Search

The formation of $\ensuremath{\alpha}$ particles on nuclear surfaces has remained a fundamental problem since the dawn of nuclear physics. This $\ensuremath{\alpha}$-particle formation strongly affects the $\ensuremath{\alpha}$-decay lifetimes of heavy and superheavy elements, level scheme of light nuclei, and synthesis of elements in stars. However, despite its importance, the $\ensuremath{\alpha}$-particle formation in medium-mass nuclei is seldom investigated. Based on the $^{48}\mathrm{Ti}(p,p\ensuremath{\alpha})^{44}\mathrm{Ca}$ reaction analysis, this study reports that $\ensuremath{\alpha}$-particle formation in the medium-mass $^{48}\mathrm{Ti}$ nucleus is pronounced more compared to that expected through mean-field approximations. Moreover, the estimated average distance between the $\ensuremath{\alpha}$ particle and residue equals approximately 4.5 fm. This result poses a challenge to describe the four nucleon correlations using microscopic nuclear models.

The properties of the $\ensuremath{\alpha}+^{28}\mathrm{Si}$ and $^{16}\mathrm{O}+^{16}\mathrm{O}$ molecular states, which are embedded in the excited states of $^{32}\mathrm{S}$ and can have an impact on the stellar reactions, are investigated using antisymmetrized molecular dynamics. From the analysis of the cluster spectroscopic factors, the candidates of $\ensuremath{\alpha}+^{28}\mathrm{Si}$ and $^{16}\mathrm{O}+^{16}\mathrm{O}$ molecular states are identified close to and above the cluster threshold energies. The calculated properties of $\ensuremath{\alpha}+^{28}\mathrm{Si}$ molecular states are consistent with those reported by $\ensuremath{\alpha}+^{28}\mathrm{Si}$ resonant scattering experiments. On the other hand, the $^{16}\mathrm{O}+^{16}\mathrm{O}$ molecular state, which is predicted to be identical to the superdeformation of $^{32}\mathrm{S}$, is inconsistent with the assignment proposed by an $\ensuremath{\alpha}$ inelastic scattering experiment. Our calculation suggests that the monopole transition from the ground state to the $^{16}\mathrm{O}+^{16}\mathrm{O}$ molecular state is rather weak and is not strongly excited by $\ensuremath{\alpha}$ inelastic scattering.

Background: The proton-induced $\ensuremath{\alpha}$ knockout reaction has been utilized for decades to investigate the $\ensuremath{\alpha}$ cluster formation in the ground state of nucleus. However, even today, the theoretical description of the reaction is not precise enough for the quantitative study. For example, the $\ensuremath{\alpha}$ spectroscopic factors reduced from $\ensuremath{\alpha}$ knockout experiments with reaction analyses using phenomenological $\ensuremath{\alpha}$ cluster wave functions disagree with those given by a structure theory. In some cases they also scatter depending on the kinematical condition of the experiment. This suggests that the theoretical description of the $\ensuremath{\alpha}$ knockout reaction is insufficient from a quantitative viewpoint.Purpose: We show that the distorted wave impulse approximation can describe $^{20}\mathrm{Ne}(p,p\ensuremath{\alpha})^{16}\mathrm{O}$ reaction quantitatively if reliable inputs are used; the optical potential, the $p\ensuremath{-}\ensuremath{\alpha}$ cross section, and the $\ensuremath{\alpha}$ cluster wave function. We also investigate the relationship between the $\ensuremath{\alpha}$ cluster wave function and the $\ensuremath{\alpha}$ knockout cross section.Method: The $^{20}\mathrm{Ne}(p,p\ensuremath{\alpha})^{16}\mathrm{O}$ reaction is described by the distorted wave impulse approximation. An input of the calculation, the $\ensuremath{\alpha}\ensuremath{-}^{16}\mathrm{O}$ cluster wave function, is obtained by the antisymmetrized molecular dynamics and the Laplace expansion method.Results: In contrast to the previous work, the $^{20}\mathrm{Ne}(p,p\ensuremath{\alpha})^{16}\mathrm{O}$ data at 101.5 MeV is successfully reproduced by the present framework without any free adjustable parameters. It is also found that the knockout cross section is sensitive to the surface region of the cluster wave function because of the peripherality of the reaction.Conclusions: Using a reliable $\ensuremath{\alpha}$ cluster wave function, $p\ensuremath{-}\ensuremath{\alpha}$ cross section, and distorting potentials, it is found that the $^{20}\mathrm{Ne}(p,p\ensuremath{\alpha})^{16}\mathrm{O}$ cross section is quantitatively reproduced by the present framework. This success demonstrates that the proton-induced $\ensuremath{\alpha}$ knockout reaction is a quantitative probe for the $\ensuremath{\alpha}$ clustering.

