New concept of clustering is discussed in $Lambda$ hypernuclei using a new-type microscopic cluster model wave function, which has a structure that constituent clusters are confined in a container, whose size is a variational parameter and which we r
efer to as Hyper-Tohsaki-Horiuchi-Schuck-Ropke (Hyper-THSR) wave function. By using the Hyper-THSR wave function, $2alpha + Lambda$ cluster structure in ${^{9}_Lambda{rm Be}}$ is investigated. We show that full microscopic solutions in the $2alpha + Lambda$ cluster system, which are given as $2alpha + Lambda$ Brink-GCM wave functions, are almost perfectly reproduced by the single configurations of the Hyper-THSR wave function. The squared overlaps between the both wave functions are calculated to be $99.5$%, $99.4$%, and $97.7$% for $J^pi=0^+$, $2^+$, and $4^+$ states, respectively. We also simulate the structural change by adding the $Lambda$ particle, by varying the $Lambda N$ interaction artificially. As the increase of the $Lambda N$ interaction, the $Lambda$ particle gets to move more deeply inside the core and invokes strongly the spatial core shrinkage, and accordingly distinct localized $2alpha$ clusters appear in the nucleonic intrinsic density, though in ${^{8}{rm Be}}$ rather gaslike $2alpha$-cluster structure is shown. The origin of the localization is associated with the strong effect of Pauli principle. We conclude that the container picture of the $2alpha$ and $Lambda$ clusters is essential in understanding the cluster structure in ${^{9}_Lambda{rm Be}}$, in which the very compact spatial localization of clusters is shown in the density distribution.
The theory of quartet condensation is further developed. The onset of quartetting in homgeneous fermionic matter is studied with the help of an in-medium modified four fermion equation. It is found that at very low density quartetting wins over pairi
ng. At zero temperature, in analogy to pairing, a set of equations for the quartet order parameter is given. Contrary to pairing, quartetting only exists for strong coupling and breaks down for weak coupling. Reasons for this finding are detailed. In an application to nuclear matter, the critical temperature for alpha particle condensation can reach values up to around 8 MeV. The disappearance of alpha particles with increasing density, i.e. the Mott transition, is investigated. In finite nuclei the Hoyle state, that is the second 0+ state of 12C is identified as an alpha-particle condensate state. It is conjectured that such states also exist in heavier n-alpha nuclei, like 16O, 20Ne, etc. The sixth 0+ state in 16O is proposed as an analogue to the Hoyle state. The Gross-Pitaevski equation is employed to make an estimate of the maximum number of alpha particles a condensate state can contain. Possible quartet condensation in other systems is discussed briefly.
We present a new picture that the $alpha$-linear-chain structure for ${^{12}{rm C}}$ and ${^{16}{rm O}}$ has one-dimensional $alpha$ condensate character. The wave functions of linear-chain states which are described by superposing a large number of
Brink wave functions have extremely large overlaps of nearly $100%$ with single Tohsaki-Horiuchi-Schuck-Ropke (THSR) wave functions, which were proposed to describe the $alpha$ condensed gas-like states. Although this new picture is different from the conventional idea of the spatial localization of $alpha$ clusters, the density distributions are shown to have localized $alpha$-clusters which is due to the inter-$alpha$ Pauli repulsion.
We report an investigation of the structure of $^{12}$C nucleus employing a newly developed configuration-mixing method. In the three-dimensional coordinate-space representation, we generate a number of Slater determinants with various correlated str
uctures using the imaginary-time algorithm. We then diagonalize a many-body Hamiltonian with the Skyrme interaction in the space spanned by the Slater determinants with parity and angular momentum projections. Our calculation reasonably describes the ground and excited states of $^{12}$C nucleus, both for shell-model-like and cluster-like states. The excitation energies and transition strengths of the ground-state rotational band are well reproduced. Negative parity excited states, $1_1^-$, $2_1^-$, and $3_1^-$, are also reasonably described. The second and third $0^+$ states, $0_2^+$ and $0_3^+$, appear at around 8.8 MeV and 15 MeV, respectively. The $0_2^+$ state shows a structure consistent with former results of the alpha-cluster models, however, the calculated radius of the $0_2^+$ state is smaller than those calculations. The three-{alpha} linear-chain configuration dominates in the $0_3^+$ state.
Isoscalar monopole strength function in $^{16}$O up to $E_{x}simeq40$ MeV is discussed. We found that the fine structures at the low energy region up to $E_{x} simeq 16$ MeV in the experimental monopole strength function obtained by the $^{16}$O$(alp
ha,alpha^{prime})$ reaction can be rather satisfactorily reproduced within the framework of the $4alpha$ cluster model, while the gross three bump structures observed at the higher energy region ($16 lesssim E_{x} lesssim 40$ MeV) look likely to be approximately reconciled by the mean-field calculations such as RPA and QRPA. In this paper, it is emphasized that two different types of monopole excitations exist in $^{16}$O; one is the monopole excitation to cluster states which is dominant in the lower energy part ($E_{x} lesssim 16$ MeV), and the other is the monopole excitation of the mean-field type such as one-particle one-hole ($1p1h$) which {is attributed} mainly to the higher energy part ($16 lesssim E_{x} lesssim 40$ MeV). It is found that this character of the monopole excitations originates from the fact that the ground state of $^{16}$O with the dominant doubly closed shell structure has a duality of the mean-field-type {as well as} $alpha$-clustering {character}. This dual nature of the ground state seems to be a common feature in light nuclei.
The 4-alpha condensate state for ^{16}O is discussed with the THSR (Tohsaki-Horiuchi-Schuck-Roepke) wave function which has alpha-particle condensate character. Taking into account a proper treatment of resonances, it is found that the 4-alpha THSR w
ave function yields a fourth 0^+ state in the continuum above the 4-alpha-breakup threshold in addition to the three 0^+ states obtained in a previous analysis. It is shown that this fourth 0^+ ((0_4^+)_{THSR}) state has an analogous structure to the Hoyle state, since it has a very dilute density and a large component of alpha+^{12}C(0_2^+) configuration. Furthermore, single-alpha motions are extracted from the microscopic 16-nucleon wave function, and the condensate fraction and momentum distribution of alpha particles are quantitatively discussed. It is found that for the (0_4^+)_{THSR} state a large alpha-particle occupation probability concentrates on a single-alpha 0S orbit and the alpha-particle momentum distribution has a delta-function-like peak at zero momentum, both indicating that the state has a strong 4-alpha condensate character. It is argued that the (0_4^+)_{THSR} state is the counterpart of the 0_6^+ state which was obtained as the 4-alpha condensate state in the previous 4-alpha OCM (Orthogonality Condition Model) calculation, and therefore is likely to correspond to the 0_6^+ state observed at 15.1 MeV.
