We review our calculation method, Gaussian expansion method （GEM）, to solve accurately the Schrodinger equations for bound, resonant and scattering states of few-body systems. Use is made of the Rayleigh-Ritz variat...We review our calculation method, Gaussian expansion method （GEM）, to solve accurately the Schrodinger equations for bound, resonant and scattering states of few-body systems. Use is made of the Rayleigh-Ritz variational method for bound states, the complex-scaling method for resonant states and the Kohn-type variational principle to S-matrix for scattering states. GEM was proposed 30 years ago and has been applied to a variety of subjects in few-body （3- to 5-body） systems, such as 1） few-nucleon systems, 2） few-body structure of hypernuelei, 3） clustering structure of light nuclei and unstable nuclei, 4） exotic atoms/molecules, 5） cold atoms, 6） nuclear astrophysics and 7） structure of exotic hadrons. Showing examples in our published papers, we explain i） high accuracy of GEM calculations and its reason, ii） wide applicability of GEM to various few-body systems, iii） successful predictions by GEM calculations before measurements. The total bound-state wave function is expanded in terms of few-body Gaussian basis functions spanned over all the sets of rearrangement Jacobi coordinates. Gaussians with ranges in geometric progression work very well both for short- range and long-range behavior of the few-body wave functions. Use of Gaussians with complex ranges gives much more accurate solution than in the case of real-range Gaussians, especially, when the wave function has many nodes （oscillations）. These basis functions can well be applied to calculations using the complex-scaling method for resonances. For the few-body scattering states, the amplitude of the interaction region is expanded in terms of those few-body Gaussian basis functions.展开更多
The dissociation temperatures of quarkonium states in a thermal medium are obtained in the framework of the quark model with the help of the Gaussian Expansion Method（GEM）.This is the first time this method has been...The dissociation temperatures of quarkonium states in a thermal medium are obtained in the framework of the quark model with the help of the Gaussian Expansion Method（GEM）.This is the first time this method has been applied to the dissociation problem of mesons.The temperature-dependent potential is obtained by fitting the lattice results.Solving the Schr¨odinger equation with the GEM,the binding energies and corresponding wave functions of the ground states and the excited states are obtained at the same time.The accuracy and efficiency of the GEM provide a great advantage for the dissociation problem of mesons.The results show that the ground states1^1S（0 ）and 1^3S（1 ）have much higher dissociation temperatures than other states,and the spin-dependent interaction has a significant effect on the dissociation temperatures of 1^3S（1 ）and 1^1S0.We also suggest using the radius of the bound state as a criterion of quarkonium dissociation.This can help to avoid the inaccuracy caused by the long tail of quarkonium binding energy dependence on temperature.展开更多
In the QCD-inspired potential model where the quark-antiquark interaction consists of the usual one- gluon-exchange and the mixture of long-range scalar and vector linear confining potentials with the lowest order rel...In the QCD-inspired potential model where the quark-antiquark interaction consists of the usual one- gluon-exchange and the mixture of long-range scalar and vector linear confining potentials with the lowest order relativistic correction, we investigate the mass spectra and electromagnetic processes of a bottomonium system by using the Gaussian expansion method. It reveals that the vector component of the mixing confinement is anticonfining and takes around 18.51% of the confining potential. Combining the new experimental data released by Belle, BaBar and LHC, we systematically discuss the energy levels of the bottomouium states and make the predictions of the electromagnetic decays for further experiments.展开更多
文摘We review our calculation method, Gaussian expansion method （GEM）, to solve accurately the Schrodinger equations for bound, resonant and scattering states of few-body systems. Use is made of the Rayleigh-Ritz variational method for bound states, the complex-scaling method for resonant states and the Kohn-type variational principle to S-matrix for scattering states. GEM was proposed 30 years ago and has been applied to a variety of subjects in few-body （3- to 5-body） systems, such as 1） few-nucleon systems, 2） few-body structure of hypernuelei, 3） clustering structure of light nuclei and unstable nuclei, 4） exotic atoms/molecules, 5） cold atoms, 6） nuclear astrophysics and 7） structure of exotic hadrons. Showing examples in our published papers, we explain i） high accuracy of GEM calculations and its reason, ii） wide applicability of GEM to various few-body systems, iii） successful predictions by GEM calculations before measurements. The total bound-state wave function is expanded in terms of few-body Gaussian basis functions spanned over all the sets of rearrangement Jacobi coordinates. Gaussians with ranges in geometric progression work very well both for short- range and long-range behavior of the few-body wave functions. Use of Gaussians with complex ranges gives much more accurate solution than in the case of real-range Gaussians, especially, when the wave function has many nodes （oscillations）. These basis functions can well be applied to calculations using the complex-scaling method for resonances. For the few-body scattering states, the amplitude of the interaction region is expanded in terms of those few-body Gaussian basis functions.
基金Supported by National Natural Science Foundation of China(11475085,11535005,11775118,11690030)the Fundamental Research Funds for the Central Universities(020414380074)the International Science&Technology Cooperation Program of China(2016YFE0129300)
文摘The dissociation temperatures of quarkonium states in a thermal medium are obtained in the framework of the quark model with the help of the Gaussian Expansion Method（GEM）.This is the first time this method has been applied to the dissociation problem of mesons.The temperature-dependent potential is obtained by fitting the lattice results.Solving the Schr¨odinger equation with the GEM,the binding energies and corresponding wave functions of the ground states and the excited states are obtained at the same time.The accuracy and efficiency of the GEM provide a great advantage for the dissociation problem of mesons.The results show that the ground states1^1S（0 ）and 1^3S（1 ）have much higher dissociation temperatures than other states,and the spin-dependent interaction has a significant effect on the dissociation temperatures of 1^3S（1 ）and 1^1S0.We also suggest using the radius of the bound state as a criterion of quarkonium dissociation.This can help to avoid the inaccuracy caused by the long tail of quarkonium binding energy dependence on temperature.
基金Supported by National Natural Science Foundation of China (11175146, 11047023, 11265017)Fundamental Research Funds for Central Universities (XDJK2012D005)
文摘In the QCD-inspired potential model where the quark-antiquark interaction consists of the usual one- gluon-exchange and the mixture of long-range scalar and vector linear confining potentials with the lowest order relativistic correction, we investigate the mass spectra and electromagnetic processes of a bottomonium system by using the Gaussian expansion method. It reveals that the vector component of the mixing confinement is anticonfining and takes around 18.51% of the confining potential. Combining the new experimental data released by Belle, BaBar and LHC, we systematically discuss the energy levels of the bottomouium states and make the predictions of the electromagnetic decays for further experiments.