The C 12 + 12 C fusion reaction plays a vital role in the explosive phenomena of the universe. The resonances in the Gamow window rule its reaction rate and products. Hence, the determination of the resonance parameters by nuclear models is indispensable as the direct measurement is not feasible. Here, for the first time, we report the resonances in the C 12 + 12 C fusion reaction described by a full-microscopic nuclear model. The model plausibly reproduces the measured low-energy astrophysical S-factors and predicts the resonances in the Gamow window. Contradictory to the hindrance model, we conclude that there is no low-energy suppression of the S-factor.

Background: The coupling of clusters and deformed structures is important for the dynamics of a nuclear structure. Threshold energy is discussed to explain cluster structure coupling to deformed states but the relation between threshold energy and excitation energy involves open problems. Negative-parity superdeformed (SD) states were observed via a $\ensuremath{\gamma}$-spectroscopy experiment in $^{35}\mathrm{Cl}$. However, their detailed structure is unclear.Purpose: An analysis of the coupling of cluster structures in deformed states and high-lying cluster states in $^{35}\mathrm{Cl}$ is used to investigate cluster structures coupling to deformed states and excitation energy of high-lying cluster states.Method: Antisymmetrized molecular dynamics (AMD) and the generator coordinate method (GCM) are used. An AMD wave function corresponds to a Slater determinant of Gaussian wave packets. Energy variational calculations with constraints on deformation and clustering are used to obtain wave functions of deformed structures and $\ensuremath{\alpha}\text{\ensuremath{-}}^{31}\mathrm{P}$ and $t\text{\ensuremath{-}}^{32}\mathrm{S}$ cluster structures. The wave functions are adopted as the GCM basis, and wave functions of ground and excited states are calculated.Results: Various deformed bands are obtained and predicted. A ${K}^{\ensuremath{\pi}}={\frac{1}{2}}^{\ensuremath{-}}$ deformed band (corresponding to the observed SD band) dominates the deformed structure and compact $\ensuremath{\alpha}\text{\ensuremath{-}}^{31}\mathrm{P}$ and $t\text{\ensuremath{-}}^{32}\mathrm{S}$ cluster structure components. Particle-hole configurations of dominant components with deformed and cluster structures are similar. In high-lying states, almost pure $\ensuremath{\alpha}\text{\ensuremath{-}}^{31}\mathrm{P}$ and $t\text{\ensuremath{-}}^{32}\mathrm{S}$ cluster states are obtained in negative-parity states, and excitation energies of the $t\text{\ensuremath{-}}^{32}\mathrm{S}$ cluster states exceed those of $\ensuremath{\alpha}\text{\ensuremath{-}}^{31}\mathrm{P}$ cluster states.Conclusions: Particle-hole configurations of cluster structures with a small intercluster distance are important for coupling to low-energy deformed states. Threshold energies reflect excitation energies of almost pure high-lying cluster states.

The existence of C 12 + 16 O molecular resonances at sub-barrier energy has been a significant problem in nuclear astrophysics because they strongly affect the C 12 + 16 O fusion reaction rate in type Ia supernovae and heavy stars. However, experimental surveys have been limited to 4 MeV and cannot access the deep sub-barrier energy due to a very small fusion cross section. Here we predict a couple of resonances with J π = 0 + , 2 + , and 4 + in the deep sub-barrier energy based on the antisymmetrized molecular dynamics calculation that reproduces the known resonances and low-lying spectrum of Si 28 .

