Alpha cluster condensation in 12C and 16O

A new $\alpha$-cluster wave function is proposed which is of the $\alpha$-particle condensate type. Applications to $^{12}$C and $^{16}$O show that states of low density close to the 3 resp. 4 $\alpha$-particle threshold in both nuclei are possibly of this kind. It is conjectured that all self-conjugate 4$n$ nuclei may show similar features.Comment: 4 pages, 2 tables, 2 figure

How quantum bound states bounce and the structure it reveals

We investigate how quantum bound states bounce from a hard surface. Our analysis has applications to ab initio calculations of nuclear structure and elastic deformation, energy levels of excitons in semiconductor quantum dots and wells, and cold atomic few-body systems on optical lattices with sharp boundaries. We develop the general theory of elastic reflection for a composite body from a hard wall. On the numerical side we present ab initio calculations for the compression of alpha particles and universal results for two-body states. On the analytical side we derive a universal effective potential that gives the reflection scattering length for shallow two-body states.Comment: final publication version, new lattice results on alpha particle compression, 5 pages, 2 figure

Relation between the phenomenological interactions of the algebraic cluster model and the effective two--nucleon forces

We determine the phenomenological cluster--cluster interactions of the algebraic model corresponding to the most often used effective two--nucleon forces for the $^{16}$O + $\alpha$ system.Comment: Latex with Revtex, 1 figure available on reques

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

2α+t2\alpha+t cluster structure in 11^{11}B

The cluster structures of the excited states in $^{11}$B are studied by analyzing the isoscalar monopole and quadrupole strengths in the $^{11}$B($d$,$d'$) reaction at $E_d=200$ MeV. The excitation strengths are compared with the predictions by the shell-model and antisymmetrized molecular-dynamics (AMD) calculations. It is found that the large monopole strength for the $3/2^-_3$ state at $E_x=8.56$ MeV is well described by the AMD calculation and is an evidence for a developed $2\alpha+t$ cluster structure.Comment: Revised according to the referees' comment