Analysis of previous microscopic calculations for second 0+0^+ state in 12^{12}C in terms of 3-alpha particle Bose-condensed state

The wave function of the second $0^+$ state of $^{12}$C which was obtained long time ago by solving the microscopic 3$\alpha$ problem is shown to be almost completely equivalent to the wave function of the 3$\alpha$ 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 $\alpha$ particles, Bose-condensed into an identical s-wave function.Comment: revtex, 5 pages, 2 figures, submitted to Phys. Rev.

Nuclear alpha-clustering, superdeformation, and molecular resonances

Nuclear alpha-clustering has been the subject of intense study since the advent of heavy-ion accelerators. Looking back for more than 40 years we are able today to see the connection between quasimolecular resonances in heavy-ion collisions and extremely deformed states in light nuclei. For example superdeformed bands have been recently discovered in light N=Z nuclei such as $^{36}$Ar, $^{40}$Ca, $^{48}$Cr, and $^{56}$Ni by $\gamma$-ray spectroscopy. The search for strongly deformed shapes in N=Z nuclei is also the domain of charged-particle spectroscopy, and our experimental group at IReS Strasbourg has studied a number of these nuclei with the charged particle multidetector array {\sc Icare} at the {\sc Vivitron} Tandem facility in a systematical manner. Recently the search for $\gamma$-decays in $^{24}$Mg has been undertaken in a range of excitation energies where previously nuclear molecular resonances were found in $^{12}$C+$^{12}$C collisions. The breakup reaction $^{24}$Mg$+^{12}$C has been investigated at E$_{lab}$($^{24}$Mg) = 130 MeV, an energy which corresponds to the appropriate excitation energy in $^{24}$Mg for which the $^{12}$C+$^{12}$C resonance could be related to the breakup resonance. Very exclusive data were collected with the Binary Reaction Spectrometer in coincidence with {\sc Euroball IV} installed at the {\sc Vivitron}.Comment: 10 pages, 4 eps figures included. Invited Talk 10th Nuclear Physics Workshop Marie and Pierre Curie, Kazimierz Dolny Poland, Sep. 24-28, 2003; To be published in International Journal of Modern Physics

Vanishing spin alignment : experimental indication of triaxial 28Si+28Si\bf ^{28}Si + {^{28}Si} nuclear molecule

Fragment-fragment-$\gamma$ coincidences have been measured for $\rm ^{28}Si + {^{28}Si}$ at an energy corresponding to the population of a conjectured resonance in $^{56}$Ni. Fragment angular distributions as well as $\gamma$-ray angular correlations indicate that the spin orientations of the outgoing fragments are perpendicular to the orbital angular momentum. This differs from the $\rm ^{24}Mg+{^{24}Mg}$ and the $\rm ^{12}C+{^{12}C}$ resonances, and suggests two oblate $\rm ^{28}Si$ nuclei interacting in an equator-to-equator molecular configuration.Comment: 14 pages standard REVTeX file, 3 ps Figures -- Accepted for publication in Physical Review C (Rapid Communication

Collective Modes of Tri-Nuclear Molecules

A geometrical model for tri-nuclear molecules is presented. An analytical solution is obtained provided the nuclei, which are taken to be prolately deformed, are connected in line to each other. Furthermore, the tri-nuclear molecule is composed of two heavy and one light cluster, the later sandwiched between the two heavy clusters. A basis is constructed in which Hamiltonians of more general configurations can be diagonalized. In the calculation of the interaction between the clusters higher multipole deformations are taken into account, including the hexadecupole one. A repulsive nuclear core is introduced in the potential in order to insure a quasi-stable configuration of the system. The model is applied to three nuclear molecules, namely $^{96}$Sr + $^{10}$Be + $^{146}$Ba, $^{108}$Mo + $^{10}$Be + $^{134}$Te and $^{112}$Ru + $^{10}$Be + $^{130}$Sn.Comment: 24 pages, 9 figure

Nuclear Alpha-Particle Condensates

The $\alpha$-particle condensate in nuclei is a novel state described by a product state of $\alpha$'s, all with their c.o.m. in the lowest 0S orbit. We demonstrate that a typical $\alpha$-particle condensate is the Hoyle state ($E_{x}=7.65$ MeV, $0^+_2$ state in $^{12}$C), which plays a crucial role for the synthesis of $^{12}$C in the universe. The influence of antisymmentrization in the Hoyle state on the bosonic character of the $\alpha$ particle is discussed in detail. It is shown to be weak. The bosonic aspects in the Hoyle state, therefore, are predominant. It is conjectured that $\alpha$-particle condensate states also exist in heavier $n\alpha$ nuclei, like $^{16}$O, $^{20}$Ne, etc. For instance the $0^+_6$ state of $^{16}$O at $E_{x}=15.1$ MeV is identified from a theoretical analysis as being a strong candidate of a $4\alpha$ condensate. The calculated small width (34 keV) of $0^+_6$, consistent with data, lends credit to the existence of heavier Hoyle-analogue states. In non-self-conjugated nuclei such as $^{11}$B and $^{13}$C, we discuss candidates for the product states of clusters, composed of $\alpha$'s, triton's, and neutrons etc. The relationship of $\alpha$-particle condensation in finite nuclei to quartetting in symmetric nuclear matter is investigated with the help of an in-medium modified four-nucleon equation. A nonlinear order parameter equation for quartet condensation is derived and solved for $\alpha$ particle condensation in infinite nuclear matter. The strong qualitative difference with the pairing case is pointed out.Comment: 71 pages, 41 figures, review article, to be published in "Cluster in Nuclei (Lecture Notes in Physics) - Vol.2 -", ed. by C. Beck, (Springer-Verlag, Berlin, 2011

From the stable to the exotic: clustering in light nuclei

A great deal of research work has been undertaken in alpha-clustering study since the pioneering discovery of 12C+12C molecular resonances half a century ago. Our knowledge on physics of nuclear molecules has increased considerably and nuclear clustering remains one of the most fruitful domains of nuclear physics, facing some of the greatest challenges and opportunities in the years ahead. The occurrence of "exotic" shapes in light N=Z alpha-like nuclei is investigated. Various approaches of the superdeformed and hyperdeformed bands associated with quasimolecular resonant structures are presented. Evolution of clustering from stability to the drip-lines is examined: clustering aspects are, in particular, discussed for light exotic nuclei with large neutron excess such as neutron-rich Oxygen isotopes with their complete spectroscopy.Comment: 15 pages, 5 figures, Presented at the International Symposium on "New Horizons in Fundamental Physics - From Neutrons Nuclei via Superheavy Elements and Supercritical Fields to Neutron Stars and Cosmic Rays" held at Makutsi Safari Farm, South Africa, December 23-29, 2015. arXiv admin note: substantial text overlap with arXiv:1402.6590, arXiv:1303.0960, arXiv:1408.0684, arXiv:1011.342