Clustering and deformation are important for dynamics of nuclear structure, and cluster structures couple to deformed states. However, its mechanism is unclear. Cluster structures that couple to each deformed state and the mechanism are investigated in $^{35}$Cl. The antisymmetrized molecular dynamics (AMD) and the generator coordinate method (GCM) are used. An AMD function is a Slater determinant of Gaussian wave packets. By energy variational calculations with constraints for deformation and clustering, wave functions that have deformed and $\alpha$-$^{31}$P and $t$-$^{32}$S cluster structures are obtained. Adopting those wave functions as GCM basis, wave functions of ground and excited states are calculated. Various cluster deformed bands are obtained and predicted. The $K^\pi = \frac{1}{2}^-$ deformed bands contains large amount of $\alpha$-$^{31}$P and $t$-$^{32}$S cluster structure components. Particle-hole configurations of both cluster structures are same as dominant components of the $K^\pi = \frac{1}{2}^-$ bands in small intercluster distance. Particle-hole configurations of cluster structure in small intercluster distance are important for coupling of cluster structure to deformed states.

Background: Various cluster states of astrophysical interest are expected to exist in the excited states of $^{28}\mathrm{Si}$. However, they have not been identified firmly, because of the experimental and theoretical difficulties.Purpose: To establish the $^{24}\mathrm{Mg}+\ensuremath{\alpha},^{16}\mathrm{O}+^{12}\mathrm{C}$, and $^{20}\mathrm{Ne}+2\ensuremath{\alpha}$ cluster bands, we theoretically search for the negative-parity cluster bands that are paired with the positive-parity bands to constitute the inversion doublets. We also offer the isoscalar monopole and dipole transitions as a promising probe for the clustering. We numerically show that these transition strengths from the ground state to the cluster states are very much enhanced.Method: The antisymmetrized molecular dynamics with Gogny D1S effective interaction is employed to calculate the excited states of $^{28}\mathrm{Si}$. The isoscalar monopole and dipole transition strengths are directly evaluated from wave functions of the ground and excited states.Results: Negative-parity bands having $^{24}\mathrm{Mg}+\ensuremath{\alpha}$ and $^{16}\mathrm{O}+^{12}\mathrm{C}$ cluster configurations are obtained in addition to the newly calculated $^{20}\mathrm{Ne}+2\ensuremath{\alpha}$ cluster bands. All of them are paired with the corresponding positive-parity bands to constitute the inversion doublets with various cluster configurations. The calculation shows that the bandheads of the $^{24}\mathrm{Mg}+\ensuremath{\alpha}$ and $^{20}\mathrm{Ne}+2\ensuremath{\alpha}$ cluster bands are strongly excited by the isoscalar monopole and dipole transitions.Conclusions: The present calculation suggests the existence of inversion doublets with the $^{24}\mathrm{Mg}+\ensuremath{\alpha},^{16}\mathrm{O}+^{12}\mathrm{C}$, and $^{20}\mathrm{Ne}+2\ensuremath{\alpha}$ configurations. Because of the enhanced transition strengths, we offer the isoscalar monopole and dipole transitions as good probe for the $^{24}\mathrm{Mg}+\ensuremath{\alpha}$ and $^{20}\mathrm{Ne}+2\ensuremath{\alpha}$ cluster bands.

