Coupled-channel Formalism Research Articles

Coupled-channel Treatment of Isobaric Analog Resonances in (p,p′) Capture Processes

With the advent of nuclear reactions on unstable isotopes, there has been a renewed interest in using isobaric analogue resonances (IAR) as a tool for probing the nuclear structure. The position and width of isobaric analogue resonances in nucleon-nucleus scattering are accurate and detailed indicators of the positions of resonances and bound states with good single-particle characters. We report on implementation within our coupled-channels code FRESCO of the charge-exchange interaction term that transforms an incident proton into a neutron. Isobaric analog resonances are seen as peaks in γ-ray spectrum when the proton is transformed into a neutron at an energy near a neutron bound state. The Lane coupled-channels formalism was extended to follow the non-orthogonality of this neutron channel with that configuration of an inelastic outgoing proton, and the target being left in a particle-hole excited state. This is tested for 208Pb, for which good (p,p'γ) coincidence data exists.

Molecular state NΞ in the coupled-channel formalism

The relativistic six-quark equations for the molecule NΞ are found in the dispersion relation technique. The relativistic six-quark amplitudes of the hexaquark including the quarks of three flavors (u, d, s) are calculated. The pole of these amplitudes determines the mass of NΞ state M = 2252 MeV. The binding energy is equal to 3 MeV.

Dirac analyses of proton inelastic scatterings from an s-d shell nucleus 20Ne

Proton inelastic scatterings from an s-d shell nucleus 20Ne are analyzed using an optical potential model in the Dirac coupled channel formalism. Lorentz covariant scalar and vector optical potentials are included in the calculation, and the first-order rotational collective model is used to obtain the transition potentials for the low-lying excited collective states of the ground state rotational band of the nucleus. Dirac coupled channel equations are solved phenomenologically to reproduce the differential cross section and analyzing power data by varying the optical potential and deformation parameters. The multistep process via coupled channels turns out to be important in describing the 4+ excited state of the ground state rotational band. The calculated deformation parameters of the excited states are compared with those of nonrelativistic calculations based on the Schrodinger equations. The Dirac equations are reduced to obtain Schrodinger-like second-order differential equations, and the obtained effective central and spin-orbit optical potentials are analyzed and compared with those of other s-d shell nuclei.

Coupled-channel continuum eigenchannel basis

The goal of this Letter 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-channel 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 requires less computational efforts than the use of any other basis. The solutions are stable and converge as the cutoff energy increases.

A chiral quark model for meson electroproduction in the region of D-wave resonances

The meson scattering and electroproduction amplitudes in the D13, D33 and D15 partial waves are calculated in a coupled-channel formalism incorporating quasi-bound quark-model states, extending our previous studies of the P11, P33 and S11 partial waves. The vertices of the baryon-meson interaction including the s- and d-wave pions and $\rho$-mesons, the s-wave $\eta$-meson, and the $s$- and p-wave $\sigma$-mesons are determined in the Cloudy Bag Model, with some changes of the parameters to reproduce the widths of the resonances. The helicity amplitudes and the electroproduction amplitudes exhibit consistent behavior in all channels but tend to be too weak compared to the experiment. We discuss possible origins of this discrepancy which arises also in the constituent quark model calculations.

Comparison of the multi-configuration, time-dependent Hartree (MCTDH) method with the Arthurs and Dalgarno coupled-channel method for rotationally inelastic scattering

Calculations of rotationally inelastic scattering at thermal energies for a model atom–diatom system have been performed using two completely different methodologies. The first method is the multi-configuration time-dependent Hartree (MCTDH) wave packet method, and the second is the well known, time-independent, Arthurs and Dalgarno coupled channel formalism. Excellent agreement is obtained between the two calculations. The advantages and drawbacks of these two methods are somewhat complementary, so that the decision to use one or the other approach will depend on what type of computational results are desired.

Coupled channel approach to hyperonic interactions from lattice QCD

Abstract We studied hyperonic interactions by lattice QCD simulations through a coupled channel formalism. Our approach to baryon–baryon interactions derives a potential from inverting the Schrodinger equation using a Nambu–Bethe–Salpeter (NBS) wave function simulated on the lattice. The quark mass dependences and flavor SU(3) breaking effects of the potential matrix are also discussed by comparing with results of gauge configurations obtained with different quark masses. Our numerical results are obtained from three ensembles of 2 + 1 -flavor QCD gauge configurations, which correspond to m π ∼ 700 , 570 and 410 MeV , provided by the PACS-CS Collaboration.

Coupled Channel Approach to S-Wave Hyperonic Interactions from Lattice QCD

We studied hyperonic interactions by lattice QCD simulation throuth coupled channel formalism. Our approach to baryon-baryon interactions is deriving a potential from inverting Schrodinger equation using Nambu-Bethe-Salpeter (NBS) wave function simulated on the lattice. The quark mass dependences and flavor SU(3) breaking effects of the potential matrix are also discussed by comparing with results of gauge configurations with different quark masses. Our numerical results are obtained from three ensembles of 2+1 flavor QCD gauge configurations, which corresponds to mπ ~ 700, 570 and 410 MeV, provided by the PACS-CS Collaboration.

