Search

$^{20}$Ne can be considered as a double-magic $^{16}$O core nucleus surrounded by four nucleons, the constituents of an $\alpha$-like quartet. Similar to other nuclei ($^{212}$Po, $^{104}$Ti, etc.) with a quartet on top of a double-magic core nucleus, significant $\alpha$-like correlations are expected. Correlations in the ground state of $^{20}$Ne are investigated using different approaches. The quartetting wave function approach (QWFA) predicts a large $\alpha$-like cluster contribution near the surface of the nuclei. The Tohsaki-Horiuchi-Schuck-R\"opke (THSR) approach describes $\alpha$-like clustering in nuclear systems. The results of the QWFA in the Thomas-Fermi and shell-model approximation are compared with THSR calculations for the container model. Results for the $\alpha$ formation probability and the rms radii are shown., Comment: 15 pages, 15 figures. arXiv admin note: text overlap with arXiv:1810.01274

We searched for the $\alpha$ condensed state in $^{13}$C by measuring the $\alpha$ inelastic scattering at $E_{\alpha} = 388$ MeV at forward angles including 0 degrees. We performed the distorted-wave Born-approximation calculation with the single-folding potential and the multipole decomposition analysis to determine the isoscalar transition strengths in $^{13}$C. We found a bump structure around $E_x = 12.5$ MeV due to the isoscalar monopole ($IS0$) transition. A peak-fit analysis suggested that this bump consisted of several $1/2^-$ states. We propose that this bump is due to the mirror state of the 13.5 MeV-state in $^{13}$N, which dominantly decays to the $\alpha$ condensed state in $^{12}$C. It was speculated that the $1/2^-$ states around $E_x = 12.5$ MeV were candidates for the $\alpha$ condensed state, but the $3\alpha + n$ orthogonality condition model suggests that the $\alpha$ condensed state is unlikely to emerge as the negative parity states. We also found two $1/2^+$ or $3/2^+$ states at $E_x = 14.5$ and 16.1 MeV excited with the isoscalar dipole ($IS1$) strengths. We suggest that the 16.1-MeV state is a possible candidate for the $\alpha$ condensed state predicted by the cluster-model calculations on the basis of the good correspondence between the experimental and calculated level structures. However, the theoretical $IS1$ transition strength for this state is significantly smaller than the measured value. Further experimental information is strongly desired to establish the $\alpha$ condensed state in $^{13}$C., Comment: 24 pages, 12 figures, published in PTEP

Background: $\alpha+{^{12}{\rm C}}$ clustering in $^{16}{\rm O}$ has been of historical importance in nuclear clustering. In the last 15 years the $4\alpha$ condensate state has been proposed as a new-type cluster state. Purpose: The aim is to reveal a dynamical process of the formation of different kinds of cluster states, in terms of a "container" aspect of clusters, in $^{16}{\rm O}$. Method: The so-called THSR wave function for the $4\alpha$ clusters is extended to inclusion of two different containers occupied independently by the $^{12}{\rm C}$ $(3\alpha)$ and $\alpha$ clusters. Results: The five $J^\pi=0^+$ states with $4\alpha$ tetrahedral shape, $\alpha+{^{12}{\rm C}}$ cluster structures, and the $4\alpha$ condensate character, are found to be represented, to good approximation, by single configurations of the extended THSR wave function with containers of appropriate shape and size. Conclusions: It is demonstrated in $^{16}{\rm O}$ that the dynamical evolution of cluster structures can be caused by size and shape evolution of a container occupied with clusters. The $\alpha$ condensate with gaslike $4\alpha$ configuration appears as a limit of the cluster formation., Comment: 6 pages, 4 figures, 3 tables

Quartetting ($\alpha$-like clustering) occurs in low density matter ($\le 0.03$ fm$^{-3}$) which exists, e.g., at the surface of nuclei. It is of interest for the $\alpha$ preformation to calculate the $\alpha$ decay of heavy nuclei such as $^{212}$Po, but also in light nuclei (e.g., $^{20}$Ne) which shows strong signatures of quartetting. We analyze the intrinsic structure of the $\alpha$-like cluster and the center of mass motion of the quartet, in particular the role of Pauli blocking. The Thomas-Fermi model for the (daughter) core nucleus is improved introducing quasiparticle nucleon states. Calculations performed for harmonic oscillator basis states show that the effective potential for the quartet center of mass motion remains nearly constant within the core nucleus. The relation to the THSR (Tohsaki-Horiuchi-Schuck-R\"opke) approach is discussed., Comment: 26 pages, 9 figures

