A new α-cluster wave function is proposed which is of the α-particle condensate type. Applications to 12 C and 16 O show that states of low density close to the 3 resp. 4 α-particle threshold in both nuclei are possibly of this kind. It is conjectured that all self-conjugate 4n nuclei may show similar features. Keywords: Binding energies, Collective levels, α-like correlations, Bose-Einstein condensation, nuclear matter, α-particle matter. PACS: 03.75.F, 21.10. Dr, 21.10.Re, 21.65.+f Many properties of finite quantum systems such as nuclei, quantum dots, atomic clusters or ultracould gases in a trap are fairly well described within a mean-field approximation neglecting the correlations between the quasiparticles. However, sometimes correlations become strong, giving rise to the formation of clusters, and they have to be taken into account. An intriguing problem is when bosonic clusters as bound states of fermions are produced, and the Bose character of the composite clusters competes with the fermionic properties of their constituents. As an example, we will discuss the relevance of α-like four-nucleon correlations in atomic nuclei. Special attention will be paid to such correlations which correspond to an α-type condensate in low-density symmetric nuclear matter, similar to the Bose-Einstein condensation observed for finite numbers of bosonic atoms such as Rb or Na in traps.It is a well known fact that in light nuclei many states are of the cluster type [1][2][3][4]. In the case of cluster states of stable nuclei where we have only very few excess nucleons in addition to the clusters, they are all located close to or above the threshold energy of breakup into constituent clusters. This fact which is known as the threshold rule [5] means that the inter-cluster binding is weak in cluster states. The threshold rule can be considered as a necessary condition for the formation of the cluster structure, because if the inter-cluster binding is strong the clusters overlap strongly and the clusters will loose their identities.For example one of the fundamental questions of the cluster model is what kind of α-particle cluster states can be expected to exist around the threshold energy E thr nα = nE α of nα breakup in self-conjugate 4n nuclei. One possible answer to this question, which is strongly under debate, is the existence of the cluster state of a linear nα chain structure. The idea of the linear α chain state, originally due to Morinaga [6], is so fascinating that recently the formation of linear 6α chain states in 24 Mg was studied extensively by experiments and also theoretically [7]. The possibility of the linear 3α chain state in 12 C, which is the simplest linear α chain state was studied in detail by many authors solving the 3α problem microscopically [4]. However, these three-body studies all showed that the 3α-cluster states around the 3α threshold energy E thr 3α do not have a linear chain structure. For example it was found that the calculated second 0 + state in 12 C, which corresponds to the observe...

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The wave function of the second 0 + state of 12 C which was obtained long time ago by solving the microscopic 3α problem is shown to be almost completely equivalent to the wave function of the 3α condensed state which has been proposed recently by the present authors. This equivalence of the wave functions is shown to hold in two cases where different effective two-nucleon forces are adopted. This finding gives strong support for interpreting the second 0 + state of 12 C which is the key state for the synthesis of 12 C in stars ( 'Hoyle' state ), and which is one of the typical mysterious 0 + states in light nuclei, as a gas-like structure of three α particles, Bose-condensed into an identical s-wave function.The α clustering nature of the nucleus 12 C has been studied by many authors using various approaches [1]. Among these studies, solving the fully microscopic threebody problem of α clusters gives us the most important and reliable theoretical information of α clustering in 12 C within the assumption that no α cluster is distorted or broken except for the change of the size parameter of the α cluster's internal wave function. As representatives for the solution of the microscopic 3α problem where the antisymmetrization of nucleons is exactly treated, we here quote two works: one by Uegaki et al.[2] and the other by Kamimura et al. [3] both of which were published almost a quarter century ago. In these works, the 12 C levels are described by the wave function of the form A{χ(s, t)φ 3 α } with A standing for the antisymmetrizer, φ 3 α ≡ φ(α 1 )φ(α 2 )φ(α 3 ) for the product of the internal wave functions of 3 α clusters, and s and t for the Jacobi coordinates of the center-of-mass motion of 3 α clusters. Here φ(α i ) (i = 1, 2, 3) is the internal wave function of the α-cluster α i having the form φ(The wave function χ(s, t) of the relative motion of 3 α clusters is obtained by solving the eigen-energy problem of the full three-body equation of motion; φ Recently, based on the investigations by Röpke, Schuck, and coauthors on the possibility of α-particle condensation in low-density nuclear matter [6], the present authors proposed a conjecture that near the nα threshold in self-conjugate 4n nuclei there exist excited states of dilute density which are composed of a weekly

