Coupled-channel Formalism Research Articles

Hexaquarks in the coupled-channel formalism

The relativistic six-quark equations are found in the framework of the dispersion relation technique. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The relativistic six-quark amplitudes of hexaquarks including the quarks of three flavors ($u$, $d$, $s$) are calculated. The poles of these amplitudes determine the masses of six-quark systems.

Lineshapes for composite particles with unstable constituents

We discuss on very general grounds possible lineshapes of composite particles with one unstable constituent. Expressions are derived in a coupled-channel formalism for constituents interacting in an S-wave with no assumption made on the width of one of them. We show how easy-to-use formulae, already existing in the literature, emerge for narrow constituents and identify the parameter that controls the regime of their applicability.

Channel coupling effects on the fusion excitation functions forSi28+Zr90,94in sub- and near-barrier regions

Fusion excitation functions and angular distributions of evaporation residues (ERs) have been measured for $^{28}\mathrm{Si}+^{90,94}\mathrm{Zr}$ systems around the Coulomb barrier using the recoil mass spectrometer, Heavy Ion Reaction Analyzer (HIRA). For both systems, the experimental fusion cross sections are strongly enhanced compared to the predictions of the one-dimensional barrier penetration model (1-d BPM) below the barrier. Coupled channels formalism has been employed to theoretically explain the observed sub-barrier fusion cross section enhancement. The enhancement could be explained by considering the coupling of the low-lying inelastic states of the projectile and target in the $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ system. In the sub-barrier region, the measured fusion cross sections for $^{28}\mathrm{Si}+^{94}\mathrm{Zr}$ turned out to be about an order of magnitude higher than the ones for the $^{28}\mathrm{Si}+^{90}\mathrm{Zr}$ system, which could not be explained by coupling to inelastic states alone. This observation indicates the importance of multinucleon transfer reaction channels with positive $Q$ values in the sub-barrier fusion cross section enhancement, because $^{90,94}\mathrm{Zr}$ are believed to have similar collective strengths. This implies that no strong isotopic dependence of fusion cross sections is expected as far as the couplings to collective inelastic states are concerned. In addition, the role of projectile and multiphonon couplings in the enhancement has been explored.

Structure ofGe72,74nuclei probed with a combined analysis of heavy-ion fusion reactions and Coulomb excitation

We study the fusion reactions of the $^{72}\mathrm{Ge}+^{72}\mathrm{Ge}$ and $^{74}\mathrm{Ge}+^{74}\mathrm{Ge}$ systems in terms of the full order coupled-channels formalism. We obtain the fusion excitation function as well as the fusion barrier distribution of these reactions using the coupling matrix suggested from the recent Coulomb excitation experiments. We compare those results with the results obtained by the coupling matrix based on the pure vibrational and rotational models. The barrier distribution for the $^{74}\mathrm{Ge}+^{74}\mathrm{Ge}$ reaction obtained with the experimental coupling matrix is in good agreement with that obtained with the vibrational model, in contrast to the rotational model. On the other hand, the calculations for $^{72}\mathrm{Ge}+^{72}\mathrm{Ge}$ system show that the fusion barrier distribution obtained with the experimental coupling matrix significantly differs from those obtained with vibrational and rotational models. Our study indicates that the shape of $^{74}\mathrm{Ge}$ is closer to spherical than to deformed, while $^{72}\mathrm{Ge}$ has a shape admixture in its ground state, which can be described by neither the vibrational nor the rotational models, as suggested by the Coulomb excitation experiments. This finding will resolve the debates concerning the structure of these nuclei.

Formation of Neutron-Rich and Superheavy Elements in Astrophysical Objects

We calculate the reaction and the fusion cross-sections of neutron-rich heavy nuclei taking light exotic isotopes as projectiles. Results of neutron-rich Pb and U isotopes are demonstrated as the representative targets and He, B as the projectiles. The Gluaber Model and the Coupled Channel Formalism are used to evaluate the reaction and the fusion cross-sections for the cases considered. Based on the analysis of these cross-sections, we predict the formation of heavy, superheavy and super-superheavy elements through rapid neutron/ light nuclei capture r-process of the nucleosynthesis in astrophysical objects.

Analysis of cross sections and Vector Analysing Powers of (d,p) reactions within the CDCC+DWBA approach.