Molecular structures in the charmonium spectrum: the XYZ puzzle

We study in the framework of a constituent quark model the possible contributions of molecular structures to the XYZ charmonium-like states. We analyze simultaneously the structures and the possible molecular components in the coupled channel formalism. In the 1++ sector two states appear which could be identified with X(3872) and X(3940). The recently confirmed X(3915) state appears as a mixture of and components as a JPC = 0++ state in agreement with the new measurements. A second broad resonance which may correspond with the so-called Y(3940) state is found with these quantum numbers. In the JPC = 1−− sector we also found significant contributions of the molecular structures which may affect the phenomenology. In particular the study allows us to understand the G(3900) state recently observed in Belle and BaBar. All these resonances together with the prediction of the model of a structure for Z(3930) provide a reasonable scenario for the so-called XYZ states with masses near 3.9 GeV.

Λ and Σ resonances coupled to vector and pseudoscalar mesons

Abstract The vector and pseudoscalar meson–baryon systems have been studied in a coupled channel formalism recently, which has lead to findings of some important results. The formalism consists of obtaining a detailed vector meson–baryon interaction originating from the s -, t -, u -channel diagrams and a contact interaction, all derived from the Lagrangian invariant under the gauge of the hidden local symmetry (HLS). We find the contributions from all the diagrams (except s -channel) to be important, contrary to the systems involving light Goldstone bosons where Weinberg–Tomozawa interaction gives the dominant contribution. Further, the transitions between the pseudoscalar meson–baryon (PB) and vector meson–baryon (VB) channels is obtained consistently by extending the Kroll–Ruderman theorem by replacing the photon by a vector meson, assuming the vector meson dominance. We find that the low-lying resonances couple strongly to VB channels. This information can be very useful in studying processes like photoproduction of low-lying resonances. Further, we find dynamical generation of new states in PB–VB coupled systems which can be related to the known resonances: Λ ( 2000 ) , Σ ( 1750 ) , Σ ( 1940 ) and Σ ( 2000 ) .

Kinematically complete picture of positron-impact ionisation of hydrogen

Kinematically complete fully quantum-mechanical solution of the positron-hydrogen scattering problem is presented above the breakup threshold. The calculations are performed within the convergent coupled-channel formalism. This leads to an unexpected formula for calculating the total ionisation cross section that appears to resolve the remaining discrepancy between theory and experiment.

Continuum effects in the scattering of exotic nuclei

We discuss continuum effects in the scattering of exotic nuclei, and more specifically on the 11Be + 64Zn scattering. 11Be is a typical example of an exotic nucleus, with a low binding energy. Elastic, inelastic and breakup cross-sections of the 11Be + 64Zn system are computed in the Continuum Discretized Coupled Channel formalism, at energies near the Coulomb barrier. We show that converged cross-sections need high angular momenta as well as as large excitation energies in the wave functions of the projectile. Extensions to other systems are simulated by different collision energies, and by varying the binding energy of 11Be.

Dynamic polarization potential due to6Li breakup on12C

For ${}^{6}$Li scattering from ${}^{12}$C at five laboratory energies from 90 to 318 MeV, we study the dynamic polarization potential, DPP, due to the breakup of the projectile. The breakup is evaluated using standard continuum discretized coupled-channels formalism applied to a two-body cluster model of the projectile. The DPP is evaluated over a wide radial range using both direct $S$-matrix-to-potential inversion and trivially equivalent local potential methods which yield substantially and systematically different results. The radius at which the real DPP changes from external repulsion to interior attraction varies systematically with energy. This should be experimentally testable because, according to notch tests, this crossover radius is within a radial range to which elastic scattering should be sensitive. The imaginary DPP has an emissive (generative) region at the lower energies; this may be associated with counterintuitive properties of $|{S}_{L}|$.

Absence of a maximum in theSfactor at deep sub-barrier energies in the fusion reaction40Ca + 40Ca

The fusion reaction ${}^{40}$Ca + ${}^{40}$Ca was very recently reinvestigated by the Legnaro group and cross sections down to $\ensuremath{\mu}$b were measured. In the present work this reaction is analyzed within the coupled-channel formalism including ${2}^{+}$, ${3}^{\ensuremath{-}}$, and ${5}^{\ensuremath{-}}$ phonon states. The heavy-ion entrance channel potential is calculated within the double-folding prescription and comprises a direct local term and a local equivalent of the nonlocal knock-on exchange component. The single-particle densities entering the folding integrals are prescribed according to the density matrix expansion. Coupling potentials are calculated from the $G$-matrix Michigan three-range Yukawa-type semirealistic nucleon-nucleon interaction (M3Y) as well as one modern parametrization of the density-dependent Gogny effective interaction. Realistic deformation parameters are used. The best fit to the data is not pointing to a possible maximum in the astrophysical $S$-factor as in a previous study on sub-barrier fusion involving ${}^{48}$Ca projectiles.

