arXiv subjects
Publications and source records attributed to C. G. Bao.
The analytical expression of the fractional parentage coefficients for the total spin-states of a spinor N-boson system has been derived. Thereby an S-conserved theory for the spinor Bose-Einstein condensation has been proposed. A set of equations has been established to describe the first excited band of the condensates. Numerical solution for $^{23}$Na has been given as an example.
For the spinor Bose-Einstein condensates both the total spin $S$ and its Z-component $S_{Z}$ should be conserved. However, in existing theories, only the conservation of $S_{z}$ has been taken into account. To remedy, this paper is the first attempt to take the conservation of both $% S$ and $S_{Z}$ into account. For this purpose, a total spin-state with the good quantum numbers $S$ and $S_{Z}$ is introduced in the trial wave function, thereby a generalized Gross-Pitaevskii equation has been derived. With this new equation, the ground bands of the $^{23}$Na and $% ^{87}$Rb condensates have been studied, where the levels distinct in $S$ split. It was found that the level density is extremely dense in the bottom of the ground band of $^{23}$Na, i.e., in the vicinity of the ground state. On the contrary, for $^{87}$Rb, the levels are extremely dense in the top of the ground band,
The constraints imposed by symmetry on the open channels of dipositronium has been studied, and the symmetry-adapted lowest open channel of each quantum state has been identified. Based on this study, the existence of two more 0^+ bound states has been theoretically confirmed, and a 0^+ narrow resonance has been predicted. A variational calculation has been performed to evaluate the critical strength of the repulsive interaction . Two 0^- states are found to have their critical strengths very close to 1, they are considered as candidates of new narrow resonances or loosely bound states .
The symmetry constraints imposing on the quantum states of a dot with 13 electrons has been investigated. Based on this study, the favorable structures (FSs) of each state has been identified. Numerical calculations have been performed to inspect the role played by the FSs. It was found that, if a first-state has a remarkably competitive FS, this FS would be pursued and the state would be crystal-like and have a specific core-ring structure associated with the FS. The magic numbers are found to be closely related to the FSs.
The orbital angular momentum L as an integer can be ultimately factorized as a product of prime numbers. We show here a close relation between the resolution of L and the classification of quantum states of an N-electron 2-dimensional system. In this scheme, the states are in essence classified into different types according to the m(k)-accessibility, namely the ability to get access to symmetric geometric configurations. The m(k)-accessibility is an universal concept underlying all kinds of 2-dimensional systems with a center. Numerical calculations have been performed to reveal the electronic structures of the states of the dots with 9 and 19 electrons,respectively. This paper supports the Laughlin wave finction and the composite fermion model from the aspect of symmetry.
An analysis of the channel wave functions is made to clarify the types of resonance emerging from Ps-Ps and Ps-Ps* collisions. The ordering of the energy levels of the states of the dipositronium is evaluated based on the inherent nodal structures of wave functions and on existing theoretical results. A few very probable low-lying narrower resonances, namely the 0+(A2), 1-(E),..., benefiting from the centrifugal barrier have been proposed.
It was found in this paper that the dominant component of the wave function of the second 0^+ state of 4^He and the corresponding component of the 3^H+p channel have different spatial permutation symmetries. This fact will hinder the wave function to extend from the interior region to the outgoing channel and will lead to a narrower width.
Symmetry has imposed very strong constraints on the structures of internal wave functions and on the accessibility of outgoing channels. Based on symmetry consideration, the existence of a number of bound excited states and low-lying resonances has been suggested.
Inherent nodal surfaces existing in the wavefunctions of intrashell states of 4-valence-electron atoms have been investigated. The decisive effect of these surfaces has been demonstrated, the ordering of low-lying levels has been predicted, a primary classification scheme has been proposed, the existence of three rotation bands has been suggested.
The inherent nodal structures of the wavefunctions of 6-nucleon systems have been investigated. The existence of a group of six low-lying states dominated by L=0 has been deduced. The spatial symmetries of these six states are found to be mainly {4,2} and {2,2,2}.
The feature of the low-lying spectrum and a complete set of quantum numbers of the (e+e+e-e-) system have been deduced based on symmetry consideration. The existence of a low odd-parity L=1 excited state with the spins of the two electrons coupled to s1=1 and the two positrons coupled to s2=0 (or s1=0 and s2=1) and a low even-parity L=0 excited state with s1=s2=1 have been predicted. The discussion is generalized to 2-dimensional (e+e+e-e-) systems.
The inherent nodal structures of the wavefunctions of 4-nucleon systems have been investigated. The quantum numbers of the excited states (resonances) have been deduced. It was found that all the T=0 even-parity resonances are dominated by {2,1,1} component with L=1, all the T=0 odd-parity resonances are dominated by {3,1} component with L=1, and all the T=1 odd-parity resonances are also dominated by {3,1} component with L=1. The understanding of the inherent nodal structure is found to be crucial to a systematic understanding of the spectrum.