We investigate structure of $^{13}_\Lambda{\rm C}$ and discuss the difference and similarity between the structures of $^{12}{\rm C}$ and $^{13}_\Lambda{\rm C}$ by answering the questions if the linear-chain and gaslike cluster states, which are proposed to appear in $^{12}{\rm C}$, survives, or new structure states appear or not. We introduce a microscopic cluster model called, Hyper-Tohsaki-Horiuchi-Schuck-R\"opke (H-THSR) wave function, which is an extended version of the THSR wave function so as to describe $\Lambda$ hypernuclei. We obtained two bound states and two resonance (quasi-bound) states for $J^\pi=0^+$ in $^{13}_\Lambda{\rm C}$, corresponding to the four $0^+$ states in $^{12}{\rm C}$. However, the inversion of level ordering between the spectra of $^{12}{\rm C}$ and $^{13}_\Lambda{\rm C}$, i.e. that the $0_3^+$ and $0_4^+$ states in $^{13}_\Lambda{\rm C}$ correspond to the $0_4^+$ and $0_3^+$ states in $^{12}{\rm C}$, respectively, is shown to occur. The additional $\Lambda$ particle reduces sizes of the $0_2^+$ and $0_3^+$ states in $^{13}_\Lambda{\rm C}$ very much, but the shrinkage of the $0_4^+$ state is only a half of the other states. In conclusion, the Hoyle state becomes quite a compact object with ${^{9}_\Lambda{\rm Be}}+\alpha$ configuration in $^{13}_\Lambda{\rm C}$ and is no more gaslike state composed of the $3\alpha$ clusters. Instead, the $0_4^+$ state in $^{13}_\Lambda{\rm C}$, coming from the $^{12}{\rm C}(0_3^+)$ state, appears as a gaslike state composed of $\alpha+\alpha+^{5}_\Lambda{\rm He}$ configuration, i.e. the Hoyle analog state. A linear-chain state in a $\Lambda$ hypernucleus is for the first time predicted to exist as the $0_3^+$ state in $^{13}_\Lambda{\rm C}$ with more shrunk arrangement of the $3\alpha$ clusters along $z$-axis than the $3\alpha$ linear-chain configuration realized in the $^{12}{\rm C}(0_4^+)$ state., Comment: 9 pages, 6 figures, figures rearranged, accepted for publication in PLB

We present a microscopic calculation of alpha-cluster formation in heavy nuclei by using the quartetting wave function approach. The interaction of the quartet with the core nucleus is taken in local density approximation. The alpha-cluster formation is found to be particularly sensitive to the interplay of the mean field felt by the alpha-cluster and the Pauli blocking as a consequence of antisymmetrization. The striking feature of alpha-cluster formation probability across the major shell closures of 82 protons and 126 neutrons is reproduced. The shell (or subshell) effects on the alpha-cluster formation in superheavy nuclei are also analyzed., Comment: 11 pages, 6 figures, 1 table, discussion added, accepted for publication in Phys. Rev. C

A microscopic calculation of $\alpha$-cluster preformation probability and $\alpha$ decay width in the typical $\alpha$ emitter $^{212}$Po is presented. Results are obtained by improving a recent approach to describe $\alpha$ preformation in $^{212}$Po [Phys. Rev. C 90, 034304 (2014)] implementing four-nucleon correlations (quartetting). Using the actually measured density distribution of the $^{208}$ Pb core, the calculated alpha decay width of $^{212}$Po agrees fairly well with the measured one., Comment: 7 pages, 5 figures, 1 table, submitted to Phys. Rev. C

