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Register a new userThe possibility of $^{14}$C cluster as a building block of medium mass nuclei
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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.
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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.
In this contribution, we present the cluster shell model which is analogous to the Nilsson model, but for cluster potentials. Special attention is paid to the consequences of the discrete symmetries of three alpha-particles in an equilateral triangle configuration. This configuration is characterized by a special structure of the rotational bands which can be used as a fingerprint of the underlying geometric configuration. The cluster shell model is applied to the nucleus 13C.
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.
We review recent studies of the cluster structure of light nuclei within the framework of the algebraic cluster model (ACM) for nuclei composed of k alpha-particles and within the framework of the cluster shell model (CSM) for nuclei composed of k alpha-particles plus x additional nucleons. The calculations, based on symmetry considerations and thus for the most part given in analytic form, are compared with experiments in light cluster nuclei. The comparison shows evidence for Z_2, D_{3h} and T_d symmetry in the even-even nuclei 8Be (k=2), 12C (k=3) and 16O (k=4), respectively, and for the associated double groups Z_2 and D_{3h} in the odd nuclei 9Be, 9B (k=2, x=1) and 13C (k=3, x=1), respectively.
In the past decade, coupled-cluster theory has seen a renaissance in nuclear physics, with computations of neutron-rich and medium-mass nuclei. The method is efficient for nuclei with product-state references, and it describes many aspects of weakly bound and unbound nuclei. This report reviews the technical and conceptual developments of this method in nuclear physics, and the results of coupled-cluster calculations for nucleonic matter, and for exotic isotopes of helium, oxygen, calcium, and some of their neighbors.
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