Coupled-channel Effects Research Articles

Effect of channel coupling on the elastic scattering of lithium isotopes

Herein, we investigated the channel coupling (CC) effect on the elastic scatterings of lithium (Li) isotopes ($A =$ 6--9) for the $^{12}$C and $^{28}$Si targets at $E/A =$ 50--60 MeV. The wave functions of the Li isotopes were obtained using the stochastic multi-configuration mixing (SMCM) method based on the microscopic-cluster model. The proton radii of the $^{7}$Li, $^{8}$Li, and $^{9}$Li nuclei became smaller as the number of valence neutrons increased. The valence neutrons in the $^{8}$Li and $^{9}$Li nuclei exhibited a glue-like behavior, thereby attracting the $\alpha$ and $t$ clusters. Based on the transition densities derived from these microscopic wave functions, the elastic-scattering cross section was calculated using a microscopic coupled-channel (MCC) method with a complex $G$-matrix interaction. The existing experimental data for the elastic scatterings of the Li isotopes and $^{10}$Be nuclei were well reproduced. The Li isotope elastic cross sections were demonstrated for the $^{12}$C and $^{28}$Si targets at $E/A$ =53 MeV. The glue-like effect of the valence neutrons on the Li isotope was clearly demonstrated by the CC effect on elastic scattering. Finally, we realize that the valence neutrons stabilized the bindings of the core parts and the CC effect related to core excitation was indeed reduced.

Reaction channel coupling effects for nucleons on O16 : Induced undularity and proton-neutron potential differences

Background: Precise fitting of scattering observables suggests that the nucleon-nucleus interaction is $l$ dependent. Such $l$ dependence has been shown to be $S$-matrix equivalent to an undulatory $l$-independent potential. The undulations include radial regions where the imaginary term is emissive.Purpose: To study the dynamical polarization potential (DPP) generated in proton-$^{16}\mathrm{O}$ and neutron-$^{16}\mathrm{O}$ interaction potentials by coupling to pickup channels. Undulatory features occurring in these DPPs can be compared with corresponding features of empirical optical model potentials (OMPs). Furthermore, the additional inclusion of coupling to vibrational states of the target will provide evidence for dynamically generated nonlocality.Methods: The fresco code provides the elastic channel $S$-matrix ${S}_{lj}$ for chosen channel couplings. Inversion, ${S}_{lj}\ensuremath{\rightarrow}V(r)+\mathbf{l}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{s}\phantom{\rule{0.16em}{0ex}}{V}_{\mathrm{SO}}(r)$, followed by subtraction of the bare potential, yields an $l$-independent and local representation of the DPP due to the chosen couplings.Results: The DPPs have strongly undulatory features, including radial regions of emissivity. Certain features of empirical DPPs appear, e.g., the full inverted potential has emissive regions. The DPPs for different collective states are additive except near the nuclear center, whereas the collective and reaction channel DPPs are distinctly nonadditive over a considerable radial range, indicating dynamical nonlocality. Substantial differences between the DPPs due to pickup coupling for protons and neutrons occur; these imply a greater difference between proton and neutron OMPs than the standard phenomenological prescription.Conclusions: The onus is on those who object to undularity in the local and $l$-independent representation of nucleon elastic scattering to show why such undulations do not occur. This work suggests that it is not legitimate to halt model-independent fits to high-quality data at the appearance of undularity.

