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Register a new userTensor correlations in $^4$He and $^8$Be with antisymmetrized quasi cluster model
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In this paper, we extend the framework of improved version of simplified method to take into account the tensor contribution ($i$SMT) and propose AQCM-T, tensor version of antisymmetrized quasi cluster model (AQCM). Although AQCM-T is phenomenological, we can treat the $^3S$-$^3D$ coupling in the deuteron-like $T=0$ $NN$-pair induced by the tensor interaction in a very simplified way, which allows us to proceed to heavier nuclei. Also we propose a new effective interaction, V2m, where the triplet-even channel of the Volkov No.2 interaction is weakened to 60% so as to reproduce the binding energy of $^4$He after including the tensor term of a realistic interaction. Using AQCM-T and the new interaction, the significant tensor contribution in $^4$He is shown, which is almost comparable the central interaction, where $D$-state mixes by 8% to the major $S$-state. The AQCM-T model with the new interaction is also applied to $^8$Be. It is found that the tensor suppression gives significant contribution to the short-range repulsion between two {alpha} clusters.
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We apply tensor version of antisymmetrized quasi cluster model (AQCM-T) to 4He and 8Be while focusing on the NN correlations in alpha clusters. We adopt the NN interactions including realistic ones containing a repulsive core for the central part in addition to the tensor part. In 4He, the pn pair in the 3D channel has been known to play a decisive role in the tensor correlation and the framework is capable of treating not only this channel but also the NN correlations in the 1S and 3S channels. In 8Be, when two alpha clusters approach, the 3D pair is suppressed because of the Pauli blocking effect, which induces the decrease of the 3S component through the 3S-3D coupling. This effect results in the reduction of the attractive effect of the central-even interaction in the middle-range region.
We study $^5$He variationally as the first $p$-shell nucleus in the tensor-optimized antisymmetrized molecular dynamics (TOAMD) using the bare nucleon--nucleon interaction without any renormalization. In TOAMD, the central and tensor correlation operators promote the AMDs Gaussian wave function to a sophisticated many-body state including the short-range and tensor correlations with high-momentum nucleon pairs. We develop a successive approach by applying these operators successively with up to double correlation operators to get converging results. We obtain satisfactory results for $^5$He, not only for the ground state but also for the excited state, and discuss explicitly the correlated Hamiltonian components in each state. We also show the importance of the independent optimization of the correlation functions in the variation of the total energy beyond the condition assuming common correlation forms used in the Jastrow approach.
We treat the tensor correlation in antisymmetrized molecular dynamics (AMD) including large-relative-momentum components among nucleon pairs for finite nuclei. The tensor correlation is described by using large imaginary centroid vectors of Gaussian wave packets for nucleon pairs with opposite directions, which makes a large relative momentum. We superpose the AMD basis states, in which one nucleon pair has various relative momenta for all directions; this new method is called high-momentum AMD (HM-AMD). We show the results for $^4$He using the effective interaction having a strong tensor force. It is found that HM-AMD provides a large tensor matrix element comparable to the case of the tensor-optimized shell model (TOSM), in which the two-particle-two-hole (2p-2h) excitations are fully included to describe the tensor correlation. The results of two methods agree with each other at the level of the Hamiltonian components of $^4$He. This indicates that in HM-AMD the high-momentum components described by the imaginary centroid vectors of the nucleon pair provide the equivalent effect of the 2p-2h excitations for the tensor correlation.
The possibility of the $^8$He and $^{9}$Li clusters in atomic nuclei is discussed. Until now most of the clusters in the conventional models have been limited to the closures of the three-dimensional harmonic oscillators, such as $^4$He, $^{16}$O, and $^{40}$Ca. In the neutron-rich nuclei, however, the neutron to proton ratio is not unity, and it is worthwhile to think about more neutron-rich objects with $N>Z$ as the building blocks of cluster structures. Here the nuclei with the neutron number six, which is the subclosure of the $p_{3/2}$ subshell of the $jj$-coupling shell model, are assumed to be clusters, and thus we study the $^8$He and $^9$Li cluster structures in $^{16}$Be ($^8$He+$^8$He), $^{17}$B ($^8$He+$^9$Li), $^{18}$C ($^9$Li+$^9$Li), and $^{24}$C ($^8$He+$^8$He+$^8$He). Recent progress of the antisymmetrized quasi cluster model (AQCM) enables us to utilize $jj$-coupling shell model wave functions as the clusters rather easily. It is shown that the $^8$He+$^9$Li and $^9$Li+$^9$Li cluster configurations cover the lowest shell-model states of $^{17}$B and $^{18}$C, respectively. To predict the cluster states with large relative distances, we increase the expectation value of the principal quantum numbers by adding the nodes to the lowest states under the condition that the total angular momentum is unchanged (equal to $J^pi =0$). As a result, developed cluster states are obtained around the corresponding threshold energies. The rotational band structure of $^{24}$C, which reflect the symmetry of equilateral triangular configuration ($D_{3h}$ symmetry) of three $^8$He clusters, also appears around the threshold energy.
We propose a new approach to probe the spatial extension of the valence neutron orbital in the $^{9}$Be nucleus via the ${}^{9}$Be($p,pn$)${}^{8}$Be knockout reaction. This property of the nuclear molecular orbital has not been established in previous experimental studies and divergence exists between the theoretical descriptions of ${}^{9}$Be from different perspectives, textit{i.e.}, the antisymmetrized molecular dynamics and the container pictures of cluster dynamics. These pictures are represented by two different well-proven microscopic models, the antisymmetrized molecular dynamics (AMD) and Tohsaki-Horiuchi-Schuck-R{o}pke (THSR) wave functions. The corresponding reduced width amplitudes (RWAs) in the $^{8}$Be$+n$ channel are extracted from both the AMD and THSR wave functions, and they are found to describe drastically different valence-nucleon motion, which shows the theoretical ambiguity in describing the $pi$-orbitals in $^{9}$Be. Using the RWAs as input, the physical observables of the ${}^{9}$Be($p,pn$)${}^{8}$Be knockout reaction are predicted by the distorted-wave impulse approximation (DWIA) framework. The magnitudes of the triple-differential cross sections (TDX) are found to be highly sensitive to the RWA input. It is concluded that the ${}^{9}$Be($p,pn$)${}^{8}$Be knockout reaction could provide a feasible probing for the subtle differences between several structure models manifesting through the spatial extension of the $pi$-orbital in the $^{9}$Be nucleus.
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