup of the projectile is simulated by a finite number of square integrable wave functions. First we show that the scattering matrices can be split in a nuclear term, and in a Coulomb term. This decomposition is based on the Lippmann-Schwinger equation, and requires the scattering wave functions. We present two different methods to separate both effects. Then, we apply this separation to breakup and reaction cross sections of 7Li + 208Pb. For breakup, we investigate various aspects, such as the role of the alpha + t continuum, the angular-momentum distribution, and the balance between Coulomb and nuclear effects. We show that there is a large ambiguity in defining the Coulomb and nuclear breakup cross sections, since both techniques, although providing the same total breakup cross sections, strongly differ for the individual components. We suggest a third method which could be efficiently used to address convergence problems at large angular momentum. For reaction cross sections, interference effects are smaller, and the nuclear contribution is dominant above the Coulomb barrier. We also draw attention on different definitions of the reaction cross section which exist in the literature, and which may induce small, but significant, differences in the numerical values.
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.
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.
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