Radiative capture rates of thermal $\Lambda\Lambda + \Xi$N states into H dibaryon are calculated in the novel imaginary time method. The H dibaryon is assumed to be a bound state of $\Xi $N with spin $J^{\pi}= 0^+$, isospin $I=0$ and strangeness $-2$. We consider $E1$ transition to H from $\Xi$N $(L=1)$ scattering states which mix with $\Lambda\Lambda (L=1)$. In order to calculate the transition rates, we formulate a coupled-channel imaginary time method by extending the one-channel formula originally proposed by Yabana and Funaki. The imaginary time method allows us to avoid the sum over all the excited thermal initial states, and thus to save computational time significantly. The transition rates are given as a function of temperature and the unknown binding energy of the H dibaryon, which we take as a parameter. It is found that the transition rate is not sensitive to the choices of the H binding energy or the strengths of the channel coupling for temperatures 3 MeV or higher., Comment: 10 pages, 14 figures

The excited states in ${^{12}{\rm C}}$ are investigated by using an extended version of the so-called Tohsaki-Horiuchi- Schuck-R\"opke (THSR) wave function, where both the $3\alpha$ condensate and ${^{8}{\rm Be}} + \alpha$ cluster asymptotic configurations are included. A new method is also used to resolve spurious continuum coupling with physical states. We focus on the structures of the "Hoyle band" states, $2_2^+$, and $4_2^+$ states, which are recently observed above the Hoyle state and of the $0_3^+$ and $0_4^+$ states, which are also quite recently identified in experiment. Their resonance parameters and decay properties are reasonably reproduced. All these states have gaslike configurations of the $3\alpha$ clusters with larger root mean square radii than that of the Hoyle state. The Hoyle band is not simply considered to be the ${^{8}{\rm Be}}(0^+) +\alpha$ rotation as suggested by previous cluster model calculations, nor to be a rotation of a rigid-body triangle-shaped object composed of the $3\alpha$ particles. This is mainly due to the specificity of the Hoyle state, which has the $3\alpha$ condensate structure and gives a rise to the $0_3^+$ state with a prominent ${^{8}{\rm Be}}(0^+)+\alpha$ structure as a result of very strong monopole excitation from the Hoyle state., Comment: 5 pages, 2 figures, submitted to PRL

An effective $\alpha$ particle equation is derived for cases where an $\alpha$ particle is formed on top of a doubly magic nucleus. As an example, we consider $^{212}$Po with the $\alpha$ on top of the $^{208}$ Pb core. We will consider the core nucleus infinitely heavy, so that the $\alpha$ particle moves with respect to a fixed center, i.e., recoil effects are neglected. The fully quantal solution of the problem is discussed. The approach is inspired by the THSR (Tohsaki-Horiuchi-Schuck-R\"{o}pke) wave function concept that has been successfully applied to light nuclei. Shell model calculations are improved by including four-particle ($\alpha$-like) correlations that are of relevance when the matter density becomes low. In the region where the $\alpha$-like cluster penetrates the core nucleus, the intrinsic bound state wave function transforms at a critical density into an unbound four-nucleon shell model state. Exploratory calculations for $^{212}$Po are presented. Such preformed cluster states are only hardly described by shell model calculations. Reasons for different physics behavior of an $\alpha$-like cluster with respect to a deuteron-like cluster are discussed., Comment: 24 pages, 5 figures

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 refer to as Hyper-Tohsaki-Horiuchi-Schuck-R\"opke (Hyper-THSR) wave function. By using the Hyper-THSR wave function, $2\alpha + \Lambda$ cluster structure in ${^{9}_\Lambda{\rm Be}}$ is investigated. We show that full microscopic solutions in the $2\alpha + \Lambda$ cluster system, which are given as $2\alpha + \Lambda$ 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 $2\alpha$ clusters appear in the nucleonic intrinsic density, though in ${^{8}{\rm Be}}$ rather gaslike $2\alpha$-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 $2\alpha$ 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., Comment: 14 pages, 4 figures, 3 tables, submitted to PTEP

Using imaginary-time theory, it is shown that the triple-alpha reaction rate can be reliably calculated without the need to solve scattering problems involving three charged particles. The calculated reaction rate is found to agree well with the empirical NACRE rate, which is widely adopted in stellar evolution calculations. The reason for this is explained using $R$-matrix theory. Extremely slow convergence is found to occur when a coupled-channel expansion is introduced, which helps to explain the very different reaction rates obtained using different theoretical approaches.

