Study of ground state properties of carbon isotopes with deformed relativistic Hartree-Bogoliubov theory in continuum

We present a review of recent works on clustering phenomena in unstable nuclei studied by antisymmetrized molecular dynamics (AMD). The AMD studies in these decades have uncovered novel types of clustering phenomena brought about by the excess neutrons. Among them, this review focuses on the molecule-like structure of unstable nuclei. One of the earliest discussions on the clustering in unstable nuclei was made for neutron-rich Be and B isotopes. AMD calculations predicted that the ground state clustering is enhanced or reduced depending on the number of excess neutrons. Today, the experiments are confirming this prediction as the change of the proton radii. Behind this enhancement and reduction of the clustering, there are underlying shell effects called molecular- and atomic-orbits. These orbits form covalent and ionic bonding of the clusters analogous to the atomic molecules. It was found that this "molecular-orbit picture" reasonably explains the low-lying spectra of Be isotopes. The molecular-orbit picture is extended to other systems having parity asymmetric cluster cores and to the three cluster systems. O and Ne isotopes are the candidates of the former, while the $3\alpha$ linear chains in C isotopes are the latter. For both subjects, many intensive studies are now in progress. We also pay a special attention to the observables which are the fingerprint of the clustering. In particular, we focus on the monopole and dipole transitions which are recently regarded as good probe for the clustering. We discuss how they have and will reveal the exotic clustering.

Antisymmetrized molecular dynamics studies for exotic clustering phenomena in neutron-rich nuclei

A theoretical method is proposed to describe the ground and excited cluster states of atomic nuclei The method makes use of the equation of motion of the Gaussian wave packets to generate the basis wave functions incorporating various cluster configurations The generated basis wave functions are superposed to diagonalize the Hamiltonian This method is regarded as the generator coordinate method which uses the real time as the generator coordinate As a application of our proposed method, we present the benchmark calculation for the $3\ensuremath{\alpha}$ system We show that our proposed method works efficiently and yields the results consistent with or better than the other cluster models We have also discussed briefly the structure of the excited ${0}^{+}$ and ${1}^{\ensuremath{-}}$ states

/pdf/real-time-evolution-method-and-its-application-to-the-3-a-3087apvjqa.pdf

Real-time evolution method and its application to the 3 α cluster system

Cluster structures of $^{14}$C were investigated with a method of antisymmetrized molecular dynamics (AMD) combined with a $3\alpha+nn$ cluster model while focusing on the monopole excitations and linear-chain $3\alpha$ band. Variation after parity and angular momentum projections was performed in the AMD framework, and the generator coordinate method was applied to take into account various $3\alpha+nn$ cluster configurations. Energy spectra and monopole and $E2$ transition strengths of $0^+$, $2^+$, and $4^+$ states 
were calculated to assign band structures. The $0^+_3$ state with remarkable monopole transition was obtained as a vibrational mode of the triangle $3\alpha$ configuration. In addition, the linear-chain $3\alpha$ band from the band-head $0^+_4$ state was obtained. $^{10}$Be$+\alpha$ decay widths of $0^+$, $2^+$, and $4^+$ states were evaluated. $\alpha$ inelastic scattering off $^{14}$C was also investigated by the microscopic coupled-channel calculation with the $g$-matrix folding model to propose possible observation of the $0^+_3$ state via $\alpha$ scattering experiments.

Cluster structures and monopole transitions of 14 C

The linear-chain states of $^{16}\mathrm{C}$ and their decay modes are theoretically investigated by using the antisymmetrized molecular dynamics. It is found that the positive-parity linear-chain states have the ${(3/{2}_{\ensuremath{\pi}}^{\ensuremath{-}})}^{2}{(1/{2}_{\ensuremath{\sigma}}^{\ensuremath{-}})}^{2}$ configuration and primary decay to $^{12}\mathrm{Be}({2}_{1}^{+})$ as well as to $^{12}\mathrm{Be}$(g.s.) by $\ensuremath{\alpha}$-particle emission. Moreover, we show that they also decay via the $^{6}\mathrm{He}+^{10}\mathrm{Be}$ channel. In the negative-parity states, it is found that two types of linear chains exist. One has the valence neutrons occupying the molecular orbits ${(3/{2}_{\ensuremath{\pi}}^{\ensuremath{-}})}^{2}(1/{2}_{\ensuremath{\sigma}}^{\ensuremath{-}})(3/{2}_{\ensuremath{\pi}}^{+})$, while the other's configuration cannot be explained in terms of the molecular orbits because of the strong parity mixing. Both configurations constitute the rotational bands with a large moment of inertia and intraband $E2$ transitions. Their $\ensuremath{\alpha}$ and $^{6}\mathrm{He}$ reduced widths are sufficiently large to be distinguished from other noncluster states although they are smaller than those of the positive-parity linear chain.

/pdf/characteristic-a-and-he-6-decays-of-linear-chain-structures-21a9hkdnet.pdf

Characteristic α and He 6 decays of linear-chain structures in C 16

A cluster-transfer experiment of $^9\rm{Be}(^9\rm{Be},^{14}\rm{C}\rightarrow\alpha+^{10}\rm{Be})\alpha$ at an incident energy of 45 MeV was carried out in order to investigate the molecular structure in high-lying resonant states in $^{14}$C. This reaction is of extremely large $Q$-value, making it an excellent case to select the reaction mechanism and the final states in outgoing nuclei. The high-lying resonances in $^{14}$C are reconstructed for three sets of well discriminated final states in $^{10}$Be. The results confirm the previous decay measurements with clearly improved decay-channel selections and show also a new state at 23.5(1) MeV. The resonant states at 22.4(3) and 24.0(3) MeV decay primarily into the typical molecular states at about 6 MeV in $^{10}$Be, indicating a well developed cluster structure in these high-lying states in $^{14}$C. Further measurements of more states of this kind are suggested.

Cluster Decay of the High-lying excited states in $^{14}$C

A cluster-transfer experiment of 9Be(9Be,14C → α+10Be)α at an incident energy of 45 MeV was carried out in order to investigate the molecular structure in high-lying resonant states in 14C. This reaction is of extremely large Q-value, making it an excellent case to select the reaction mechanism and the final states in outgoing nuclei. The high-lying resonances in 14C are reconstructed for three sets of well discriminated final states in 10Be. The results confirm the previous decay measurements with clearly improved decay-channel selections and also show a new state at 23.5(1) MeV. The resonant states at 22.4(3) and 24.0(3) MeV decay primarily into the typical molecular states at about 6 MeV in 10Be, indicating a well developed cluster structure in these high-lying states in 14C. Further measurements of more states of this kind are suggested.

https://iopscience.iop.org/article/10.1088/1674-1137/40/11/111001/pdf

Cluster decay of the high-lying excited states in 14 C

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Cluster Decay of the High-lying excited states in $^{14}$C

Cluster decay of the high-lying excited states in 14 C