Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCoupled-channel continuum eigenchannel basis
249
0
0.0
(
0
)
Authors
R. M. Id Betan
Ask ChatGPT about the research
No Arabic abstract
The goal of this paper is to calculate bound, resonant and scattering states in the coupled-channel formalism without relying on the boundary conditions at large distances. The coupled-channel solution is expanded in eigenchannel bases i.e. in eigenfunctions of diagonal Hamiltonians. Each eigenchannel basis may include discrete and discretized continuum (real or complex energy) single particle states. The coupled-channel solutions are computed through diagonalization in these bases. The method is applied to a few two-channels problems. The exact bound spectrum of the Poeschl-Teller potential is well described by using a basis of real energy continuum states. For deuteron described by Reid potential, the experimental energy and the S and D contents of the wave function are reproduced in the asymptotic limit of the cutoff energy. For the Noro-Taylor potential resonant state energy is well reproduced by using the complex energy Berggren basis. It is found that the expansion of the coupled-channel wave function in these eigenchannel bases require less computational efforts than the use of any other basis. The solutions are stable and converge as the cutoff energy increases.
rate research
Read More
In coupled-channel models the poles of the scattering S-matrix are located on different Riemann sheets. Physical observables are affected mainly by poles closest to the physical region but sometimes shadow poles have considerable effect, too. The purpose of this paper is to show that in coupled-channel problem all poles of the S-matrix can be calculated with properly constructed complex-energy basis. The Berggren basis is used for expanding the coupled-channel solutions. The location of the poles of the S-matrix were calculated and compared with an exactly solvable coupled-channel problem: the one with the Cox potential. We show that with appropriately chosen Berggren basis poles of the S-matrix including the shadow ones can be determined.
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.
A transformation of supersymmetric quantum mechanics for N coupled channels is presented, which allows the introduction of up to N degenerate bound states without altering the remaining spectrum of the Hamiltonian. Phase equivalence of the Hamiltonian can be restored by two successive supersymmetric transformations at the same energy. The method is successfully applied to the 3S1-3D1 coupled channels of the nucleon-nucleon system and a set of Moscow-type potentials is thus generated.
We present a coupled-channel Lagrangian approach (GiM) to describe the $pi N to pi N$, $2pi N$ scattering in the resonance energy region. The $2pi N$ production has been significantly improved by using the isobar approximation with $sigma N$ and $pi Delta(1232)$ in the intermediate state. The three-body unitarity is maintained up to interference pattern between the isobar subchannels. The scattering amplitudes are obtained as a solution of the Bethe-Salpeter equation in the $K$ matrix approximation. As a first application we perform a partial wave analysis of the $pi N to pi N$, $pi^0pi^0 N$ reactions in the Roper resonance region. We obtain $R_{sigma N}(1440)=27^{+4}_{-9}$,% and $R_{sigma N}(1440)=12^{+5}_{-3}$,% for the $sigma N$ and $pi Delta$ decay branching ratios of $N^*(1440)$ respectively. The extracted $pi N$ inelasticities and reaction amplitudes are consistent with the results from other groups.
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
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