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 pairing. 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., Comment: Contribution to MBT17 conference, Rostock, september 9-13, 2013, to be published in iop conference series

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-R\"opke (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., Comment: 5 pages, 5 figures

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 structures 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., Comment: 15 pages, 13 figures

We investigate the $\alpha$+\oo\ cluster structure in the inversion-doublet band ($K^\pi=0_{1}^\pm$) states of \nene\ with an angular-momentum-projected version of the Tohsaki-Horiuchi-Schuck-R\"{o}pke (THSR) wave function, which was successful "in its original form" for the description of, e.g., the famous Hoyle state. In contrast with the traditional view on clusters as localized objects, especially in inversion doublets, we find that these {\it single} THSR wave functions, which are based on the concept of nonlocalized clustering, can well describe the $K^{\pi}=0_1^-$ band and the $K^{\pi}=0_1^+$ band. For instance, they have 99.98% and 99.87% squared overlaps for $1^-$ and $3^- $ states (99.29%, 98.79% and 97.75% for $0^+, 2^+$ and $4^+$ states), respectively, with the corresponding exact solution of the $\alpha$+\oo\ resonating group method. These astounding results shed a completely new light on the physics of low energy nuclear cluster states in nuclei: The clusters are nonlocalized and move around in the whole nuclear volume, only avoiding mutual overlap due to the Pauli blocking effect., Comment: 6 pages, 4 figures, Published in PRL

Large-scale calculation based on the multi-configuration Skyrme density functional theory is performed for the light N=Z even-even nucleus, 12C. Stochastic procedures and the imaginary-time evolution are utilized to prepare many Slater determinants. Each state is projected on eigenstates of parity and angular momentum. Then, performing the configuration mixing calculation with the Skyrme Hamiltonian, we obtain low-lying energy-eigenstates and their explicit wave functions. The generated wave functions are completely free from any assumption and symmetry restriction. Excitation spectra and transition probabilities are well reproduced, not only for the ground-state band, but for negative-parity excited states and the Hoyle state., Comment: 4 pages, 1 figure, Talk at 2nd International Nuclear Physics Conference "Nuclear Structure and Dynamics", Opatija, Croatia, July 9 - 13, 2012

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$(\alpha,\alpha^{\prime})$ reaction can be rather satisfactorily reproduced within the framework of the $4\alpha$ 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., Comment: 35 pages, 5 figures

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)

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 wave 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., Comment: 16 pages, 15 figures, submitted to PRC.

$\alpha$ particle condensation is a novel state in nuclear systems. We briefly review the present status on the study of $\alpha$ particle condensation and address the open problems in this research field: $\alpha$ particle condensation in heavier systems other than the Hoyle state, linear chain and $\alpha$ particle rings, Hoyle-analogue states with extra neutrons, $\alpha$ particle condensation related to astrophysics, etc., Comment: 12 pages. To be published in J. of Phys. G special issue on Open Problems in Nuclear Structure (OPeNST)

Certain aspects of the recently proposed antisymmetrised alpha particle product state wave function, or THSR alpha cluster wave function, for the description of the ground state in 8Be, the Hoyle state in 12C, and analogous states in heavier nuclei, are elaborated in detail. For instance, the influence of antisymmetrisation in the Hoyle state on the bosonic character of the alpha particles is studied carefully. It is shown to be weak, so that bosonic aspects are predominant. The de Broglie wave length of alpha particles in the Hoyle state is shown to be much larger than the inter-alpha distance. It is pointed out that the bosonic features of low density alpha gas states have measurable consequences, one of which, that is enhanced multi-alpha decay properties, likely already have been detected. Consistent with experiment, the width of the proposed analogue to the Hoyle state in 16O at the excitation energy of E_x=15.1 MeV is estimated to be very small (34 keV), lending credit to the existence of heavier Hoyle-like states. The intrinsic single boson density matrix of a self-bound Bose system can, under physically desirable boundary conditions, be defined unambiguously. One eigenvalue then separates out, being close to the number of alpha's in the system. Differences between Brink and THSR alpha cluster wave functions are worked out. No cluster model of the Brink type can describe the Hoyle state with a single configuration. On the contrary, many superpositions of the Brink type are necessary, implying delocalisation towards an alpha product state. It is shown that single alpha particle orbits in condensates of different nuclei are almost the same. It is thus argued that alpha particle antisymmetrised product states of the THSR type are a very promising novel and useful concept in nuclear physics., Comment: 16 pages, 14 figures, to appear in PRC