Background: Direct evidence of the $\ensuremath{\alpha}\text{-cluster}$ manifestation in bound states has not been obtained yet, although a number of experimental studies were carried out to extract the information of the clustering. In particular in conventional analyses of $\ensuremath{\alpha}\text{-transfer}$ reactions, there exist a few significant problems on reaction models, which are insufficient to qualitatively discuss the cluster structure.Purpose: We aim to verify the manifestation of the $\ensuremath{\alpha}\text{-cluster}$ structure from observables. As the first application, we plan to extract the spatial information of the cluster structure of the $^{20}\mathrm{Ne}$ nucleus in its ground state through the cross section of the $\ensuremath{\alpha}\text{-transfer}$ reaction $^{16}\mathrm{O}(^{6}\mathrm{Li},\phantom{\rule{0.16em}{0ex}}d)^{20}\mathrm{Ne}$.Methods: For the analysis of the transfer reaction, we work with the coupled-channel Born approximation (CCBA) approach, in which the breakup effect of $^{6}\mathrm{Li}$ is explicitly taken into account by means of the continuum-discretized coupled-channel method based on the three-body $\ensuremath{\alpha}+d+^{16}\mathrm{O}$ model. The two methods are adopted to calculate the overlap function between $^{20}\mathrm{Ne}$ and $\ensuremath{\alpha}+^{16}\mathrm{O}$; one is the microscopic cluster model (MCM) with the generator coordinate method, and the other is the phenomenological two-body potential model (PM).Results: We show that the CCBA calculation with the MCM wave function gives a significant improvement of the theoretical result on the angular distribution of the transfer cross section, which is consistent with the experimental data. Employing the PM, it is discussed which region of the cluster wave function is probed on the transfer cross section.Conclusions: It is found that the surface region of the cluster wave function is sensitive to the cross section. The present work is situated as the first step in obtaining important information to systematically investigate the cluster structure.

Background: The sharp ${1}^{\ensuremath{-}}$ resonances with enhanced isoscalar dipole transition strengths are observed in many light nuclei at relatively small excitation energies, but their nature has been unclear.Purpose: We show those resonances can be attributed to the cluster states with asymmetric configurations such as $\ensuremath{\alpha}+^{16}\mathrm{O}$. We explain why asymmetric cluster states are strongly excited by the isoscalar dipole transition. We also provide a theoretical prediction of the isoscalar dipole transitions in $^{20}\mathrm{Ne}$ and $^{44}\mathrm{Ti}$.Method: The transition matrix is analytically derived to clarify the excitation mechanism. The nuclear model calculations by Brink--Bloch wave function and antisymmetrized molecular dynamics are also performed to provide a theoretical prediction for $^{20}\mathrm{Ne}$ and $^{44}\mathrm{Ti}$.Results: It is shown that the transition matrix is as large as the Weisskopf estimate even though the ground state is an ideal shell-model state. Furthermore, it is considerably amplified if the ground state has cluster correlation. The nuclear model calculations predict large transition matrix to the $\ensuremath{\alpha}+^{16}\mathrm{O}$ and $\ensuremath{\alpha}+^{40}\mathrm{Ca}$ cluster states comparable with or larger than the Weisskopf estimate.Conclusions: We conclude that the asymmetric cluster states are strongly excited by the isoscalar dipole transition. Combined with the isoscalar monopole transition that populates the ${0}^{+}$ cluster states, the isoscalar transitions are promising probes for asymmetric clusters.

Effects of cluster correlations on triaxiality have been studied using the antisymmetrized molecular dynamics. Low-lying states in 28 Si and 40 Ca are obtained by the the generator coordinate method (GCM), and the GCM basis are calculated by energy variations with constraints on quadrupole deformation parameter β and inter-cluster distance. The GCM obtain prolate superdeformed (SD) states in 28 Si and triaxial normal-deformed (ND) states in 40 Ca , which contain prolate α-24 Mg and triaxial α-36 Ar cluster structure components, respectively. Different shapes of prolate 24 Mg and oblate 36 Ar clusters cause difference of triaxiality of total systems. Cluster correlations which have oblate cluster enhance triaxiality in excited states.

Superdeformed (SD) states in 40 Ar have been studied using the deformed-basis antisymmetrized molecular dynamics and the generator coordinate method (GCM). GCM basis wave functions were obtained by the energy variation with a constraint on the quadrupole deformation parameter β, while other quantities such as triaxiality γ were optimized by the energy variation. An SD band is obtained just above the ground state band. The SD band involves a Kπ = 2+ side band due to the triaxiality. The calculated quadrupole electric transition strengths of the SD band reproduce well the experimental values. Triaxiality is significantly important to understand low-lying states.

