Two types of potentials are given in the present paper. The two potentials have Gaussian radial dependences. Such shapes of radial functions are suitable for using in the unitary scheme model. The first potential is g...Two types of potentials are given in the present paper. The two potentials have Gaussian radial dependences. Such shapes of radial functions are suitable for using in the unitary scheme model. The first potential is given in the form of an attractive force and the second is given in the form of a superposition of repulsive and attractive forces. The two potentials are used to calculate the binding energy of the carbon nucleus <sup>12</sup>C. For this purpose, we expand the ground-state wave function of carbon in a series of the bases of the unitary scheme model and apply the variational method. To calculate the necessary matrix elements required to obtain the binding energy of carbon, we factorized the unitary scheme model bases in the form of products of two wave functions: the first function represents the set of the A-4 nucleons and the second function represents the set of the last four nucleons by using the well-known four-body fractional parentage coefficients. Good results are obtained for the binding energy of <sup>12</sup>C by using the two potentials.展开更多
Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under t...Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.展开更多
文摘Two types of potentials are given in the present paper. The two potentials have Gaussian radial dependences. Such shapes of radial functions are suitable for using in the unitary scheme model. The first potential is given in the form of an attractive force and the second is given in the form of a superposition of repulsive and attractive forces. The two potentials are used to calculate the binding energy of the carbon nucleus <sup>12</sup>C. For this purpose, we expand the ground-state wave function of carbon in a series of the bases of the unitary scheme model and apply the variational method. To calculate the necessary matrix elements required to obtain the binding energy of carbon, we factorized the unitary scheme model bases in the form of products of two wave functions: the first function represents the set of the A-4 nucleons and the second function represents the set of the last four nucleons by using the well-known four-body fractional parentage coefficients. Good results are obtained for the binding energy of <sup>12</sup>C by using the two potentials.
基金Supported by the National Natural Science Foundation of China(No.10671176)
文摘Kerov[16,17] proved that Wigner＇s semi-circular law in Gauss[an unitary ensembles is the transition distribution of the omega curve discovered by Vershik and Kerov[34] for the limit shape of random partitions under the Plancherel measure. This establishes a close link between random Plancherel partitions and Gauss[an unitary ensembles, In this paper we aim to consider a general problem, namely, to characterize the transition distribution of the limit shape of random Young diagrams under Poissonized Plancherel measures in a periodic potential, which naturally arises in Nekrasov＇s partition functions and is further studied by Nekrasov and Okounkov[25] and Okounkov[28,29]. We also find an associated matrix mode[ for this transition distribution. Our argument is based on a purely geometric analysis on the relation between matrix models and SeibergWitten differentials.
