Narrow Results

The dibaryon states as six-quark clusters of exotic QCD states are investigated in this talk. With the inherent nodal surface structure analysis, the wave functions of the six-quark clusters (in another word, the dibaryons) are classified. The contribution of the hidden color channels are discussed. The quantum numbers of the low-lying dibaryon states are obtained. The States [ΩΩ]_(0,0⁺), [ΩΩ]_(0,2^-), [Ξ* Ω]_(1/2,0⁺), [ΞΩ]_(1/2,1⁺), [Σ* Σ*]_(0,4^-) and the hidden color channel states with the same quantum numbers are proposed to be the candidates of dibaryons, which may be observed in experiments.

Three-alpha resonance excited states has been theoretically explored by means of the α+α+α microscopic cluster model. The resonance parameters is determined by employing the Complex Scaling Method (CSM). Our model space is extended by including higher partial waves than the RGM+CSM calculation by Pichler¹. Our model has given the third 0⁺ state at 4~5MeV above the three-body threshold but the broad 0⁺ state, which was recently reported experimentally and overlapping with the 2⁺ state², has not been localized between the second and the third 0⁺ states. On the other hands, our model has given the second 2⁺ state about 2MeV and the third at 4~5MeV.

The second 2⁺ state in the 10 MeV region of ¹²C was investigated by measuring decay-α particles in the ¹²C nucleus excited by inelastic α scattering at 0°. Angular correlation functions were obtained at backward angles from 115° to 255°. Those for 9.64 MeV 3^-, 15.4 MeV 2⁺, and 18.2 MeV 2⁺ states were good agreement with the PWBA calculation. The third 0⁺ state was also investigated. The coincidence spectra at 245° of decay-α particles seem to be consisted of two 0⁺ components.

The α+⁶He low-energy reactions and the structural changes of ¹⁰Be in the microscopic α+α+N+N model are studied by the generalized two-center cluster model with the Kohn-Hulthén-Kato variation method. It is found that, in the inelastic scattering to the channel, characteristic enhancements are expected as the results of the parity-dependent non-adiabatic dynamics. In the positive parity state, the enhancement originates from the excited eigenstate generated by the resonance pole of the final channel, while that in the negative parity state is induced by the Landau-Zener level-crossing. The reaction mechanism in breakup of ¹⁰Be into the ⁵He+⁵He and α+⁶He continuums is also studied. The strong enhancement in the breakup of is discussed in connection with the non-adiabatic dynamics.

³He + p scattering phase shifts for the S- and P-waves are studied in a microscopic cluster model in order to investigate the role of the d + 2p channel in the low-energy phase shifts. In the present cluster model, the description of the ³He wave function is extended from a simple (0s)³ model to a three-body model and two different nucleon-nucleon interactions, the Minnesota and AV8' potentials, are employed. The present extended cluster model shows that the d + 2p channel is indispensable to reproduce the resonant phase shifts in the AV8' potential while it plays a minor role in the MN potential. On the contrary, the role of this channel in the S-wave non-resonant phase shifts is negligible in both potentials.

In order to search for the α condensed state in ¹⁶O, we have performed the decay particle measurement via the reaction. Although the decay branching ratio of the α + ¹²C channel was predicted to be small, the branching ratio between the α + ¹²C and channels was obtained to be 7:3 by using the result of a simple simulation.

The phase shift analysis for position location of the resonance at 1.5 MeV was carried out on the basis of the known experimental measurements of the excitation functions of the p¹⁴C elastic scattering at four angles from 90° to 165° and more than 100 energy values in the range from 600–800 keV to 2200–2400 keV. Also, the possibility to describe the available experimental data on the astrophysical S-factor for the proton capture reaction on ¹⁴C to the ground state (GS) of ¹⁵N at astrophysical energies was considered in the frame of modified potential cluster model (MPCM).