The onset of quartetting, i.e. alpha-particle condensation, in symmetric nuclear matter is studied with the help of an in-medium modified four nucleon equation. It is found that at very low density quartetting wins over pairing, because of the strong binding of the alpha-particles. The critical temperature can reach values up to around 6 MeV. Also the disappearance of alpha-particles with increasing density, i.e. the Mott transition, is investigated. In finite nuclei the Hoyle state, that is the 0_2^+ 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. For instance the 6-th 0^+ state of 16O at 15.1 MeV is identified from a theoretical analysis as being a strong candidate for an alpha condensate state. Exploratory calculations are performed for the density dependence of the alpha condensate fraction at zero temperature to address the suppression of the four-particle condensate below nuclear-matter density. Possible quartet condensation in other systems is discussed briefly, Comment: 29 pages, 21 figures

In a recent paper, arXiv0712.1191 [nucl-th], Zinner and Jensen (ZJ) expressed strong doubts about the concept of alpha-particle condensation in finite nuclei. In this article we give a reply which, essentially, is point by point (but not in the order)., Comment: 9 pages, 4 figures; section IV simplified

The internal one-particle density matrix is discussed for Bose-Einstein condensates with finite number of particles in a harmonic trap. The outcome of the digonalization of the density matrix depends on the choice of the internal coordinates: The Pethick-Pitaevskii-type internal density matrix, whose analytical eigenvalues and eigenfunctions are evaluated, yields a fragmented condensate, while the Jacobi-type internal density matrix leads to an ideal condensate. We give a criterion for the choice of the internal coordinates: In the macroscopic limit the internal density matrix should have eigenvalues and eigenfunctions of an ideal Bose-Einstein condensate, this being a very physical condition for cases where the system is also an ideal Bose condensation in the laboratory frame. One choice fulfilling this boundary condition is given by the internal Jacobi coordinates, while the internal coordinates with respect to the center of mass do not satisfy the condition. Based on our criterion, a general definition of the internal one-particle density matrix is presented in a self-bound system, consisting of interacting bosons., Comment: Shortened to Brief report

In order to explore the 4 \alpha-particle condensate state in 16O, we solve a full four-body equation of motion based on the 4 \alpha OCM (Orthogonality Condition Model) in a large 4 \alpha model space spanned by Gaussian basis functions. A full spectrum up to the 0_6^+ state is reproduced consistently with the lowest six 0^+ states of the experimental spectrum. The 0^+_6 state is obtained at about 2 MeV above the 4 \alpha breakup threshold and has a dilute density structure, with a radius of about 5 fm. The state has an appreciably large \alpha condensate fraction of 61 %, and a large component of \alpha+12C(0_2^+) configuration, both features being reliable evidence for this state to be of 4 \alpha condensate nature., Comment: 4 pages, 3 figures and 1 table

At low densities, with decreasing temperatures, in symmetric nuclear matter alpha-particles are formed, which eventually give raise to a quantum condensate with four-nucleon alpha-like correlations (quartetting). Starting with a model of alpha-matter, where undistorted alpha particles interact via an effective interaction such as the Ali-Bodmer potential, the suppression of the condensate fraction at zero temperature with increasing density is considered. Using a Jastrow-Feenberg approach, it is found that the condensate fraction vanishes near saturation density. Additionally, the modification of the internal state of the alpha particle due to medium effects will further reduce the condensate. In finite systems, an enhancement of the S state wave function of the c.o.m. orbital of alpha particle motion is considered as the correspondence to the condensate. Wave functions have been constructed for self-conjugate 4n nuclei which describe the condensate state, but are fully antisymmetrized on the nucleonic level. These condensate-like cluster wave functions have been successfully applied to describe properties of low-density states near the n alpha threshold. Comparison with OCM calculations in 12C and 16O shows strong enhancement of the occupation of the S-state c.o.m. orbital of the alpha-particles. This enhancement is decreasing if the baryon density increases, similar to the density-induced suppression of the condensate fraction in alpha matter. The ground states of 12C and 16O show no enhancement at all, thus a quartetting condensate cannot be formed at saturation densities., Comment: 7 pages, 3 figure, submitted to Phys. Rev. C

