arXiv subjects

Taiichi Yamada

Publications and source records attributed to Taiichi Yamada.

26 records · Page 2Linked to original sources

arXiv2014

Investigation of ${}^9$Be from nonlocalized clustering concept

The nonlocalized aspect of clustering, which is a new concept for self-conjugate nuclei, is extended for the investigation of the N{\not=}Z nucleus ${}^9$Be. A modified version of the THSR (Tohsaki-Horiuchi-Schuck-Röpke) wave function is introduced based on the container picture. It is found that the constructed negative-parity THSR wave function is very suitable for describing the cluster states of ${}^9$Be. Namely the nonlocalized clustering is shown to prevail in ${}^9$Be. The calculated binding energy and radius of ${}^9$Be are consistent with calculations in other models and with experimental values. The squared overlaps between the THSR wave function and the Brink+GCM wave function for the $3/2^-$ rotational band of ${}^9$Be are found to be near 96%. Furthermore, by showing the density distribution of the ground state of ${}^9$Be, the π-orbit structure is naturally reproduced by using this THSR wave function.

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arXiv2013

Nonlocalized cluster dynamics and nuclear molecular structure

A container picture is proposed for understanding cluster dynamics where the clusters make nonlocalized motion occupying the lowest orbit of the cluster mean-field potential characterized by the size parameter $``B"$ in the THSR (Tohsaki-Horiuchi-Schuck-Röpke) wave function. The nonlocalized cluster aspects of the inversion-doublet bands in $^{20}$Ne which have been considered as a typical manifestation of localized clustering are discussed. So far unexplained puzzling features of the THSR wave function, namely that after angular-momentum projection for two cluster systems the prolate THSR wave function is almost 100$\%$ equivalent to an oblate THSR wave function is clarified. It is shown that the true intrinsic two-cluster THSR configuration is nonetheless prolate. The proposal of the container picture is based on the fact that typical cluster systems, 2$α$, 3$α$, and $α$+$^{16}$O, are all well described by a single THSR wave function. It will be shown for the case of linear-chain states with two and three $α$-clusters as well as for the $α$+$^{16}$O system that localization is entirely of kinematical origin, that is, due to the inter-cluster Pauli repulsion. It is concluded that this feature is general for nuclear cluster states.

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arXiv2010

$α+α+t$ cluster structures and Hoyle-analogue states in $^{11}$B

The structure of $3/2^{-}$ and $1/2^{+}$ states in $^{11}$B is investigated with an $α+α+t$ orthogonality condition model (OCM) based on the Gaussian expansion method. Full levels up to the $3/2^{-}_{3}$ and $1/2^{+}_2$ states around the $α+α+t$ threshold ($E_x$=11.1 MeV) are reproduced consistently with the experimental energy levels. It is shown that the $3/2_{3}^{-}$ state located around the $^{7}$Li+$α$ threshold has an $α+α+t$ cluster structure, whereas the $3/2_{1}^{-}$ and $3/2_{2}^{-}$ states have a shell-model-like compact structure. We found that the $3/2_{3}^{-}$ state does not possess an $α$-condensate-like nature similar to the $0^{+}_{2}$ state of $^{12}$C (Hoyle state) which has a dilute $3α$-condensate structure described by a $(0S_α)^3$ configuration with about $70$\% probability, although the monopole transition strength of the former is as large as that of the latter. We discuss the reasons why the $3/2_{3}^{-}$ state does not have the condensate character. On the other hand, the $1/2^{+}_{1}$ state just below the $^{7}$Li+$α$ threshold has a cluster structure which can be interpreted as a parity-doublet partner of the $3/2^{-}_3$ state. We indicate that the $12.56$-MeV state ($J^π=1/2^{+}_{2}$) just above the $α+α+t$ threshold observed in the $^7$Li($^{7}$Li,$^{11}$B$^*$)$t$ reaction etc. is of the dilute-cluster-gas-like, and is a strong candidate for the Hoyle-analogue state which has a configuration of $(0S_α)^{2}(0S_{t})$ with about $65$\% probability from the analyses of the single-cluster motions in $^{11}$B. The structure property of the $1/2^{+}$ resonant state is analyzed with the complex scaling method.