Systematic analysis of inelastic α scattering off self-conjugate A=4n nuclei

We systematically measured the differential cross sections of inelastic $\ensuremath{\alpha}$ scattering off self-conjugate $A=4n$ nuclei at two incident energies ${E}_{\ensuremath{\alpha}}=130\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and $386\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ at Research Center for Nuclear Physics, Osaka University. The measured cross sections were analyzed by the distorted-wave Born-approximation (DWBA) calculation using the single-folding potentials, which are obtained by folding macroscopic transition densities with the phenomenological $\ensuremath{\alpha}N$ interaction. The DWBA calculation with the density-dependent $\ensuremath{\alpha}N$ interaction systematically overestimates the cross sections for the $\mathrm{\ensuremath{\Delta}}L=0$ transitions. However, the DWBA calculation using the density-independent $\ensuremath{\alpha}N$ interaction reasonably well describes all the transitions with $\mathrm{\ensuremath{\Delta}}L=0$--4. We examined uncertainties in the present DWBA calculation stemming from the macroscopic transition densities, distorting potentials, phenomenological $\ensuremath{\alpha}N$ interaction, and coupled channel effects in $^{12}\mathrm{C}$. It was found that the DWBA calculation is not sensitive to details of the transition densities nor the distorting potentials, and the phenomenological density-independent $\ensuremath{\alpha}N$ interaction gives reasonable results. The coupled-channel effects are negligibly small for the ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$ states in $^{12}\mathrm{C}$, but not for the ${0}_{2}^{+}$ state. However, the DWBA calculation using the density-independent interaction at ${E}_{\ensuremath{\alpha}}=386\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ is still reasonable even for the ${0}_{2}^{+}$ state. We concluded that the macroscopic DWBA calculations using the density-independent interaction are reliably applicable to the analysis of inelastic $\ensuremath{\alpha}$ scattering at ${E}_{\ensuremath{\alpha}}\ensuremath{\sim}100\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}/\mathrm{u}$.

Coupled channel effects on resonance states of positronic alkali atom

S-wave Feshbach resonance states belonging to dipole series in positronic alkali atoms (e+Li, e+Na, e+K, e+Rb and e+Cs) are studied by coupled-channel calculations within a three-body model. Resonance energies and widths below a dissociation threshold of alkali-ion and positronium are calculated with a complex scaling method. Extended model potentials that provide positronic pseudo-alkali-atoms are introduced to investigate the relationship between the resonance states and dissociation thresholds based on a three-body dynamics. Resonances of the dipole series below a dissociation threshold of alkali-atom and positron would have some associations with atomic energy levels that results in longer resonance lifetimes than the prediction of the analytical law derived from the ion–dipole interaction.

Nπ scattering in the Roper channel

We present results from our recent lattice QCD study of Nπ scattering in the positive-parity nucleon channel, where the puzzling Roper resonance N*(1440) resides in experiment. Using a variety of hadron operators, that include qqq-like, Nπ in p-wave and Nσ in s-wave, we systematically extract the excited lattice spectrum in the nucleon channel up to 1.65 GeV. Our lattice results indicate that Nπ scattering in the elastic approximation alone does not describe a low-lying Roper. Coupled channel effects between Nπ and Nππ seem to be crucial to render a low-lying Roper in experiment, reinforcing the notion that this state could be a dynamically generated resonance. After giving a brief motivation for studying the Roper channel and the relevant technical details to this study, we will discuss the results and the conclusions based on our lattice investigation and in comparison with other lattice calculations.

Charmonium-nucleon interactions from the time-dependent HAL QCD method

The charmonium-nucleon effective central interactions have been computed by the time-dependent HAL QCD method. This gives an updated result of a previous study based on the time-independent method, which is now known to be problematic because of the difficulty in achieving the ground-state saturation. We discuss that the result is consistent with the heavy quark symmetry. No bound state is observed from the analysis of the scattering phase shift; however, this shall lead to a future search of the hidden-charm pentaquarks by considering channel-coupling effects.

Properties of open and hidden charm mesons in light quark matter

In this work we study the implications of light-quark pionic matter at finite temperatures on the properties of open and hidden charm mesons. The meson-meson interactions are described by means of a chiral unitary approach accounting for coupled channels effects. The in-medium Lippmann-Schwinger Equations, which consider the change in self-energy that the mesons acquire from interacting with the surrounding pionic matter, are solved self-consistently, and the spectral functions of the mesons in the hot pion bath are obtained. It is observed that the charmed mesons develop a quite substantial pion-induced width, being of several tens at a temperature of 150 MeV. The $J/\Psi$ meson stays narrow, but its pionic width at 150 MeV, found to be around 0.1 MeV, is already larger that its vacuum width.