¹²C isotope composing 3$\alpha$ cluster was investigated in this study. Therefore, ¹²C can be considered as a 3-body system. For studying the interactions in 3$\alpha$ clusters, a central potential was applied. Jacobi relative coordinates were also employed and center of mass motion was removed. In this paper, the Klein–Gordon (K–G) equation was solved using Nikiforov–Uvarov potential. At the end, the energy spectrum and wave function of isotope ¹²C were determined and the results were compared with the experimental data which showed good coincidence reflecting the success of our model in prediction.

Prospects of interesting hypernuclear structures are discussed for typical light p-shell systems with the cluster model application and also for the medium-heavy systems with shell-model applications. Corresponding to the recent experimental progress, importance of production reaction spectroscopy are emphasized.

We present a brief history of the structure study of ¹⁶O as a typical example in the development of the cluster model theory over 50 years.

A new cluster model of α decay is proposed where the effective potential between α-cluster and daughter nucleus is obtained from the double folding integral of the renormalized M3Y nucleon-nucleon interaction and of the density distributions of α particle and daughter nucleus. Without introducing any extra adjustment on the potential, the new model (named as the density-dependent cluster model) can successfully reproduce the experimental half-lives of α decay within a factor of 3. The model also works well for new superheavy elements which are the current interests of nuclear physics and chemistry.

A numerical representation for nuclei is suggested and considered as a basis of a cluster model. The binding energy of the cluster representation of a nucleus is introduced. Basic assumptions of the shell model are obtained as the physical side of the suggested cluster representation. ⁸Be₄-decay to two α-particles and ⁹B₅ decay to two α-particles and proton are interpreted.

The two-neutron halo nucleus ¹¹Li has been investigated in this work. Jacobi coordinates is used to describe the three-body system, using two configurations that are the T-configuration and Y-configuration. The calculations have been calculated based on a cluster model. The ¹¹Li nucleus is considered as three-body system core (⁹Li)+n+n. The core here has been considered as a deformed core. The calculations confirmed that the core has some deformation and has an oblate shape which in turn has effects on the structure of three-body system.

The continued interest in the study of radiative neutron capture on atomic nuclei is due, on the one hand, to the important role played by this process in the analysis of many fundamental properties of nuclei and nuclear reactions, and, on the other hand, to the wide use of the capture cross-section data in the various applications of nuclear physics and nuclear astrophysics, and, also, to the importance of the analysis of primordial nucleosynthesis in the Universe. This paper is devoted to the description of results for the processes of the radiative neutron capture on certain light atomic nuclei at thermal and astrophysical energies. The consideration of these processes is done within the framework of the potential cluster model (PCM), general description of which was given earlier. The methods of usage of the results obtained, based on the phase shift analysis intercluster potentials, are demonstrated in calculations of the radiative capture characteristics. The considered capture reactions are not part of stellar thermonuclear cycles, but involve in the basic reaction chain of primordial nucleosynthesis in the course of the Universe formation.

The alpha (α) elastic scattering from different targets potential over the energy range 10–240 MeV has been analyzed in the framework of the single-folding (SF) optical model. Four targets are considered, namely, ²⁴Mg, ²⁸Si, ³²S and ⁴⁰Ca. The SF calculations for the real central part of the nuclear optical potential are performed by folding an effective α–α interaction with the α-cluster distribution density in the target nucleus. The imaginary part of the optical potential is expressed in the phenomenological Woods–Saxon (WS) form. The calculated angular distributions of the elastic scattering differential cross-section using the derived semimicroscopic potentials successfully reproduce 36 sets of data all over the measured angular ranges. The obtained results confirm the validity of the α-cluster structure of the considered nuclei. For the sake of comparison, the same sets of data are reanalyzed using microscopic double-folded optical potentials based upon the density-dependent Jeukenne–Lejeune–Mahaux (JLM) effective nucleon–nucleon interaction.

