1-20 Bottomonium-like States in Coupled-channel Model with on-shell Approximation

At present the Bottomonium spectra have not been so well explored as the Charmonium spectra. Espescially,the Bottomonium states found in experiment are less than the Charmonium states. However, prior to the discoveryof Zc(3900) in the +J= invariant mass spectra, the charged states possibly composed of at least four-quark is wellestablished in Bottomonium sector, namely the Zb(10610) and Zb(10650) states[1]. They are narrow structures in themass spectra of the ±Υ(nS) (n=1;2;3) and ±hb(mP) (m=1; 2). It is possible to predict other Bottomonium-likestates in the coupled-channel model based on the measured masses and widths of these states. The coupled-channelmodel considers the important rescattering process of final hadrons and is usually proceeded from the Bethe-Salpeterequation, whose expression in the on-shell approximation is written as follows[2]:

1-30 Using X(3823)->J= +.. to Identify Coupled-channel Effects

Very recently, the Belle and BESIII experiments observed a new charmonium-like state X(3823), which is a good candidate for the D-wave charmonium (13D2). Because the X(3823) is just near the DˉD threshold, the decay X(3823) ! J= +?? can be a golden channel to test the significance of coupled-channel effects. In this work[1], this decay is considered including both the hidden-charm dipion and the usual quantum chromodynamics multipole expansion (QCDME) contributions.

The Φp bound state in the unitary coupled-channel approximation

The strong attractive interaction of the φ meson and the proton has recently been reported by the ALICE Collaboration.The corresponding scattering length f_(0) is given as Re(f_(0))=0.85±0.34(stat)±0.14(syst)and Im(f_(0))=0.16±0.10(stat)±0.09(syst)fm.The fact that the real part is significant in contrast to the imaginary part indicates a dominant role of elastic scattering,whereas the inelastic process is less important.In this work,such scattering processes are inspected based on a unitary coupled-channel approach inspired by the Bethe-Salpeter equation.The φp scattering length is calculated based on this approach,and it is found that the experimental value of the φp scattering length can be obtained only if the attractive interaction of the φ meson and the proton is taken into account.A significant outcome of such attractive interaction is a two-pole structure in the φp scattering amplitude.One of the poles,located at(1969−i283)MeV might correspond to N(1895)1/2^(−)or N(1875)3/2^(−)as listed in the review of the Particle Data Group(PDG).The other one,located at 1949−i3 MeV should be a φN bound state,which has no counterpart in the PDG data.

Exploratory study of possible resonances in heavy meson-heavy baryon coupled-channel interactions

We use a unitary coupled-channel model to study the DAc-D∑c interactions. In our calculation, SU（3）flavor symmetry is applied to determine the coupling constants. Several resonant and bound states with different spin and parity are dynamically generated in the mass range of the recently observed pentaquarks. The approach is also extended to the hidden beauty sector to study the BΛb-B∑b interactions. As the b-quark mass is heavier than the c-quark mass, there are more resonances observed for the BΛb-B∑b interactions and they are more tightly bound.

Disentangling the nature of resonances in coupled-channel models

We present severM possible hadronic states found in coupled-channel models within the on-shell approx- imation. The interaction potential is constructed as a sum of the tree-level Feynman diagrams calculated with the effective Lagrangians. Based on the recent empirical data, we illustrate the possible existence of severM baryonic and mesonic states with definite quantum numbers in the model. We give their properties for the purpose of further study and discuss the potential of finding them in future experiments.

Unnatural parity resonance states in positron-excited hydrogen scattering

The coupled-channels optical method for positron scattering has been applied to investigate resonance states with unnatural parities in a positron-excited hydrogen system. The positronium formation channels and continuum channel are included via a complex equivalent local potential. Resonance states with angular momenta L =- 1 to L = 2 and parities （-1）L＋1 are calculated. Resonance energies and widths are reported and compared with other theoretical calculations. We found that the opening positronium formation channels play an important role in forming nondipole Feshbach resonances.

Investigating the effect of entrance channel mass asymmetry on fusion reactions using the Skyrme energy density formalism

In the present investigations,the fusion crosssections for the formation of 200Pb compound nucleus(CN)using 16O+184 W,30Si+170Er,and 40Ar+160Gd nuclear reactions at energies above the Coulomb barrier were calculated to understand the effect of entrance channel mass asymmetry(α)on the fusion reactions;the Skyrme energy density formalism(SEDF)was used for this calculation.The SEDF uses the Hartree-Fock-Bogolyubov(HFB)computational program with Skyrme forces such as SkM*,SLy4,and SLy5 to obtain the nucleus-nucleus potential parameters for the above reactions.Using the SEDF model with SkM*,SLy4,and SLy5 interaction forces,the theoretical fusion cross-sections were determined above the barrier energy and compared with the available experimental fusion cross-sections.The results show a close agreement between the theoretical and experimental values for all selected systems at energies well above the barrier.However,near the barrier energies,the theoretical values were observed to be higher than the experimental values.