Inelastic $\alpha$ scattering on 16O is studied at 400 MeV by using an ice target. Near the 4-alpha breakup threshold of 14.4 MeV, a broad peak is observed at an excitation energy of 13.6+/-0.2 MeV with a width of 0.6+/-0.2 MeV. The spin-parity is estimated to be 0+ from the momentum-transfer dependence. The observed width is significantly larger than those of the neighboring 0+ states indicating a state with a well-developed alpha cluster structure. The magnitude of the cross section is sensitive to the density distribution of the constituent alpha clusters. The observed cross section is consistent with the theoretical prediction for the alpha cluster condensed state characterized by its dilute density distribution with a large root-mean-square radius of about 4.3 fm., Comment: 12 pages, 5 fugures, submitted to Phys. Lett. B

On-site underground background measurements were performed for the planned reactor-neutrino oscillation experiment KASKA at Kashiwazaki-Kariwa nuclear power station in Niigata, Japan. A small-diameter boring hole was excavated down to 70m underground level, and a detector unit for $\gamma$-ray and cosmic-muon measurements was placed at various depths to take data. The data were analyzed to obtain abundance of natural radioactive elements in the surrounding soil and rates of cosmic muons that penetrate the overburden. The results will be reflected in the design of the KASKA experiment., Comment: 9 pages, 7 figures, final version for publication. Table 1 and Fig.5 have changed

One of the current most-demanded experiments in neutrino physics is to measure the last mixing angle theta_13. KASKA is an experiment to detect new type of reactor neutrino oscillation and to measure sin^2 2theta_13 accurately using the world's most powerful nuclear reactor complex; Kashiwazaki-Kariwa nuclear power station. KASKA utilizes near and far detectors of identical structure at nearly optimized baselines and underground depths to cancel most of the systematics and reduce backgrounds. The expected sensitivity is sin^2 2theta_13~0.015, which is 10 times better sensitivity than the current upper limit measured by CHOOZ reactor experiment. Extension of KASKA project has potential to accurately measure other anti-nu_e oscillation parameters. Intense and precisely known neutrino flux measured by the KASKA-theta_13 phase can be used to pin down sin^2 2theta_12 at a baseline ~50km and to measure Dm^2_13 for the first time at a baseline ~5km. This Letter of Intent describes physics motivation, detector system and expected performance of the KASKA experiment., Comment: 86 pages, 61 figures

In order to discuss the spatial extention of the second 0+ state of 12C (Hoyle state), we analyze the inelastic form factor of electron scattering to the Hoyle state, which our 3 alpha condensate wave function reproduces very well like previous 3 alpha RGM/GCM models. The analysis is made by varying the size of the Hoyle state artificially. As a result, we find that only the maximum value of the form factor sensitively depends on its size, while the positions of maximum and minimum are almost unchanged. This size dependence is found to come from a characteristic feature of the transition density from the ground state to the Hoyle state. We further show the theoretical predictions of the inelastic form factor to the second 2+ state of 12C, which was recently observed above the Hoyle state, and of the inelastic form factor to the calculated third 0+ state of 16O, which was conjectured to correspond to the 4 alpha condensed state in previous theoretical work by the present authors., Comment: 5 pages, 10 figures, submitted to Phys. Rev. C (R)

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 references

The states with $J^\pi=0^+$, $2^+$, and $4^+$ of $^{12}$C with excitation energies less than about 15 MeV are investigated with the alpha condensate wave function with spatial deformation and by using the method of ACCC (analytic continuation in the coupling constant) which is necessary for a proper treatment of resonance states. The calculated energy and width of the recently observed $2_2^+$ state are found to be well reproduced. The obtained $2_2^+$ wave function has a large overlap with a single condensate wave function of $3\alpha$ gas-like structure. The density distribution is shown to be almost the same as that of the $0_2^+$ state that is regarded as a $3\alpha$ Bose-condensed state, if the energy of the $2_2^+$ state is scaled down to the same value as the one of the $0_2^+$ state. Furthermore, the kinetic energy, nuclear interaction energy, and Coulomb interaction energy of the calculated $2_2^+$ state are shown to be very similar to those of the $0_2^+$ state. We conclude that the $2_2^+$ state has a structure similar to the $0_2^+$ state of Bose-condensate character with a dilute $3\alpha$ gas-like structure. In addition the resonance states, $0_3^+$, $0_4^+$, $4_2^+$, are also discussed., Comment: 23 pages, 21 figures. Submitted to PRC

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. C