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Register a new userDescription of Four-Body Breakup Reaction with the Method of Continuum-Discretized Coupled-Channels
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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.
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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.
We present a practical way of smoothing discrete breakup S-matrix elements calculated by the continuum-discretized coupled-channel method (CDCC). This method makes the smoothing procedure much easier. The reliability of the smoothing method is confirmed for the three-body breakup reactions, 58Ni(d,pn) at 80 MeV and 12C(6He,4He2n) at 229.8 MeV.
This is a review on recent developments of the continuum discretized coupled-channels method (CDCC) and its applications to nuclear physics, cosmology and astrophysics, and nuclear engineering. The theoretical foundation of CDCC is shown, and a microscopic reaction theory for nucleus-nucleus scattering is constructed as an underlying theory of CDCC. CDCC is then extended to treat Coulomb breakup and four-body breakup. We also propose a new theory that makes CDCC applicable to inclusive 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 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.
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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