Masses of scalar and axial-vector B mesons revisited

The SU(3) quark model encounters a great challenge in describing even-parity mesons. Specifically, the qbar{q} quark model has difficulties in understanding the light scalar mesons below 1 GeV, scalar and axial-vector charmed mesons and 1^+ charmonium-like state X(3872). A common wisdom for the resolution of these difficulties lies on the coupled channel effects which will distort the quark model calculations. In this work, we focus on the near mass degeneracy of scalar charmed mesons, D_{s0}^* and D_0^{*0}, and its implications. Within the framework of heavy meson chiral perturbation theory, we show that near degeneracy can be qualitatively understood as a consequence of self-energy effects due to strong coupled channels. Quantitatively, the closeness of D_{s0}^* and D_0^{*0} masses can be implemented by adjusting two relevant strong couplings and the renormalization scale appearing in the loop diagram. Then this in turn implies the mass similarity of B_{s0}^* and B_0^{*0} mesons. The P_0^* P'_1 interaction with the Goldstone boson is crucial for understanding the phenomenon of near degeneracy. Based on heavy quark symmetry in conjunction with corrections from QCD and 1/m_Q effects, we obtain the masses of B^*_{(s)0} and B'_{(s)1} mesons, for example, M_{B_{s0}^*}= (5715pm 1),mathrm{MeV}+delta Delta _S, M_{B'_{s1}}=(5763pm 1),mathrm{MeV}+delta Delta _S with delta Delta _S being 1/m_Q corrections. We find that the predicted mass difference of 48 MeV between B'_{s1} and B_{s0}^* is larger than that of 20–30 MeV inferred from the relativistic quark models, whereas the difference of 15 MeV between the central values of M_{B'_{s1}} and M_{B'_1} is much smaller than the quark model expectation of 60–100 MeV. Experimentally, it is important to have a precise mass measurement of D_0^* mesons, especially the neutral one, to see if the non-strange scalar charmed meson is heavier than the strange partner as suggested by the recent LHCb measurement of the D_0^{*pm }.

Effects of coupled channels on cb̄ masses and decays in NRQM with OGEP

The complete spectrum of [Formula: see text] states is obtained in a phenomenological nonrelativistic quark model (NRQM), which consists of a confinement potential and one gluon exchange potential (OGEP) as effective quark–antiquark potential with coupled channel effects. We make predictions for the radiative decay (E1 and M1) widths and weak decay widths of [Formula: see text] states in the framework of NRQM formalism.

Study of similarity and dissimilarity between10Be and9Li nuclei with microscopic structure and reaction models

We apply the microscopic nuclear structure and reaction models to the elastic scattering of the10Be and9Li nuclei. The states of the10Be and9Li nuclei are described as an α + α(t) + n + n four-body system based on the cluster wave function, respectively. The elastic scattering cross section is obtained by the microscopic coupled channel (MCC) calculation with the MPa interaction, which is the latest version of the complex G-matrix interaction derived from the ESC NN interaction model. We compare the channel coupling (CC) effect of the10Be nucleus with that of the9Li nucleus in the elastic scattering cross sections calculated with the same incident energy per nucleon. At the backward angles, the CC effect on the elastic scattering cross section for the incident10Be nucleus is clearly larger than that for the incident9Li nucleus. We investigate the dissimilarity for the CC effect through the dynamical polarization potential.

Effect of Coupled Channels on Semiclassical and Quantum Mechanical Calculations for Heavy Ion Fusion Reactions

Effect of Coupled Channels on Semiclassical and Quantum Mechanical Calculations for Heavy Ion Fusion Reactions

Cb¯ spectrum and decay properties with coupled channel effects

The mass spectrum of $c\bar{b}$ states has been obtained using the phenomenological relativistic quark model (RQM) with coupled channel effects. The Hamiltonian used in the investigation has confinement potential and confined one gluon exchange potential (COGEP). In the frame work of RQM a study of M1 and E1 radiative decays of $c\bar{b}$ states has been made. The weak decay widths in the spectator quark approximation have been estimated. An overall agreement is obtained with the experimental masses and decay widths.