NEGATIVE PARITY TETRAQUARKS WITH THE OPEN CHARM

The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson–meson states with the four-quark states is considered. The four-quark amplitudes of the negative parity tetraquarks including the quarks of three flavors (u, d, s) and the charmed quark are constructed. The poles of these amplitudes determine the masses of tetraquarks. The mass values of low-lying tetraquarks with the spin-parity JP = 0-, 1-, 2-, 3- are calculated.

Consistent description of hindrance in sub-barrier fusion ofCa48withS36,Ca48, andZr96

Recent fusion reaction data for the systems ${}^{36}\mathrm{S}+{}^{48}\mathrm{Ca}$, ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, and ${}^{96}\mathrm{Zr}+{}^{48}\mathrm{Ca}$ are analyzed within the coupled-channel formalism. The heavy-ion entrance channel potential is calculated employing an improved double-folding prescription. The nonlocal kernel arising from the knock-on exchange component of the effective $N\ensuremath{-}N$ interaction is localized within the lowest order of the Perey-Saxon approach, including full recoil. The single-particle densities entering the folding integrals are prescribed according to the density matrix expansion method. The investigation is more elaborated because each case is tested with four different types of $N\ensuremath{-}N$ effective forces: The two standard parametrizations of the density-independent M3Y force (Reid and Paris) and two parametrizations of the density-dependent Gogny force (D1S and D1N). A consistent description of all three reactions is achieved by keeping fixed the nuclear structure input for $^{48}\mathrm{Ca}$. The inclusion of 2${}^{+}$ and 3${}^{\ensuremath{-}}$ phonon states in the coupled-channel calculation, within an energy excitation window identical for all three reactions explains better the hindrance in extreme sub-barrier fusion cross sections. The interactions providing the best fit to the data are not pointing to a possible maximum in the astrophysical $S$ factor, thereby confirming the conclusion reached by the Legnaro group for these cases.

Parity nonconservation in deuteron photoreactions

We calculate the asymmetries in parity nonconserving deuteron photodisintegration due to circularly polarized photons gamma+d to n+p with the photon laboratory energy ranging from the threshold up to 10 MeV and the radiative capture of thermal polarized neutrons by protons n+p to gamma+d. We use the leading order electromagnetic Hamiltonian neglecting the smaller nuclear exchange currents. Comparative calculations are done by using the Reid93 and Argonne v18 potentials for the strong interaction and the DDH and FCDH "best" values for the weak couplings in a weak one-meson exchange potential. A weak NDelta transition potential is used to incorporate also the Delta(1232)-isobar excitation in the coupled-channels formalism.

A Relativistic Coupled-Channel Formalism for Electromagnetic Form Factors of 2-Body Bound States

We discuss a Poincar\'e invariant coupled-channel formalism which is based on the point-form of relativistic quantum mechanics. Electromagnetic scattering of an electron by a 2-body bound state is treated as a 2-channel problem for a Bakamjian-Thomas-type mass operator. In this way retardation effects in the photon-exchange interaction are fully taken into account. The electromagnetic current of the 2-body bound state is then extracted from the one-photon-exchange optical potential. As an application we calculate electromagnetic pion and deuteron form factors. Wrong cluster properties, inherent in the Bakamjian-Thomas framework, are seen to cause spurious (unphysical) contributions in the current. These are separated and eliminated in an unambiguous way such that one is left with a current that has all the desired properties.

Hindrance of the excitation of the Hoyle state and the ghost of the [formula omitted] state in 12C

While the Hoyle state (the isoscalar 02+ excitation at 7.65 MeV in 12C) has been observed in almost all the electron and α inelastic scattering experiments, the second 2+ excited state of 12C at Ex≈10 MeV, believed to be an excitation of the Hoyle state, has not been clearly observed in these measurements excepting the high-precision (α,α′)C12 experiments at Eα=240 and 386 MeV. Given the (spin and isospin zero) α-particle as a good probe for the nuclear isoscalar excitations, it remains a puzzle why the peak of the 22+ state could not be clearly identified in the measured (α,α′)C12 spectra. To investigate this effect, we have performed a microscopic folding model analysis of the α+C12 scattering data at 240 and 386 MeV in both the Distorted Wave Born Approximation (DWBA) and coupled-channel (CC) formalism, using the nuclear transition densities given by the antisymmetrized molecular dynamics (AMD) approach and a complex CDM3Y6 density dependent interaction. Although AMD predicts a very weak transition strength for the direct (01+→22+) excitation, our detailed analysis has shown evidence that a weak ghost of the 22+ state could be identified in the 240 MeV (α,α′)C12 data for the 03+ state at 10.3 MeV, when the CC effects by the indirect excitation of the 22+ state are taken into account. Based on the same AMD structure input and preliminary (α,α′)C12 data at 386 MeV, we have estimated relative contributions from the 22+ and 03+ states to the excitation of 12C at Ex≈10 MeV as well as possible contamination by 31− state.

S-WAVE BOTTOM TETRAQUARKS

The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson–meson states with the four-quark states is considered. The four-quark amplitudes of the tetraquarks, including u, d, s, and bottom quarks, are constructed. The poles of these amplitudes determine the masses and widths of S-wave bottom tetraquarks.