The accurate calculations of the cluster formation model (CFM) have been extended to determine the alpha cluster preformation probability for the three even–even superheavy isotopes (Hs, Ds and Cn) with atomic number $Z=108,110$ and 112 and neutron numbers $144\le N\le 188$ in the mass region from 252 to 300. According to the hypothesized CFM, the calculations of the formation energy and surface energy, which depended on differences of binding energies are crucial for determining the realistic values of the preformation probability. Our results showed reasonable agreement with the results of previous work for the heavy nuclei. In addition, realistic values of the preformation probability certified that CFM can successfully be used to calculate the alpha cluster preformation probability for other wide range of superheavy nuclei.

In this work, the elastic scattering of ⁶Li+${}^{28}$Si system at wide range energies from 76 to 318MeV is analyzed. The analysis is carried out in the framework of the optical model (OM). Two different methods are adopted for nuclear optical potential of this system. The first method is the double folding cluster (DFC) for the real part supplied with an imaginary part in the Woods–Saxon (WS) form. In the second one, the double folding (DF) model based upon São Paulo potential (SPP) is used as real and imaginary parts each multiplied by a corresponding normalization factor. For ${}^{28}$Si, the full $\alpha$-cluster density is considered while the $\alpha$-deuteron ($\alpha$–$D$) structure is considered for ⁶Li. Therefore, the DFC real central part is calculated by folding both $\alpha$–$n$ and $\alpha$–$\alpha$ effective interaction between target and nuclei over the cluster densities of the target and projectile. The derived renormalized potentials give a successful description of the data. The present results are in good agreement with the previous work. This agreement confirms the validity of the present methods to generate nucleus–nucleus optical potentials.

Inspired by the prevalent $n+p$ cluster structure of deuterons, which appears at an excitation energy of 2.225MeV, the recently measured angular distributions (ADs) for ${}^{15}$N($d$,$d{)}^{15}$N and ${}^{15}$N($d$,$p{)}^{16}$N systems at an energy of 15MeV X. Y. Li et al., [Phys. Rev. C 106, (2022) 025807] are microscopically analyzed using the continuum discretized coupled channel (CDCC) method. The extracted $U_{\text{eff}}$ potential, considered as the coherent sum of cluster folding and dynamical polarization potentials, both derived from the CDCC computations, was then employed to investigate the ${}^{15}$N($d$,$p{)}^{16}$N neutron transfer reaction leading to the (2⁻, 0.0MeV), (0⁻, 0.12MeV), (3⁻, 0.298MeV), and (1⁻, 0.397MeV) ${}^{16}$N states. Since extracting reliable information on spectroscopic factors (SFs) is highly dependent on the interaction potential, the extracted $U_{\text{eff}}$ was employed to get such information. The investigation gives evidence for the applicability of the $U_{\text{eff}}$ in describing the elastic scattering and the neutron transfer ADs data. The extracted SFs for the ${}^{16}$N states under consideration are consistent with those that have been reported before.

Various low temperature treatments of Ni${}_{50.6}$Ti${}_{49.4}$ have shown an unexpected effect on the martensitic start temperature. Periodic diffuse intensity distributions in reciprocal space indicate the formation of short pure Ni strings along the $〈$111$〉$ directions in the B2 ordered lattice, precursing the formation of Ni₄Ti₃ precipitates formed at higher annealing temperatures.

Work in the last two decades on Bayesian nonparametric methods for mixture models finds that a posterior distribution is a double mixture. One first selects a partition of the objects based on a distribution on the partitions, and then performs a traditional parametric posterior analysis on the data corresponding to each cluster of the given partition. It is known that such a partition distribution favors partitions for which the clustering process is defined by predictive quantities such as predictive densities or weights. If a posterior distribution is a statistical guide to the unknown, this partition distribution could be used as a basis for a statistical model for clustering in which the partition is a parameter. The corresponding maximum likelihood estimator or posterior mode is used as an estimator of the partition. We also discuss methods to approximate these estimators based on a weighted Chinese restaurant process. A numerical example on a leukemia data set is given.