Molecular Structure with Exotic Clusters in light Neutron-rich Nuclei

The excited states of Be-12, Be-14 and B-15 have been studied with a method of antisymmetrized molecular dynamics. In the predicted excited states we find novel molecule-like structures with very exotic clusters such as 6He+8He in Be-14 and 6He+9Li in B-15. The origin of the He-6 cluster development in the very neutron-rich nuclei is understood by the new-type correlation among 4 neutrons and 2 protons. In this paper we also present our recent challenge to study $sd$-shell nuclei. Shape coexistence problems in Ar-36 and Ca-40 are discussed.Comment: 10 pages, 5 figures. The proceedings of Yukawa International Seminar 2001 on "Physics of Unstable Nuclei". To appear in Prog. Theor. Phy

Entanglement entropy and Schmidt number as measures of delocalization of α\alpha clusters in one-dimensional nuclear systems

We calculated the von Neumann entanglement entropy and the Schmidt number of one dimentional (1D) cluster states and showed that these are useful measures to estimate entanglement caused by delocalization of clusters. We analyze system size dependence of these entanglement measures in the linear-chain $n\alpha$ states given by Tohsaki-Horiuchi-Schuck-R\"opke wave functions for 1D cluster gas states. We show that the Schmidt number is an almost equivalent measures to the von Neumann entanglement entropy when the delocalization of clusters occurs in the entire system but it shows different behaviors in a partially delocalized state containing localized clusters and delocalized ones. It means that the R\'enyi-2 entanglement entropy, which relates to the Schmidt number, is found to be almost equivalent to the von Neumann entanglement entropy for the full delocalized cluster system but it is less sensitive to the partially delocalized cluster system than the von Neumann entanglement entropy. We also propose a new entanglement measure which has a generalized form of the Schmidt number. Sensitivity of these measures of entanglement to the delocalization of clusters in low-density regions was discussed.Comment: 15 pages, 10 figure

Analysis of delocalization of clusters in linear-chain α\alpha-cluster states with entanglement entropy

I investigate entanglement entropy of one dimension (1D) cluster states to discuss the delocalization of clusters in linear-chain $3\alpha$- and $4\alpha$-cluster states. In analysis of entanglement entropy of 1D Tohsaki-Horiuchi-Schuck-R\"opke (THSR) and Brink-Bloch cluster wave functions, I show clear differences in the entanglement entropy between localized cluster wave functions and delocalized cluster wave functions. In order to clarify spatial regions where the entanglement entropy is generated by the delocalization of clusters, I analyze the spatial distribution of entanglement entropy. In the linear-chain $3\alpha$ cluster state, the delocalization occurs dominantly in a low-density tail region while it is relatively suppressed in an inner region because of Pauli blocking effect between clusters. In the linear-chain 4$\alpha$ state having a larger system size than the linear-chain $3\alpha$ state, the delocalization occurs in the whole system. The entanglement entropy is found to be a measure of the delocalization of clusters in the 1D cluster systems.Comment: 19 pages, 9 figure

Isoscalar monopole and dipole excitations of cluster states and giant resonances in 12^{12}C

