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Register a new userStructure of $^{14}$C and $^{14}$O nuclei within a five-cluster model
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Within a five-particle model (three $alpha$-particles plus two nucleons), the structure functions of mirror nuclei $^{14}$C and $^{14}$O are studied. Using the variational approach with Gaussian bases, the energies and wave functions are calculated for these five-particle systems. Two spatial configurations in the ground-state wave function are revealed. The r.m.s. charge radius of $^{14}$O nucleus is found to be $2.415pm0.005$ fm. The charge density distributions and the form factors of both nuclei are predicted. The pair correlation functions are analyzed, and the r.m.s. relative distances are calculated. The momentum distributions of particles are found.
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The spatial structure of $^{14}$N nucleus is studied within a five-particle model (three $alpha$-particles plus two nucleons). Using the variational approach with Gaussian bases, the ground-state energy and wave function are calculated for this five-particle system. Two spatial configurations in the ground-state wave function are revealed. The density distributions, pair correlation functions, and the momentum distributions of particles are analyzed and compared with those of the mirror nuclei $^{14}$C and $^{14}$O.
The structure of mirror $^{14}$C and $^{14}$O nuclei has been studied in the framework of the five-particle model (three $alpha$-particles and two nucleons). Interaction potentials are proposed, which allowed the energy and radius of $^{14}$C nucleus, as well as the energy of $^{14}$O one, to agree with experimental data. On the basis of the variational approach with the use of Gaussian bases, the energies and wave functions for five-particle systems under consideration are calculated. The charge radius of $^{14}$O nucleus, as well as the charge density distributions and the form factors for both nuclei, are predicted.
The possibility of the $^{14}$C cluster being a basic building block of medium mass nuclei is discussed. Although $alpha$ cluster structures have been widely discussed in the light $Napprox Z$ mass region, the neutron to proton ratio deviates from unity in the nuclei near $beta$-stability line and in neutron-rich nuclei. Thus, more neutron-rich objects with $N>Z$ could become the building blocks of cluster structures in such nuclei. The $^{14}$C nucleus is strongly bound and can be regarded as such a candidate. In addition, the path to the lowest shell-model configuration at short relative distances is closed for the $^{14}$C+$^{14}$C structure contrary to the case of the $^{12}$C+$^{12}$C structure; this allows to keep appreciable separation distance between the $^{14}$C clusters. The recent development of antisymmetrized quasi-cluster model (AQCM) allows us to utilize $jj$-coupling shell model wave function for each cluster in a simplified way. The AQCM results for the $^{14}$C+$^{14}$C structure in $^{28}$Mg are compared with the ones of cranked relativistic mean field (CRMF) calculations. Although theoretical frameworks of these two models are quite different, they give similar results for the nucleonic densities and rotational properties of the structure under investigation. The existence of linear chain three $^{14}$C cluster structure in $^{42}$Ar has also been predicted in AQCM. These results confirm the role of the $^{14}$C cluster as a possible building block of cluster structures in medium mass nuclei.
A cluster-transfer experiment of $^9rm{Be}(^9rm{Be},^{14}rm{C}rightarrowalpha+^{10}rm{Be})alpha$ 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.
An experiment for $p(^{14}rm{C}$,$^{14}rm{C}^{*}rightarrow^{10}rm{Be}+alpha)mathit{p}$ inelastic excitation and decay was performed in inverse kinematics at a beam energy of 25.3 MeV/u. A series of $^{14}rm{C}$ excited states, including a new one at 18.3(1) MeV, were observed which decay to various states of the final nucleus of $^{10}rm{Be}$. A specially designed telescope-system, installed around the zero degree, played an essential role in detecting the resonant states near the $alpha$-separation threshold. A state at 14.1(1) MeV is clearly identified, being consistent with the predicted band-head of the molecular rotational band characterized by the $pi$-bond linear-chain-configuration. Further clarification of the properties of this exotic state is suggested by using appropriate reaction tools.
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