How large is the contribution of excited mesons in coupled-channel effects?

We study the excited $B$ mesons' contributions to the coupled-channel effects under the framework of ${}^3P_0$ model for the bottomonium. Contrary to what has been widely accepted, the contributions of $P$ wave $B$ mesons are generally the largest and this result is independent of the potential parameters to some extent. We also push the calculation beyond $B(1P)$ and carefully analyze the contributions of $B(2S)$. A form factor is a key ingredient to suppress the contributions of $B(2S)$ for low lying bottomonia. However, this suppression mechanism is not efficient for highly excited bottomonia such as $\Upsilon(5S)$ and $\Upsilon(6S)$. We give explanations why this difficulty happens to ${}^3P_0$ model and suggest analyzing flux-tube breaking model for the full calculation of coupled-channel effects.

Coupled channel calculations using semi-classical and quantum mechanical approaches for light and medium mass systems

A semi-classical and full quantum mechanical approaches have been used to study the effect of channel coupling on the calculations of the total fusion reaction cross-section σfus, the fusion barrier distribution Dfus and the reaction probability for the light systems (4He+233U, 13C+48Ti) and the medium system (46Ti+46Ti). The semi-classical approach used in the present work is based on the method of the Alder and Winther for Coulomb excitation. The results obtained from our semi-classical and full quantum mechanical calculations are compared with the available experimental data. The semi-classical calculations agree reasonably with the full quantum mechanical treatment and they were able to reproduce the experimental data in details for the total fusion reaction cross-section σfus, the fusion barrier distribution Dfus and the probability of the reaction.

Coupled channel calculations using semi-classical and quantum mechanical approaches for light and medium mass systems

A semi-classical and full quantum mechanical approaches have been used to study the effect of channel coupling on the calculations of the total fusion reaction cross-section σfus, the fusion barrier distribution Dfus and the reaction probability for the light systems (4He+233U, 13C+48Ti) and the medium system (46Ti+46Ti). The semi-classical approach used in the present work is based on the method of the Alder and Winther for Coulomb excitation. The results obtained from our semi-classical and full quantum mechanical calculations are compared with the available experimental data. The semi-classical calculations agree reasonably with the full quantum mechanical treatment and they were able to reproduce the experimental data in details for the total fusion reaction cross-section σfus, the fusion barrier distribution Dfus and the probability of the reaction.

P -wave coupled channel effects in electron-positron annihilation

$P$-wave coupled channel effects arising from the $D\overline{D}$, $D{\overline{D}}^{*}+\mathrm{c}.\mathrm{c}.$, and ${D}^{*}{\overline{D}}^{*}$ thresholds in ${e}^{+}{e}^{\ensuremath{-}}$ annihilations are systematically studied. We provide an exploratory study by solving the Lippmann-Schwinger equation with short-ranged contact potentials obtained in the heavy quark limit. These contact potentials can be extracted from the $P$-wave interactions in the ${e}^{+}{e}^{\ensuremath{-}}$ annihilations, and then be employed to investigate possible isosinglet $P$-wave hadronic molecules. In particular, such an investigation may provide information about exotic candidates with quantum numbers ${J}^{\mathrm{PC}}={1}^{\ensuremath{-}+}$. In the mass region of the $D\overline{D}$, $D{\overline{D}}^{*}+\mathrm{c}.\mathrm{c}.$, and ${D}^{*}{\overline{D}}^{*}$ thresholds, there are two quark model bare states, i.e. the $\ensuremath{\psi}(3770)$ and $\ensuremath{\psi}(4040)$, which are assigned as $({1}^{3}{D}_{1})$ and $({3}^{1}{S}_{1})$ states, respectively. By an overall fit of the cross sections of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}D\overline{D}$, $D{\overline{D}}^{*}+\mathrm{c}.\mathrm{c}.$, ${D}^{*}{\overline{D}}^{*}$, we determine the physical coupling constants to each channel and extract the pole positions of the $\ensuremath{\psi}(3770)$ and $\ensuremath{\psi}(4040)$. The deviation of the ratios from that in the heavy quark spin symmetry (HQSS) limit reflects the HQSS breaking effect due to the mass splitting between the $D$ and the ${D}^{*}$. Besides the two poles, we also find a pole a few MeV above the $D{\overline{D}}^{*}+\mathrm{c}.\mathrm{c}.$ threshold which can be related to the so-called $G(3900)$ observed earlier by BABAR and Belle. This scenario can be further scrutinized by measuring the angular distribution in the ${D}^{*}{\overline{D}}^{*}$ channel with high luminosity experiments.