The isoscalar monopole(ISM) and dipole(ISD) excitations in $^{12}$C are theoretically investigated with the shifted antisymmetrized molecular dynamics(AMD) plus $3\alpha$-cluster generator coordinate method(GCM). The small amplitude vibration modes are described by coherent one-particle one-hole excitations expressed by small shift of single-nucleon Gaussian wave functions within the AMD framework, whereas the large amplitude cluster modes are incorporated by superposing $3\alpha$-cluster wave functions in the GCM. The coupling of the excitations in the intrinsic frame with the rotation and parity transformation is taken into account microscopically by the angular-momentum and parity projections. The present calculation describes the ISM and ISD excitations in a wide energy region covering cluster modes in the low-energy region and the giant resonances in the high-energy region, though the quantitative description of the high-energy part is not satisfactory. The low-energy ISM and ISD strengths of the cluster modes are enhanced by the radial motion of $\alpha$ clusters, and they split into a couple of states because of the angular motion of $\alpha$ clusters. The low-energy ISM strengths exhaust 26% of the EWSR, which is consistent with the experimental data for the $^{12}$C($0^+_2$;7.65 MeV) and $^{12}$C($0^+_3$;10.3 MeV) measured by $(e,e')$, $(\alpha,\alpha')$, and ($^6$Li,$^6$Li$'$) scatterings. In the calculated low-energy ISD strengths, two $1^-$ states (the $1^-_1$ and $1^-_2$) with the significant strengths are obtained in $E=10-15$ MeV. It is indicated that the ISD excitations can be a good probe to experimentally search for new cluster states such as the $^{12}$C($1^-_2$) obtained in the present calculation.Comment: 13 pages, 6 figures. arXiv admin note: text overlap with arXiv:1511.0853

Shape coexistence in N=14 isotones: 19B, 24Ne and 28Si

Shape coexistence problems in N=14 isotones are studied with a microscopic method of antisymmetrized molecular dynamics. The present calculations reproduce features of deformation in 28Si, and predict possible shape coexistence of neutron density in neutron-rich nuclei(19B and 24Ne). We also systematically study the structures of the ground and excited states, and the molecular resonances of 28Si. Besides the shape coexistence in the low-energy region, the results indicate the high-lying levels with $\alpha$-cluster and 12C+16O molecular structures in 28Si, which are consistent with the observed spin-assigned resonances. The resonance states above the threshold energies are connected with the low-lying deformed states from a view point of molecular excitation by discussing inter-cluster wave functions.Comment: 4 pages, 3 figures, Proceedings of "Frontiers of Collective Motions (CM2002)" Nov. 6-9, 2002, Aizu-Wakamatsu, Japa

Quantum decoherence in the entanglement entropy of a composite particle and its relationship to coarse graining in the Husimi function

I investigate quantum decoherence in a one-body density matrix of a composite particle consisting of two correlated particles. Because of a two-body correlation in the composite particle, quantum decoherence occurs in the one-body density matrix that has been reduced from the two-body density matrix. As the delocalization of the distribution of the composite particle grows, the entanglement entropy increases, and the system can be well-described by a semi-classical approximation, wherein the center position of the composite particle can be regarded as a classical coordinate. I connect the quantum decoherence in the one-body density matrix of a composite particle to the coarse graining in a phase space distribution function of a single particle and associate it with the Husimi function.Comment: 4 pages, 1 figur

Isovector and isoscalar dipole excitations in 9^{9}Be and 10^{10}Be studied with antisymmetrized molecular dynamics

Isovector and isoscalar dipole excitations in $^9$Be and $^{10}$Be are investigated in the framework of antisymmetrized molecular dynamics, in which angular-momentum and parity projections are performed. In the present method, 1p-1h excitations on the ground state and large amplitude $\alpha$-cluster mode are incorporated. The isovector giant dipole resonance (GDR) in $E>20$ MeV shows the two peak structure which is understood by the dipole excitation in the 2$\alpha$ core part with the prolate deformation. Because of valence neutron modes against the $2\alpha$ core, low-energy E1 resonances appear in $E<20$ MeV exhausting about $20\%$ of the Thomas-Reiche-Kuhn sum rule and $10\%$ of the calculated energy-weighted sum. The dipole resonance at $E\sim 15$ MeV in $^{10}$Be can be interpreted as the parity partner of the ground state having a $^6$He+$\alpha$ structure and has the remarkable E1 strength because of coherent contribution of two valence neutrons. The ISD strength for some low-energy resonances are significantly enhanced by the coupling with the $\alpha$-cluster mode. The calculated E1 strength of $^9$Be reasonably describes the global feature of experimental photonuclear cross sections consisting of the low-energy strength in $E20$ MeV.Comment: 17 pages, 8 figure