Positive-parity states of 28 Si are studied with antisymmetrized molecular dynamics and multi-configuration mixing focusing on clustering and deformations. By superposition of wave functions obtained by energy variation imposing constraints on quadrupole deformation parameter β and distance between α and 24 Mg , and 12 C and 16 O clusters, two oblate bands, two prolate bands and developed α-24 Mg band are obtained. It is found that cluster structure components are contained in those bands.

We report three-center cluster structures in the excited states of 11 B (11 C ), 8 He and 14 C based on theoretical calculations with the antisymmetrized molecular dynamics (AMD). In particular we discuss the cluster gas-like states 2α + t(2α+3 He ) in 11 B (11 C ) and α + 2n + 2n in 8 He . In 14 C , the 3α linear-chain structure is discussed.

We investigated molecular states and cluster gas-like states in light nuclei based on theoretical calculations with antisymmetrized molecular dynamics. The calculated results of 13 B suggest that largely deformed states construct rotational bands, K π = 3 / 2 − and K π = 1 / 2 + , starting from 5 MeV and 8 MeV, respectively. The neutron structure of the K π = 3 / 2 − is analogous to the intruder ground state of 12 Be. In the predicted K π = 1 / 2 + band, we found largely deformed structure with a proton excited configuration. The band-head 1 / 2 + state is assigned to the 1 / 2 + (4.83 MeV), which was experimentally suggested to be the proton intruder state. Structure of 8 He were also investigated. In the results, it was found that the ground state of 8 He has both the j - j coupling feature ( p 3 / 2 closure) and the L - S coupling feature ( 4 He + 2 n + 2 n ). The results also suggest possible existence of the 0 2 + state with dineutron gas-like structure of 4 He + 2 n + 2 n , which has an analogy to the 3 α -cluster structure of the 12 C( 0 2 + ) state.

We have studied the coexistence of cluster structure and mean-field-type structure in 40 Ca using Antisymmetrized Molecular Dynamics (AMD) + Generator Coordinate Method (GCM). By energy variation with constraint, we calculated GCM basis wave functions. Superposing cluster structure wave functions and mean-field-type structure wave function, we found that α - 36 Ar and 12 C- 28 Si cluster structure are important components of normal-deformed (ND) band of 40 Ca and that of superdeformed (SD) band of 40 Ca, respectively.

We develop numerical methods to calculate electron dynamics in crystalline solids in real-time time-dependent density functional theory employing exchange-correlation potentials which reproduce band gap energies of dielectrics; a meta generalized gradient approximation (meta-GGA) proposed by Tran and Blaha [Phys. Rev. Lett. 102, 226401 (2009)] (TBm-BJ) and a hybrid functional proposed by Heyd, Scuseria, and Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE). In time evolution calculations employing the TB-mBJ potential, we have found it necessary to adopt a predictor-corrector step for stable time-evolution. Since energy functional is not known for the TB-mBJ potential, we propose a method to evaluate electronic excitation energy without referring to the energy functional. Calculations using the HSE hybrid functional is computationally expensive due to the nonlocal Fock-like term. We develop a computational method for the operation of the Fock-like term in Fourier space, for which we employ massively parallel computers equipped with graphic processing units. To demonstrate significances of utilizing potentials providing correct band gap energies, we compare electronic excitations induced by femtosecond laser pulses using the TB-mBJ, HSE, and a simple local density approximation (LDA). At low laser intensities, electronic excitations are found to be sensitive to the band gap energy: results using TB-mBJ and HSE are close to each other, while the excitation of the LDA calculation is more intensive than the others. At high laser intensities close to a damage threshold, we have found that electronic excitation energies are similar among the three cases., 22 pages, 8 figures

The new clustering aspects of sd-shell nuclei found by the recent application of the antisymmetrized molecular dynamics are reported. In this paper we present two topics, "superdeformed band of 32S and 16O + 16O clustering" and "molecular-orbital and di-nuclei states in 22Ne". In the first topic, it will be shown that the superdeformed band of 32S has a considerable amount of 16O + 16O cluster component, and can be regarded as to belong to a family of the 16O + 16O molecular bands. In the second topic, the presence of the molecularorbital band which has an α + 16O cluster core surrounded by two covalently neutrons is suggested together with an α + 18O di-nuclei band.