Downloaded from the self-conjugate 4n nuclei which we call a-nuclei are especially stable energetically, therefore the fragmentation (or fission) thresholds of respective nuclei into constituent a-nuclei plus a residual nucleus lie in series starting in the region of quite low excitation energy.Since a-nuclei are strongly bound systems, they are hardly excited even when two a-nuclei are in a close distance. The fact that inter-nucleus forces between spin-isospin saturated nuclei are generally weak promotes further the tendency that a-nuclei preserve their identity in their interaction process. Furthermore the repulsive force of a short range part of the inter-nucleus inter-at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from factorily the low-lying positive-parity excited states, 02 + at 7.66 MeV and 22 + (or 08 + ?) at ,...__,10.3 MeV shown in Fig. 1-1.From these studies, the ground rotational band (consisting of ground 01 +, 2 1 + at 4.44 MeV and 41 + at 14.08 MeV) was regarded as having a strong shellmodel-like character, although a-clustering effect is important. The latter nature (namely the persistency of a-clustering) was investigated in detail by Abe, Hiura and Tanaka 17 l by the use of the molecular orbital method preserving the spatial symmetry of [ 4 8 ]. Takigawa and Arima 18 l investigated the *> Many works were made with various frameworks and a-a potentials. Here, however, we do not mention them in detail. See a review article given by Tamagaki and Fujiwara for the works on the 3a problem.••> at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from 15 0, 15 N, 17 0 and 11 F, the spacing between the centroids of the p and the sd shells is estimated as about 17 MeV. ii) We can deduce a value of fiw = 13.4 MeV corresponding to the harmonic oscillator parameter b = 1.76 fm at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from Another standpoint for incorporating a 4p-4h configuration was the weak coupling model by Arima, Horiuchi and Sebe 58 >• 59 >• 60 > which assumed that the at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from *' The RGM study for the "O+a system was also carried out by Siinkel and Wildermuth."'l **l Similar RGM analysis of the "0-a interaction was made by Ando, Ikeda and Suzuki 106 J by comparing with the a-a and "0-16 0 cases. at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from at Purdue University Libraries ADMN on June 1, 2015 http://ptps.oxfordjournals.org/ Downloaded from *> As for wi'lr(t), harmonic oscillator functions and locally peaked Gaussian functions are also available by the use of fPNLM(J., v, S). Actually, the latter functions were examined and were found to give the same results obtained by the set (2·5) (Ref. 41)). at Purdue University Lib...

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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.

In order to study light unstable nuclei systematically, we propose a new method, the antisymmetrized molecular dynamics plus Hartree-Fock ͑AMDϩHF͒ method. This method introduces the concept of the single particle orbits into the usual AMD. Applying the AMDϩHF method to Be isotopes, it is found that the calculated lowest intrinsic states with plus and minus parities have rather good correspondence with the explanation by the two-center shell model. In addition, by active use of the single particle orbits extracted from the AMD wave function, we construct the first excited 0 ϩ state of 10 Be. The obtained state appears in the vicinity of the lowest 1 Ϫ state. This result is consistent with the experimental data. ͓S0556-2813͑97͒04510-X͔

We study the structure of excited states of 10 Be with the method of variation after spin-parity projection in the framework of antisymmetrized molecular dynamics. Present calculations describe many excited states and reproduce the experimental data of E2 and E1 transitions and the new data of the ␤ transition strength successfully. We include systematic discussions on the moleculelike structures of light unstable nuclei and the important role of the valence neutrons based on the results obtained with the framework which is free from such model assumptions as the existence of inert cores and clusters.