Calculation of Positronium Formation Cross Sections in Positron-Mg Collision

Using the optical-model, we theoretically investigate the positronium （Ps） formation in e^＋-Mg collision from the positronium threshold to 60.0eV. A complex equivalent local polarization potential is obtained to describe the rearrangement process, which reproduces Ps formation cross section. We report the total Ps （n = 1 ＋ 2） formation cross sections and compare them with the experimental measurements and other theoretical results.

Calculations of state-selective differential cross sections for charge transfer in collisions between O^(3+) and H_2

The non-dissociative charge-transfer processes in collisions between O^3＋ and H2 are investigated by using the quantum-mechanical molecular-orbital coupled-channel （QMOCC） method. The adiabatic potentials and radial coupling matrix elements utilized in the QMOCC calculations are obtained with the spin-coupled valence-bond approach. Electronic and vibrational state-selective differential cross sections are presented for projectile energies of 0.1, 1.0 and 10.0eV/u in the H2 orientation angles of 45° and 89°. The electronic and the vibrational state-selective differential cross sections show similar behaviours： they decrease as the scattering angle increases, and beyond a specific angle the oscillating structures appear. Moreover, it is also found that the vibrational state-selective differential cross sections are strongly orientation-dependent, which provides a possibility to determine the orientations of molecule H2 by identifying the vibrational state-selective differential scattering processes.

Breakup Effect of Weakly Bound Projectile on the Barrier Distribution Around Coulomb Barrier

The excitation function of quasi-elastic （QEL） scattering at a backward angle has been measured for 9^Be＋208^Pb. The barrier distribution was extracted by means of the first derivative of the measured excitation function and calculated with the coupled-channel model. The present work shows that the experimental barrier distribution extracted from QEL scattering is shifted to the low energy side by 1.5 MeV as compared with the theoretical one. This energy discrepancy indicates that breakup is important in the colliding processes of the weakly bound nucleus system.

Investigating the impact of the universal function of the nuclear proximity potential in heavy-ion fusion cross sections

The fusion barriers and cross sections of 15 colliding systems with 320≤Z_(1)Z_(2)≤1512 are investigated in detail to understand the influence of the universal function of proximity potential formalism in the heavy-ion fusion mechanism.To realize this goal,we select three versions of the phenomenological proximity potentials,including Prox.77,Zhang 2013,and Guo 2013,to calculate the nucleus-nucleus potential.The experimental fusion cross sections for the selected reactions are analyzed using the standard coupled-channel calculations,including couplings to the low-lying 2^(+)and 3^(-)states in the target and projectile.The calculated results show that the universal functions of the Guo 2013 and Prox.77 models provide the lowest and highest fusion barriers,respectively.In addition,it is found that the height of the fusion barriers is enhanced by increasing the mass number of the projectile from light to heavy ones.The highest sensitivity to the mass number of the projectile belongs to the results of Prox.77.A discussion is also presented on the influence of the universal function on the radial behavior of the interaction potential in the allowed region for overlapping configurations.Our results reveal that the best fit to the experimental data of the fusion cross sections for the reactions involving light and medium nuclei is obtained using the universal function of the Zhang 2013 model.For the heavier systems,the results of the Guo 2013 model at sub-barrier energies provide a good description of the available data.

New insight into the exotic states strongly coupled with the DD^(*)from the T_(cc)^t(+)

We have investigated the internal structure of the open-and hidden-charmed(DD^(*)/DD^(*))molecules in the unified framework.We first fit the experimental lineshape of the Tt state and extract the DD^(*)interaction,from which the T is assumed to arise solely.Then we obtain the DD^(*)interaction by charge conjugation.Our results show that the DD*interaction is attractive but insufficient to form X(3872)as a bound state.Instead,its formation requires the crucial involvement of the coupled channel effect between the DD^(*)and cc components,although the cc accounts for approximately 1%only.Besides X(3872),we have obtained a higher-energy state around 3957.9 MeV with a width of 16.7 MeV,which may be a potential candidate for the X(3940).In J^(PC)=1^(+-)sector,we have found two states related to the iso-scalar X(3872)and h_(c)(2P),respectively.Our combined study provides valuable insights into the nature of these DD^(+)/DD^(+)exotic states.