The structures of excited states in $^{34}$S are investigated using the antisymmetrized molecular dynamics and generator coordinate method (GCM). The GCM basis wave functions are calculated via energy variation with a constraint on the quadrupole deformation parameter $\beta$. By applying the GCM after parity and angular momentum projections, the coexistence of two positive- and one negative-parity superdeformed (SD) bands are predicted, and low-lying states and other deformed bands are obtained. The SD bands have structures of $^{16}$O + $^{16}$O + two valence neutrons in molecular orbitals around the two $^{16}$O cores in a cluster picture. The configurations of the two valence neutrons are $\delta^2$ and $\pi^2$ for the positive-parity SD bands and $\pi^1\delta^1$ for the negative-parity SD band. The structural changes of the yrast states are also discussed.

A new constraint of clustering for the AMD calculation is proposed. This new constraint gives us large improvement in studying the cluster structure by AMD which sometimes meets difficulty in giving rise to some specific cluster configurations. The usefulness of this new constraint is verified by applying it to the the study of the third $K^\pi = 0^+$ band of $^{20}$Ne which has been discussed to have $2\alpha$-$^{12}$C structure. This band has not been easy even to construct by AMD. We see that the AMD+GCM calculation by the use of the new constraint gives rise to the third $K^\pi = 0^+$ band which contains the $2\alpha$-$^{12}$C structure as an important component., Comment: 13 pages, 4 figures

Although several analyses of the α-transfer reaction16O(6Li, d)20Ne using the distorted wave Born approximation have been performed with the aim to clarify the α-cluster structure of20Ne, they have resulted in poor information on the clustering due to insufficiency of models for the analyses. In this work we propose a precise model employing the coupled-channels Born approximation with the microscopically calculated cluster wave function to elucidate the surface manifestation of the α-particle in the ground state of20Ne. Our calculation has shown improvement of the theoretical calculation compared with that in the previous analyses. We have confirmed numerically that the angular distributed cross section at the forward angles probes only the surface region of the α-cluster wave function. The breakup effect of6Li has been investigated and concluded that only the back coupling is important for the (6Li, d) reaction.

The isoscalar monopole and dipole transitions and their relationship to the clustering are discussed. By exploiting the Bayman-Bohr theorem, analytical formulae for the transition matrices are derived to show that the cluster states are very strongly populated by the IS monopole and dipole transitions. For the quantitative discussion, the AMD calculations for20Ne,44Ti and24Mg are presented. It is demonstrated that IS monopole and dipole transitions are excellent probe for the clustering.

The asymmetric cluster states in 28Si are discussed on the basis of antisymmetrized molecular dynamics. It is found that the inversion doublet bands having the 24Mg+α, 20Ne+8Be and 16O+12C cluster configurations appear in the energy range of Ex = 10 ~ 15 MeV. It is demonstrated that the 24Mg+α, 20Ne+8Be cluster states have pronounced isoscalar monopole (IS0) and dipole (IS1) transition strengths from the ground state. This result suggests that the IS0 and IS1 strength are good probe for these cluster states.

We propose a simple method to approximately evaluate reduced width amplitude (RWA) of a two-body spinless cluster channel using the norm overlap with the Brink-Bloch cluster wave function at the channel radius. The applicability of the present approximation is tested for the $^{16}$O+$\alpha$ channel in $^{20}$Ne as well as the $\alpha$+$\alpha$ channel in $^8$Be. The approximation is found to be reasonable to evaluate the RWA for states near the threshold energy and it is useful to estimate the $\alpha$-decay width of resonance states. The approximation is also applied to $^9$Li, and the partial decay width of the $^6$He($0^+_1$)+$t$ channel is discussed., Comment: 20 pages, 10 figures

