Momentum distribution and correlation of two-nucleon relative motion in 6^6He and 6^6Li

The momentum distribution of relative motion between two nucleons gives information on the correlation in nuclei. The momentum distribution is calculated for both $^{6}$He and $^6$Li which are described in a three-body model of $\alpha$+$N$+$N$. The ground state solution for the three-body Hamiltonian is obtained accurately using correlated basis functions. The momentum distribution depends on the potential model for the $N$-$N$ interaction. With use of a realistic potential, the $^6$He momentum distribution exhibits a dip around 2 fm$^{-1}$ characteristic of $S$-wave motion. In contrast to this, the $^6$Li momentum distribution is very similar to that of the deuteron; no dip appears because it is filled with the $D$-wave component arising from the tensor force.Comment: 14 pages, 9 figure

Correlated-Gaussian approach to linear-chain states -Case of four α\alpha-particles-

We show that correlated Gaussians with good angular momentum and parity provide flexible basis functions for specific elongated shape. As its application we study linear-chain states of four-alpha particles in variation-after-projection calculations in which all the matrix elements are evaluated analytically. We find possible chain states for $J=0^+$, $2^+$, $4^+$ and perhaps $6^+$ with the bandhead energy being about 33 MeV from the ground state of $^{16}$O. No chain states with $J\geq 8$ are found. The nature of the rotational sequence of the chain states is clarified in contrast to a rigid-body rotation. The quadrupole deformation parameters estimated from the chain states increase from 0.59 to 1.07 for $2^+$ to $6^+$. This work suggests undeveloped fields for the correlated Gaussians beyond those problems which have hitherto been solved successfully.Comment: 13 pages, 6 figures, accepted for publication in Phys. Rev.

Structure of Light Unstable Nuclei Studied with Antisymmetrized Molecular Dynamics

Structures of light unstable nuclei, Li, Be, B, and C isotopes are systematically studied with a microscopic method of antisymmetrized molecular dynamics. The theoretical method is found to be very useful to study ground and excited states of various nuclei covering unstable nuclei. The calculations succeed to reproduce many experimental data for nuclear structures; energies, radii, magnetic dipole moments, electric quadrupole moments, transition strength. In the theoretical results it is found that various exotic phenomena in unstable nuclei such as molecular-like structures, neutron skin, and large deformations may appear in unstabel nuclei. We investigate the structure change with the increase of neutron number and with the increase of the excitation energies, and find the drastic changes between shell-model-like structures and clustering structures. The mechanism of clustering developments in unstable nuclei are discussed.Comment: 73 pages, Revtex, 42 postscript figures (using epsf.sty). to be published in Suppl. Prog. Theor. Phy

New Treatment of Resonances with Bound State Approximation by Using Pseudo Potential

We propose a new approach to extract the wave functions of resonances by the bound state approximation which gives the mixed states of the resonance components and the continuum ones. In our approach, on the basis of the method of analytic continuation in the coupling constant (ACCC), we construct Pad\'e rational function by adopting the positive energies as well as the negative ones. We report the result of the application of this new method to the second $2^+$ state of $^{12}$C which was studied with the ACCC method in our previous work. It is found that the resonance parameters obtained by the ACCC method are well reproduced by the new method. Some advantages over the ACCC method are also shown.Comment: 10pages, 2figures, submitted to Prog. Theor. Phys, changed content, added reference

Green's function method for strength function in three-body continuum

Practical methods to compute dipole strengths for a three-body system by using a discretized continuum are analyzed. New techniques involving Green's function are developed, either by correcting the tail of the approximate wave function in a direct calculation of the strength function or by using a solution of a driven Schroedinger equation in a summed expression of the strength. They are compared with the complex scaling method and the Lorentz integral transform, also making use of a discretized continuum. Numerical tests are performed with a hyperscalar three-body potential in the hyperspherical-harmonics formalism. They show that the Lorentz integral transform method is less practical than the other methods because of a difficult inverse transform. These other methods provide in general comparable accuracies.Comment: 22 pages, 8 figures, to appear in Progress of Theoretical Physic

Electric dipole response of 6^6He: Halo-neutron and core excitations

Electric dipole ($E1$) response of $^{6}$He is studied with a fully microscopic six-body calculation. The wave functions for the ground and excited states are expressed as a superposition of explicitly correlated Gaussians (CG). Final state interactions of three-body decay channels are explicitly taken into account. The ground state properties and the low-energy $E1$ strength are obtained consistently with observations. Two main peaks as well as several small peaks are found in the $E1$ strength function. The peak at the high-energy region indicates a typical macroscopic picture of the giant dipole resonance, the out-of-phase proton-neutron motion. The transition densities of the lower-lying peaks exhibit in-phase proton-neutron motion in the internal region, out-of-phase motion near the surface region, and spatially extended neutron oscillation, indicating a soft-dipole mode (SDM) and its vibrationally excited mode.Comment: 12 pages, 12 figures, to appear in Phys. Rev.

Probing neutron-skin thickness with total reaction cross sections

We analyze total reaction cross sections, $\sigma_R$, for exploring their sensitivity to the neutron-skin thickness of nuclei. We cover 91 nuclei of O, Ne, Mg, Si, S, Ca, and Ni isotopes. The cross sections are calculated in the Glauber theory using the density distributions obtained with the Skyrme-Hartree-Fock method in 3-dimensional coordinate space. Defining a reaction radius, $a_R=\sqrt{\sigma_R/\pi}$, to characterize the nuclear size and target (proton or $^{12}$C) dependence, we find an empirical formula for expressing $a_R$ with the point matter radius and the skin thickness, and assess two practical ways of determining the skin thickness from proton-nucleus $\sigma_R$ values measured at different energies or from $\sigma_R$ values measured for different targets.Comment: 6 pages, 5 figures, to appear in Phys. Rev.

Clustering and Triaxial Deformations of 40^{40}Ca

We have studied the positive-parity states of $^{40}$Ca using antisymmetrized molecular dynamics (AMD) and the generator coordinate method (GCM). Imposing two different kinds of constraints on the variational calculation, we have found various kinds of $^{40}{\rm Ca}$ structures such as a deformed-shell structure, as well as $\alpha$-$^{36}$Ar and $^{12}$C-$^{28}$Si cluster structures. After the GCM calculation, we obtained a normal-deformed band and a superdeformed band together with their side bands associated with triaxial deformation. The calculated $B(E2)$ values agreed well with empirical data. It was also found that the normal-deformed and superdeformed bands have a non-negligible $\alpha$-$^{36}$Ar cluster component and $^{12}$C-$^{28}$Si cluster component, respectively. This leads to the presence of an $\alpha$-$^{36}$Ar higher-nodal band occurring above the normal-deformed band.Comment: 11pages, 9 figure