Mirror symmetry breaking in He isotopes and their mirror nuclei

We study the mirror symmetry breaking of $^6$He-$^6$Be and $^8$He-$^8$C using the $^4$He + $X$N ($X$=2, 4) cluster model. The many-body resonances are treated for the correct boundary condition using the complex scaling method. We find that the ground state radius of $^8$C is larger than that of $^8$He due to the Coulomb repulsion in $^8$C. On the other hand, the $0^+_2$ resonances of the two nuclei exhibit the inverse relation; the $^8$C radius is smaller than the $^8$He radius. This is due to the Coulomb barrier of the valence protons around the $^4$He cluster core in $^8$C, which breaks the mirror symmetry of the radius in the two nuclei. A similar variation in the radius is obtained in the mirror nuclei, $^6$He and $^6$Be. A very large spatial extension of valence nucleons is observed in the $0^+_2$ states of $^8$He and $^8$C. This property is related to the dominance of the $(p_{3/2})^2(p_{1/2})^2$ configuration for four valence nucleons, which is understood from the reduction in the strength of the couplings to other configurations by involving the spatially extended components of valence nucleons.Comment: 9 pages, 5 figure

Level Density in the Complex Scaling Method

It is shown that the continuum level density (CLD) at unbound energies can be calculated with the complex scaling method (CSM), in which the energy spectra of bound states, resonances and continuum states are obtained in terms of $L^2$ basis functions. In this method, the extended completeness relation is applied to the calculation of the Green functions, and the continuum-state part is approximately expressed in terms of discretized complex scaled continuum solutions. The obtained result is compared with the CLD calculated exactly from the scattering phase shift. The discretization in the CSM is shown to give a very good description of continuum states. We discuss how the scattering phase shifts can inversely be calculated from the discretized CLD using a basis function technique in the CSM.Comment: 14 pages, 9 figures, To be published in Progress of Theoretical Physic

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

Five-body resonances of 8C using the complex scaling method

We study the resonance spectroscopy of the proton-rich nucleus 8C in the alpha+p+p+p+p cluster model. Many-body resonances are treated on the correct boundary condition as the Gamow states using the complex scaling method. We obtain the ground state of 8C as a five-body resonance for the first time, which has dominantly the sub-closed (p_{3/2})^4 configuration and agrees with the recent experiment for energy and decay width. We predict the second 0+ state with the excitation energy of 5.6 MeV, which corresponds to the $2p2h$ state from the ground state. We evaluate the occupation numbers of four valence-protons in the 8C states and also the J^\pi distribution of proton-pair numbers of the two 0+ states of 8C. The ground state involves a large amount of the 2+ proton-pair fraction, while the excited 0+_2 state almost consists of two of the 0+ proton pairs, which can be understood from the (p_{3/2})^2(p_{1/2})^2 configuration. We also discuss the mirror symmetry between 8C and 8He with an alpha+four nucleon picture. It is found that the 0+ states retain the mirror symmetry well for the configuration properties of two nuclei.Comment: 8 pages, 6 figures. arXiv admin note: text overlap with arXiv:1111.5070, radial properties of 8C are revised in Table II

One-neutron removal strength of 7He into 6He using the complex scaling method

We study the one-neutron removal strength of the 7He ground state, which provides us with the 6He-n component in 7He. The He isotopes are described on the basis of the 4He+Xn cluster model (X=1,2,3). The complex scaling method is applied to describe not only the Gamow resonances but also the nonresonant continuum states of valence neutrons, with the correct boundary condition of particle decays. The one-neutron removal strength of 7He into the unbound states of 6He is calculated using the complex-scaled Green's function, in which a complex-scaled complete set of 4He+n+n states is adopted. Using this framework, we investigate resonant and nonresonant contributions of the strength, which individually produce specific structures in the distributions. In addition, we propose a method to obtain the real-value strength using the complex values of spectroscopic factors of Gamow states. As a result, the 6He(2+) resonance is found to give the largest contribution.Comment: 11 pages, 10 figures, Corrected typo

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

Decomposition of scattering phase shifts and reaction cross sections using the complex scaling method

We apply the complex scaling method to the calculation of scattering phase shifts and extract the contributions of resonances in a phase shift and a cross section. The decomposition of the phase shift is shown to be useful to understand the roles of resonant and non-resonant continuum states. As examples, we apply this method to several two-body systems: (i) a schematic model with the Gyarmati potential which produces many resonances, (ii) the alpha-alpha system which has a Coulomb barrier potential in addition to an attractive nuclear interaction, and (iii) the alpha-n system which has no barrier potential. Using different kinds of potentials, we discuss the reliability of this method to investigate the resonance structure in the phase shifts and cross sections.Comment: 11 pages, 9 figure

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.

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