Angular momentum projection is used to obtain eigen states of angular momentum from general wave functions. Multi-configuration mixing calculation with angular momentum projection is an important microscopic method in nuclear physics. For accurate multi-configuration mixing calculation with angular momentum projection, concentrated distribution of $z$ components $K$ of angular momentum in the body-fixed frame ($K$-distribution) is favored. Orientation of wave functions strongly affects $K$-distribution. Minimization of variance of $\hat{J}_z$ is proposed as an alignment method to obtain wave functions that have concentrated $K$-distribution. Benchmark calculations are performed for $\alpha$-$^{24}$Mg cluster structure, triaxially superdeformed states in $^{40}$Ar, and Hartree-Fock states of some nuclei. The proposed alignment method is useful and works well for various wave functions to obtain concentrated $K$-distribution.

We report the low-lying spectrum and collective $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ deformation of ${}^{43}$S as investigated by antisymmetrized molecular dynamics. Our result successfully explains the observed data including an isomeric $7/{2}_{1}^{\ensuremath{-}}$ state and illustrates the coexistence of the prolate-deformed ground band with a vanishing $N=28$ shell gap, a triaxially deformed isomeric state, and an oblate-deformed excited band at very low excitation energies.

The structures of excited states in $^{34}$S are investigated using the antisymmetrized molecular dynamics and generator coordinate method (GCM). The GCM basis wave functions are calculated via energy variation with a constraint on the quadrupole deformation parameter $\beta$. By applying the GCM after parity and angular momentum projections, the coexistence of two positive- and one negative-parity superdeformed (SD) bands are predicted, and low-lying states and other deformed bands are obtained. The SD bands have structures of $^{16}$O + $^{16}$O + two valence neutrons in molecular orbitals around the two $^{16}$O cores in a cluster picture. The configurations of the two valence neutrons are $\delta^2$ and $\pi^2$ for the positive-parity SD bands and $\pi^1\delta^1$ for the negative-parity SD band. The structural changes of the yrast states are also discussed., Comment: 8 pages, 7 figures

We propose a method to obtain adiabatic internuclear potentials via energy variation with the intercluster-distance constraint. The adiabatic $^{16}$O + $^{16,18}$O potentials obtained by the proposed method are applied to investigate the effects of valence neutrons in $^{16}$O + $^{18}$O sub-barrier fusions. Sub-barrier fusion cross sections of $^{16}$O + $^{18}$O are enhanced more compared to those of $^{16}$O + $^{16}$O because of distortion of valence neutrons in $^{18}$O., 11 pages, 5 figures

Superdeformed (SD) states in $^{40}\mathrm{Ar}$ have been studied using the deformed-basis antisymmetrized molecular dynamics. Low-energy states were calculated by the parity and angular momentum projection and the generator coordinate method (GCM). Basis wave functions were obtained by the energy variation with a constraint on the quadrupole deformation parameter $\ensuremath{\beta}$, while other quantities such as triaxiality $\ensuremath{\gamma}$ were optimized by the energy variation. By the GCM calculation, an SD band was obtained just above the ground-state band. The SD band involves a ${K}^{\ensuremath{\pi}}={2}^{+}$ side band due to the triaxiality. The calculated electric quadrupole transition strengths of the SD band reproduce the experimental values appropriately. Triaxiality is significant for understanding low-lying states.

We have studied positive-parity states of 28 Si using antisymmetrized molecular dynamics and multiconfiguration mixing with constrained variation. Applying constraints to the cluster distance and the quadrupole deformation of the variational calculation, we have obtained basis wave functions that have various structures such as α- 24 Mg and 12 C- 16 O cluster structures as well as deformed structures. Superposing those basis wave functions, we have obtained a oblate ground state band, a β vibration band, a normal-deformed prolate band, and a superdeformed band. It is found that the superdeformed bands contain large amounts of the α- 24 Mg cluster components. The results also suggest the presence of two excited bands with the developed α- 24 Mg cluster structure, where the inter-cluster motion and the 24 Mg-cluster deformation play important roles.