Single-particle resonances in a deformed relativistic potential

The positive-parity single-neutron levels in an axially-deformed relativistic quadrupole Woods-Saxon potential are analyzed. Neutron states are obtained as the solutions of the corresponding single-particle Dirac equation, using the coupled-channels method in the coordinate space. The evolution of the levels close to the continuum threshold and, in particular, the occurrence of singleneutron resonant states as the functions of the axial deformation parameter 0 β 0.5, are examined using the eigenphase representation. Calculations are performed for different values of the radius of the potential (R/r 0 ) 3 , corresponding to a variation of the mass number A.

Z^+(4430) and Analogous Heavy Flavor States

We have studied Z+(4430)as a D*D1 molecule from the quark model,state mixing effect is considered by solving the coupled channel Schrdinger equation numerically. More precise measurements of Z+(4430)mass and width,partial wave analysis are helpful to understand its structure. If it lies below the D*D1 threshold,molecule interpretation with JP=1-is favored,and JP=0-can not be ruled out. Otherwise Z+(4430)may be a virtual state with JP=2-. The analogous heavy flavor mesons Z+bb and Z++bc are considered as well,and the masses predicted in our model are in agreement with the predictions from the potential model and QCD sum rule.

Fine splitting in the charmonium spectrum with a channel coupling effect

We study the fine splitting in the charmomium spectrum in the quark model with the channel coupling effect, including DD, DD＊, D＊D＊ and DsDs, DsDs＊, Ds＊Ds＊ channels. The interaction for channel coupling is constructed from the current-current Lagrangian related to the color confinement and the onegluon exchange potentials. By adopting the massive gluon propagator from the lattice cMculation in the nonperturbative region, the coupling interaction is further simplified to four-fermion interaction. The numerical calculation still prefers the assignment 1＋＋ of X（3872）.

Self-consistent analysis of sub-barrier fusion enhancement effect in Ca+Ca and Ni+Ni

The fusion dynamic mechanism of heavy ions at energies near the Coulomb barrier is complicated and still not very clear up to now. Accordingly, a self-consistent method based on the CCFULL calculations has been developed and applied for an ongoing study of the effect of the positive Q-value neutron transfer （PQNT） channels in this work. The typical experimental fusion data of Ca ＋ Ca and Ni ＋ Ni is analyzed within the unified calculation scheme. The PQNT effect in near-barrier fusion is further confirmed based on the self-consistent analysis and extracted quantitatively.

Survey of deep sub-barrier heavy-ion fusion hindrance phenomenon for positive and negative Q-value systems using the proximity-type potential

A systematic survey of the accurate measurements of heavy-ion fusion cross sections at extreme sub-barrier energies is performed using the coupled-channels(CC)theory that is based on the proximity formalism.This work theoretically explores the role of the surface energy coefficient and energy-dependent nucleus-nucleus proxim-ity potential in the mechanism of the fusion hindrance of 14 typical colliding systems with negative Q-values,in-eluding ^(11a)B+^(197)AU,^(12)C+^(198)Pt,^(16)O+^(208)Pb,^(28)Si+^(94Mo),^(48)Ca+^(96)Zr,^(28Si+)^(64)Ni,^(58)Ni+^(58)Ni+,^(60)Ni+^(89)Y,^(12)C+^(204)Pb,^(36)S+^(64)Ni,^(36)S+^(90)Zr,^(40)Ca+^(90)Zr,^(40)Ca+^(40Ca)and ^(48)Ca+^(48)Ca,,as well as five typical colliding systems with positive Q-values,ineluding ^(12)C+^(30)Si,^24Mg+^(30)Si,^(36)Si+^(48)Ca, and ^(40)Ca+^(48)Ca.It is shown that the outcomes based on the proximity potential along with the above-mentioned physical effects achieve reasonable agreement with the experimentally observed data of the fusion cross sections(Tfus(£),astrophysical S(E)factors,and logarithmic derivatives L(E)in the energy region far below the Coulomb barrier.A discussion is also presented on the performance of the present theoretical approach in reproducing the experimental fusion barrier distributions for different colliding systems.

Study of excited nucleon states at EBAC:status and plans

We present an overview of a research program for the excited nucleon states in Excited Baryon Analysis Center （EBAC） at Jefferson Lab. Current status of our analysis of the meson production reactions based on the unitary dynamical coupled-channels model is summarized, and the N＊ pole positions extracted from the constructed scattering amplitudes are presented. Our plans for future developments are also discussed.