Tensor correlation in 4He and its Effect on the doublet splitting in 5He

We investigate the role of tensor correlation on the structures of \nuc{4}{He} and its effect on the doublet splitting in \nuc{5}{He}. We perform a configuration mixing calculation in the shell model type bases to represent the tensor correlation for $^4$He. It is found that our model describes the characteristics of the tensor correlation, which is represented by an admixture of the $0s_{1/2}$ configuration with a spatially modified $0p_{1/2}$ orbit. For $^5$He, we solve a coupled OCM equation for an extended $^4$He+$n$ model, while taking into account the tensor correlation in the $^4$He cluster. It is shown that the tensor correlation produces the Pauli blocking, in particular, for the $J^\pi={1/2}^-$ state, and its effect causes about half of the p-wave doublet splitting in $^5$He. This indicates that the strength of the effective spin-orbit interaction should be reduced by about half from the conventional one. We obtain a reliable $^4$He-$n$ interaction, including the tensor correlation, which further improves the behavior of the $d$- and $f$-wave phase shifts in the $^4$He+$n$ system.Comment: 21 pages, 9 figures, To be published in Progress of Theoretical Physic

Resonances of 7He in the complex scaling method

We study the resonance spectroscopy of 7He in the 4He+n+n+n cluster model, where the motion of valence neutrons is described in the cluster orbital shell model. Many-body resonances are treated on the correct boundary condition as the Gamow states in the complex scaling method. We obtain five resonances and investigate their properties from the configurations. In particular, the 1/2- state is found in a low excitation energy of 1.1 MeV with a width of 2.2 MeV, while the experimental determination of the position of this state is not so clear. We also evaluate the spectroscopic factors of the 6He-n components in the obtained 7He resonances. The importance of the 6He(2+) state is shown in several states of 7He.Comment: 7 pages, 4 figure

Extended 9Li+n+n three-body model of 11Li with the pairing correlation in 9Li

We discuss the binding mechanism of 11Li based on an extended three-body model of Li+n+n. In the model, we take into account the pairing correlation of p-shell neutrons in 9Li, in addition to that of valence neutrons outside the 9Li nucleus, and solve the coupled-channel two- and three-body problems of 10Li and 11Li, respectively. The results show that degrees of freedom of the pairing correlation in 9Li play an important role in the structure of 10Li and 11Li. In 10Li, the pairing correlation in 9Li produces a so-called pairing-blocking effect due to the presence of valence neutron, which degenerates s- and p-wave neutron orbits energetically. In 11Li, on the other hand, the pairing-blocking effect is surpassed by the core-n interaction due to two degrees of freedom of two valence neutrons surrounding 9Li, and as a result, the ground state is dominated by the p-shell closed configuration and does not show a spatial extension with a large r.m.s. radius. These results indicate that the pairing correlation is realized differently in odd- and even-neutron systems of 10Li and 11Li. We further improve the tail part of the 9Li-n interaction, which works well to reproduce the observed large r.m.s. radius in 11Li.Comment: 24 pages, 7 figures. to be published in Prog. Theor. Phy

Tensor-optimized shell model for the Li isotopes with a bare nucleon-nucleon interaction

We study the Li isotopes systematically in terms of the tensor-optimized shell model (TOSM) by using a bare nucleon-nucleon interaction as the AV8' interaction. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM+UCOM approach, we investigate the role of the tensor force on each spectrum of the Li isotopes. It is found that the tensor force produces quite a characteristic effect on various states in each spectrum and those spectra are affected considerably by the tensor force. The energy difference between the spin-orbit partner, the p1/2 and p3/2 orbits of the last neutron, in 5Li is caused by opposite roles of the tensor correlation. In 6Li, the spin-triplet state in the LS coupling configuration is favored energetically by the tensor force in comparison with jj coupling shell model states. In 7,8,9Li, the low-lying states containing extra neutrons in the p3/2 orbit are favored energetically due to the large tensor contribution to allow the excitation from the 0s orbit to the p1/2 orbit by the tensor force. Those three nuclei show the jj coupling character in their ground states which is different from 6Li.Comment: 12 pages, 6 figures. arXiv admin note: text overlap with arXiv:1108.393

Coulomb breakup reactions of 11^{11}Li in the coupled-channel 9^9Li~+~nn~+~nn three-body model

We investigate the three-body Coulomb breakup of a two-neutron halo nucleus $^{11}$Li. We use the coupled-channel $^9$Li + $n$ + $n$ three-body model, which includes the coupling between last neutron states and the various $2p$-$2h$ configurations in $^9$Li due to the tensor and pairing correlations. The three-body scattering states of $^{11}$Li are described by using the combined methods of the complex scaling and the Lippmann-Schwinger equation. The calculated breakup cross section successfully reproduces the experiments. The large mixing of the s-state in the halo ground state of $^{11}$Li is shown to play an important role in explanation of shape and strength of the breakup cross section. In addition, we predict the invariant mass spectra for binary subsystems of $^{11}$Li. It is found that the two kinds of virtual s-states of $^9$Li-$n$ and $n$-$n$ systems in the final three-body states of $^{11}$Li largely contribute to make low-lying peaks in the invariant mass spectra. On the other hand, in the present analysis, it is suggested that the contributions of the p-wave resonances of $^{10}$Li is hardly confirmed in the spectra.Comment: 26 pages, 11 figures, 2 tables, submitted to Phys. Rev.

Tensor correlation in 4He with the tensor-optimized shell model

We study the characteristics of the tensor correlation in $^4$He using a shell model type method. We treat the tensor force explicitly by performing a configuration-mixing calculation in the $2p2h$ basis and include single-particle states up to intermediately high angular momenta. We adopt the Gaussian expansion method for the quantitative description of the spatial shrinkage of the single-particle states to optimize the tensor correlation. We are able to describe the full strength of the tensor correlation for $^4$He in the shell model type method by realizing convergence. We call this model the tensor-optimized shell model. It is found that in $^4$He, three specific $2p2h$ configurations are strongly coupled with the $(0s)^4$ configuration due to the characteristic features of the tensor operator.Comment: 18 pages, 8 figures, Changed content, To be Published in Prog. Theor. Phys. 117(2007

Tensor-optimized antisymmetrized molecular dynamics as a successive variational method in nuclear many-body system

We study the tensor-optimized antisymmetrized molecular dynamics (TOAMD) as a successive variational method in many-body systems with strong interaction for nuclei. In TOAMD, the correlation functions for the tensor force and the short-range repulsion and their multiples are operated to the AMD state as the variational wave function. The total wave function is expressed as the sum of all the components and the variational space can be increased successively with the multiple correlation functions to achieve convergence. All the necessary matrix elements of many-body operators, consisting of the multiple correlation functions and the Hamiltonian, are expressed analytically using the Gaussian integral formula. In this paper we show the results of TOAMD with up to the double products of the correlation functions for the s-shell nuclei, 3H and 4He, using the nucleon-nucleon interaction AV8'. It is found that the energies and Hamiltonian components of two nuclei converge rapidly with respect to the multiple of correlation functions. This result indicates the efficiency of TOAMD for the power series expansion in terms of the tensor and short-range correlation functions.Comment: 7 pages, 5 figures, added references, corrected typo