We have studied positive-parity states of $^{28}$Si using antisymmetrized molecular dynamics (AMD) and multi-configuration mixing (MCM) with constrained variation. Applying constraints to the cluster distance and the quadrupole deformation of the variational calculation, we have obtained basis wave functions that have various structures such as $\alpha$-$^{24}$Mg and $^{12}$C-$^{16}$O cluster structures as well as deformed structures. Superposing those basis wave functions, we have obtained a oblate ground state band, a $\beta$ vibration band, a normal-deformed prolate band, and a superdeformed band. It is found that the normal-deformed and superdeformed bands contain large amounts of the $^{12}$C-$^{16}$O and $\alpha$-$^{24}$Mg cluster components, respectively. The results also suggest the presence of two excited bands with the developed $\alpha$-$^{24}$Mg cluster structure, where the inter-cluster motion and the $^{24}$Mg-cluster deformation play important roles., Comment: 24 pages, 10 figures

Structures of $p$- and $sd$-shell nuclei are studied with the deformed-basis antisymmetrized molecular dynamics method using the Gogny D1S and Skyrme SLy7 forces as effective interactions. By the energy variation with a constraint, energy curves as functions of quadrupole deformation parameter $\beta$ are obtained. The energy curves for $sd$-shell nuclei show structure change as a function of $\beta$, and suggest shape coexistence. Nuclear structures in the deformed region are discussed focusing on deformations and clustering. It is found that the deformations often involve cluster structures. Effective-interaction dependence is also discussed comparing the results obtained with the two effective interactions. Although the two forces give similar results when cluster structures do not develop clearly, they give different energies in the largely deformed region when an $\alpha$ cluster develops., Comment: 21 pages, 22 figures

We have studied the positive-parity states of $^{40}\mathrm{Ca}$ using antisymmetrized molecular dynamics (AMD) and the generator coordinate method (GCM). Imposing two different kinds of constraints on the variational calculation, we have found various kinds of $^{40}\mathrm{Ca}$ structures such as a deformed-shell structure, as well as $\ensuremath{\alpha}\text{\ensuremath{-}}$$^{36}\mathrm{Ar}$ and $^{12}\mathrm{C}$-$^{28}\mathrm{Si}$ cluster structures. After the GCM calculation, we obtained a normal-deformed band and a superdeformed band together with their side bands associated with triaxial deformation. The calculated $B(E2)$ values agreed well with empirical data. It was also found that the normal-deformed and superdeformed bands have non-negligible $\ensuremath{\alpha}\text{\ensuremath{-}}$$^{36}\mathrm{Ar}$ cluster and $^{12}\mathrm{C}$-$^{28}\mathrm{Si}$ cluster components, respectively. This leads to the presence of an $\ensuremath{\alpha}\text{\ensuremath{-}}$$^{36}\mathrm{Ar}$ higher nodal band occurring above the normal-deformed band.

We have studied the positive‐parity states of 40Ca using antisymmetrized molecular dynamics (AMD) and the generator coordinate method (GCM). Imposing two different kinds of constraints on the variational calculation, we have found various kinds of 40Ca structures such as a deformed‐shell structure, as well as α‐36Ar and 12C‐28Si cluster structures. After the GCM calculation, we obtained a normal‐deformed band and a superdeformed band together with their side bands associated with triaxial deformation. The calculated B(E2) values agreed well with empirical data. It was also found that the normal‐deformed and superdeformed bands contain α‐36Ar and 12C‐28Si cluster structure components, respectively. This leads to the presence of an α‐36Ar higher‐nodal band occurring above the normal‐deformed band.

We have studied the coexistence of cluster structure and mean‐field‐type structure in 20Ne and 40Ca using Antisymmetrized Molecular Dynamics (AMD) + Generator Coordinate Method (GCM). By energy variation with new constraint for clustering, we calculate cluster structure wave function. Superposing cluster structure wave functions and mean‐field‐type structure wave function, we found that 8Be‐12C, α‐36Ar and 12C‐28Si cluster structure are important components of Kπ = 03+ band of 20Ne, that of normal deformed band of 40Ca and that of super deformed band of 40Ca, respectively.