Transfer reactions like A X(d,p) A+1 X are a powerful tool to investigate nuclear structure properties (see e.g. [1–3]) and the emergence of radioactive beams with high intensity will allow the use of this kind of reactions to study the properties of exotic nuclei. Nevertheless the analysis of reactions involving deuteron remains a difficult task because of its weakly bound and composite features. To overcome these issues, R.C. Johnson et al [4] and G.H. Ratwitcher [5] proposed in the seventies the Continuum Discretized Coupled Channels (CDCC) formalism which explicitly takes into account the composite property of the deuteron and includes the effects on cross sections of the coupling between the breakup and the deuteron ground state channels. Since then the CDCC approach has been widely studied [6–8] and it has been quite successfully applied to analyse elastic [7–9] , inelastic [8,10] and transfer cross sections [11–13]. In this contribution, I will propose to re-analyse transfer reactions by the means of CDCC+adiabatic approach for a set of targets with N = 20 or N ≈ 28. I will show that with this approach, using both the differential cross sections and the vector analysing powers one can determine the orbital angular momentum and the spin of the captured nucleon without any adjustment.

A Relativistic Coupled-Channel Formalism for the Pion Form Factor

The electromagnetic form factor of a confined quark-antiquark pair is calculated within the framework of point-form relativistic quantum mechanics. The dynamics of theexchanged photon is explicitly taken into account by treating theelectromagnetic scattering of an electron by a meson as a relativistic two-channel problem for a Bakamjian-Thomas type mass operator. This approach guarantees Poincare invariance. Using a Feshbach reduction the coupled-channel problem can be converted into a one-channel problem for the elastic electron-meson channel. By comparing the one-photon-exchange optical potential at the constituent and hadronic levels, we are able to unambiguously identify the electromagnetic meson form factor. Violations of cluster-separability properties, which are inherent in the Bakamjian-Thomas approach, become negligible for sufficiently large invariant mass of the electron-meson system. In the limit of an infinitely large invariant mass, an equivalence with form-factor calculations done in front-form relativistic quantum mechanics is established analytically.

S-WAVE BOTTOM BARYONS

The masses of S-wave bottom baryons are calculated in the framework of coupled-channel formalism. The relativistic three-quark equations for the bottom baryons using the dispersion relation technique are found. The approximate solutions of these equations based on the extraction of leading singularities of the amplitude are obtained. The calculated mass values of S-wave bottom baryons are in good agreement with the experimental ones.

Low-lying exotic mesons in the coupled-channel formalism

The relativistic four-quark equations are found in the framework of the dispersion relation technique. The dynamical mixing of the four-quark amplitudes and the glueball amplitudes is considered. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The four-quark amplitudes of exotic mesons including the quarks of three flavors $(u,d,s)$ are calculated. The poles of these amplitudes determine the masses of the exotic mesons.

Coupled-channel investigation of rotationally and vibrationally inelastic collisions between He and H2

The coupled-channel formalism has been employed for He + H2 collisions including rotational (j = 0, 2) and vibrational (n = 0, 1) levels and making use of the Kraus-Mies potential energy surface. Integral and differential cross sections are obtained at the total energies 0.3884, 0.9, and 1.4116 eV for rotational and vibrational transitions separately, and for the combined processes. Considerable use has been made of the microscopic reversibility principle to extract cross sections from the S matrix for de-excitations as well as for excitations. Cross sections for vibrational excitation are found to decrease when accompanied by rotational excitation. For vibrational de-excitation, the effect of rotational excitation is to increase the cross sections. Defining a most probable impact parameter bmax from the maximum in the partial integral cross sections, vibration excitation is found to occur at low bmax, while rotational excitation is observed at comparatively higher values. For simultaneous rotational and transitions, bmax decreases with increasing energy transfer. A deflection angle ©(cl is defined in terms of the impact parameters and the turning point radii for the initial and final channels, and a correlation between this angle and the maxima in the computed angular distributions is found. The transition probabilities for the rotational excitation j = 0 2 with simultaneous vibrational excitation and their physical interpretation are also discussed within the total angular momentum coupling scheme.

INSIGHTS INTO THE π-p → ηn REACTION MECHANISM

A dynamical coupled channels formalism is used to investigate the η–meson production mechanism on the proton induced by pions, in the total center-of-mass energy region from threshold up to 2 GeV. We show how and why studying exclusively total cross section data might turn out to be misleading in pinning down the reaction mechanism.

Tetraquarks with charm in coupled-channel formalism

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 approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The four-quark amplitudes of cryptoexotic mesons including the quarks of three flavours (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 are calculated.