Coupled-channel effects for the bottomonium with realistic wave functions

With Gaussian expansion method (GEM), realistic wave functions are used to calculate coupled-channel effects for the bottomonium under the framework of ${}^3P_0$ model. The simplicity and accuracy of GEM are explained. We calculate the mass shifts, probabilities of the $B$ meson continuum, $S-D$ mixing angles, strong and dielectric decay widths. Our calculation shows that both $S-D$ mixing and the $B$ meson continuum can contribute to the suppression of the vector meson's dielectric decay width. We suggest more precise measurements on the radiative decays of $\Upsilon(10580)$ and $\Upsilon(11020)$ to distinguish these two effects. The above quantities are also calculated with simple harmonic oscillator (SHO) wave function approximation for comparison. The deviation between GEM and SHO indicates that it is essential to treat the wave functions accurately for near threshold states.

Hindered magnetic dipole transitions between P -wave bottomonia and coupled-channel effects

In the hindered magnetic dipole transitions of heavy quarkonia, the coupled-channel effects originating from the coupling of quarkonia to a pair of heavy and anti-heavy mesons can play a dominant role. Here, we study the hindered magnetic dipole transitions between two $P$-wave bottomonia, $\chi_b(n P)$ and $h_b(n^\prime P)$, with $n\neq n^\prime$. In these processes the coupled-channel effects are expected to lead to partial widths much larger than the quark model predictions. We estimate these partial widths which, however, are very sensitive to unknown coupling constants related to the vertices $\chi_{b0}(nP)B\bar B$. A measurement of the hindered M1 transitions can shed light on the coupled-channel dynamics in these transitions and hence on the size of the coupling constants. We also suggest to check the coupled-channel effects by comparing results from quenched and fully dynamical lattice QCD calculations.

Investigating multichannel quantum tunneling in heavy-ion fusion reactions with Bayesian spectral deconvolution

Excitations of colliding nuclei during a nuclear reaction considerably affect fusion cross sections at energies around the Coulomb barrier. It has been demonstrated that such channel coupling effects can be represented in terms of a distribution of multiple fusion barriers. I here apply a Bayesian approach to analyze the so-called fusion barrier distributions. This method determines simultaneously the barrier parameters and the number of barriers. I particularly investigate the $^{16}\mathrm{O}+^{144}\mathrm{Sm}$ and $^{16}\mathrm{O}+^{154}\mathrm{Sm}$ systems in order to demonstrate the effectiveness of the method. The present analysis indicates that the fusion barrier distribution for the former system is most consistent with three fusion barriers, even though the experimental data show only two distinct peaks.

Hadronic resonances enhanced by thresholds

We present a neat example of a meson--baryon system where the vicinity of two different thresholds enhances the binding of a hadronic resonance, a pentaquark. As a consequence the pattern of states may change when moving among different flavor sectors, what poses a warning on naive extrapolations to heavy flavor sectors based on systematic expansions. For this purpose we simultaneously analyze the $N\bar D$ and $NB$ two-hadron systems looking for possible bound states or resonances. When a resonance is controlled by a coupled-channel effect, going to a different flavor sector may enhance or diminish the binding. This effect may, for example, generate significant differences between the charmonium and bottomonium spectra above open-flavor thresholds or pentaquark states in the open-charm and open-bottom sectors.