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arXiv2009

Internal One-Particle Density Matrix for Bose-Einstein Condensates with Finite Number of Particles in a Harmonic Potential

Investigations on the internal one-particle density matrix in the case of Bose-Einstein condensates with a finite number ($N$) of particles in a harmonic potential are performed. We solve the eigenvalue problem of the Pethick-Pitaevskii-type internal density matrix and find a fragmented condensate. On the contrary the condensate Jacobi-type internal density matrix gives complete condensation into a single state. The internal one-particle density matrix is, therefore, shown to be different in general for different choices of the internal coordinate system. We propose two physically motivated criteria for the choice of the adequate coordinate systems which give us a unique answer for the internal one-particle density matrix. One criterion is that in the infinite particle number limit ($N=\infty$) the internal one-particle density matrix should have the same eigenvalues and eigenfunctions as those of the corresponding ideal Bose-Einstein condensate in the laboratory frame. The other criterion is that the coordinate of the internal one-particle density matrix should be orthogonal to the remaining $(N - 2)$ internal coordinates. This second criterion is shown to imply the first criterion. It is shown that the internal Jacobi coordinate system satisfies these two criteria while the internal coordinate system adopted by Pethick and Pitaevskii for the construction of the internal one-particle density matrix does not. It is demonstrated that these two criteria uniquely determine the internal one-particle density matrix which is identical to that calculated with the Jacobi coordinates. The relevance of this work concerning $α$-particle condensates in nuclei, as well as bosonic atoms in traps, is pointed out.

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arXiv2008

Monopole Excitation to Cluster States

We discuss strength of monopole excitation of the ground state to cluster states in light nuclei. We clarify that the monopole excitation to cluster states is in general strong as to be comparable with the single particle strength and shares an appreciable portion of the sum rule value in spite of large difference of the structure between the cluster state and the shell-model-like ground state. We argue that the essential reasons of the large strength are twofold. One is the fact that the clustering degree of freedom is possessed even by simple shell model wave functions. The detailed feature of this fact is described by the so-called Bayman-Bohr theorem which tells us that SU(3) shell model wave function is equivalent to cluster model wave function. The other is the ground state correlation induced by the activation of the cluster degrees of freedom described by the Bayman-Bohr theorem. We demonstrate, by deriving analytical expressions of monopole matrix elements, that the order of magnitude of the monopole strength is governed by the first reason, while the second reason plays a sufficient role in reproducing the data up to the factor of magnitude of the monopole strength. Our explanation is made by analysing three examples which are the monopole excitations to the $0^+_2$ and $0^+_3$ states in $^{16}$O and the one to the $0^+_2$ state in $^{12}$C. The present results imply that the measurement of strong monopole transitions or excitations is in general very useful for the study of cluster states.

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arXiv2005

Single $α$-particle orbits and Bose-Einstein condensation in $^{12}$C

The $α$-bosonic properties such as single-$α$ orbits and occupation numbers in $J^π$=$0^+$, $2^+$, $1^-$ and $3^-$ states of $^{12}$C around the $3α$ threshold are investigated with the semi-microscopic $3α$ cluster model. As in other studies, we found that the $0^+_2$ ($2^+_2$) state has dilute-$3α$-condensate-like structure in which the $α$ particle is occupied in the single $S$ ($D$) orbit with about 70% (80%) probability. The radial behaviors of the single-$α$ orbits as well as the occupation numbers are discussed in detail in comparison with those for the $0^+_1$ and $2^+_1$ states together with the $1^-_1$ and $3^-_1$ states.

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arXiv2004

$ΛΛ$-$ΞN$-$ΣΣ$ coupling in $^{~6}_{ΛΛ}$He with the Nijmegen soft-core potentials

The $ΛΛ$-$ΞN$-$ΣΣ$ coupling in $^{~6}_{ΛΛ}$He is studied with the [$α$ + $Λ$ + $Λ$] + [$α$ + $Ξ$ + $N$] + [$α$ + $Σ$ + $Σ$] model, where the $α$ particle is assumed as a frozen core. We use the Nijmegen soft-core potentials, NSC97e and NSC97f, for the valence baryon-baryon part, and the phenomenological potentials for the $α-B$ parts ($B$=$N$, $Λ$, $Ξ$ and $Σ$). We find that the calculated $ΔB_{ΛΛ}$ of $^{~6}_{ΛΛ}$He for NSC97e and NSC97f are, respectively, 0.6 and 0.4 MeV in the full coupled-channel calculation, the results of which are about half in comparison with the experimental data, $ΔB^{exp}_{ΛΛ}=1.01\pm0.20^{+0.18}_{-0.11}$ MeV. Characteristics of the $S=-2$ sector in the NSC97 potentials are discussed in detail.

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arXiv2003

Dilute Multi Alpha Cluster States in Nuclei

Dilute multi $α$ cluster condensed states with spherical and axially deformed shapes are studied with the Gross-Pitaevskii equation and Hill-Wheeler equation, where the $α$ cluster is treated as a structureless boson. Applications to self-conjugate $4N$ nuclei show that the dilute $Nα$ states of $^{12}$C to $^{40}$Ca with $J^π=0^+$ appear in the energy region from threshold up to about 20 MeV, and the critical number of $α$ bosons that the dilute $Nα$ system can sustain as a self-bound nucleus is estimated roughly to be $N_{cr}\sim10$. We discuss the characteristics of the dilute $Nα$ states with emphasis on the $N$ dependence of their energies and rms radii.

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