Excitations of the Roper resonances

We present a method that incorporates solutions of a broad class of quark models into the coupled-channel formalism for the K matrix. The method is applied to the calculation of the P11 and P33 scattering amplitudes in the region of the N(1440) and Δ(1600) resonances. Solving the Lippmann-Schwinger equation for the K matrix we find a strong enhancement of the bare quark-model meson-baryon coupling constants consistent with the values used in effective Lagrangian approaches.

Effect on the heavy-ion fusion and elastic scattering cross sections of common approximations assumed in coupled-channel calculations

We study the effects of several approximations commonly used in coupled-channel analyses of fusion and elastic scattering cross sections. Our calculations are performed considering couplings to inelastic states in the context of the frozen approximation, which is equivalent to the coupled-channel formalism when dealing with small excitation energies. Our findings indicate that, in some cases, the effect of the approximations on the theoretical cross sections can be larger than the precision of the experimental data.

The N*(1710) as a resonance in the ππN system

We study the ππN system by solving the Faddeev equations, for which the input two-body t-matrices are obtained by solving the Bethe-Salpeter equation in the coupled-channel formalism. The potentials for the ππ, πN sub-systems and their coupled channels are obtained from chiral Lagrangians, which have been earlier used to study resonances in these systems successfully. In this work, we find a resonance in the ππN system with a mass of 1704 − i375/2MeV and with quantum numbers I = 1/2, J π = 1/2+. We identify this state with the N *(1710). This peak is found where the energies of the ππ sub-system fall in the region of the σ-resonance. We do not find evidence for the Roper resonance in our study indicating a more complex structure for this resonance, nor for any state with total isospin I = 3/2 or 5/2.

The physical meaning of scattering matrix singularities in coupled-channel formalisms⋆

The physical meaning of bare and dressed scattering matrix singularities has been investigated. Special attention has been attributed to the role of the well-known invariance of the scattering matrix with respect to the field transformation of the effective Lagrangian. Examples of evaluating bare and dressed quantities in various models are given.

Model-independent resonance parameter extraction from the trace of K and T matrices

A model-independent method for the determination of resonance parameters as K-matrix pole parameters from a T matrix is presented. The method is based on eliminating the dependence on the choice of channel basis by analyzing the trace of the K and T matrices in the coupled-channel formalism, rather than individual matrix elements of the multichannel scattering matrix.

Folding description of the fine structure of α decay to2+vibrational and transitional states

We analyze \ensuremath{\alpha}-decays to ground and ${2}^{+}$ vibrational states in even-even nuclei by using a coupled channels formalism. The \ensuremath{\alpha}-nucleus interaction is simulated by a double folding procedure using M3Y plus Coulomb two-body forces. Collective excitations are described by vibrations of the nuclear surface. We use a repulsive potential, with one independent parameter, in order to simulate Pauli principle and to adjust the energy of the resonant state to the experimental $Q$-value. The decaying state is identified with the zero nodes resonance inside the resulting pocket-like potential. We have found that the fine structure is very sensitive to the strength of the repulsive core and the vibrational parameter of the \ensuremath{\alpha}-nucleus potential. A satisfactory agreement with existing experimental data was obtained by using the vibrational strength as a free parameter. It turns out that the inverse of this parameter is proportional to the logarithm of the hindrance factor squared. Based on this fact we have made predictions for 15 vibrational \ensuremath{\alpha}-emitters.

Search for missing baryon resonances via associated strangeness photoproduction

Differential cross-section and single polarization observables in the process γp →K + Λ are investigated within a constituent-quark model and a dynamical coupled-channel formalism. The effects of two new nucleon resonances and of the K*(892)- and K1(1270)-exchanges are briefly presented.

Microscopic calculations of double and triple giant resonance excitations in heavy ion collisions

We perform microscopic calculations of the inelastic cross sections for the double and triple excitation of giant resonances induced by heavy-ion probes within a semiclassical coupled-channels formalism. The channels are defined as eigenstates of a bosonic quartic Hamiltonian constructed in terms of collective random-phase approximation phonons. Therefore, they are superpositions of several multiphonon states, also with different numbers of phonons, and the spectrum is anharmonic. The inclusion of ($n+1$) phonon configurations affects the states whose main component is a $n$-phonon one and leads to an appreacible lowering of their energies. We check the effects of such further anharmonicities on the previously published results for the cross section for the double excitation of giant resonances (GR). We find that the only effect is a shift of the peaks toward lower energies, the double GR cross section being unmodified by the explicity inclusion of the three-phonon channels in the dynamical calculations. The latter provide an important contribution to the cross section in the triple GR energy region, which, however, is still smaller than the experimental available data. The inclusion of four-phonon configurations in the structure calculations does not modify the results.