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Register a new userStructure of $^{14}$C and $^{14}$O nuclei calculated in the variational approach
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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.
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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.
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.
The results of investigations of the dissociation of a $^{14}$N nucleus of momentum 2.86~A~GeV/c in photo-emulsion are presented. The main characteristics of these reactions, that is the cross sections for various fragmentation channels, are given. The fragmentation was analyzed by means of an invariant approach. The momentum and correlation characteristics of $alpha$ particles for the $^{14}$N$to3alpha$+X channel in the laboratory system and the rest systems of 3$alpha$ particles were considered. The results obtained for the $^{14}$N nucleus are compared with similar data for the $^{12}$C and $^{16}$O nuclei.
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.
[Background] Proton-induced knockout reactions of the form $(p,pN)$ have experienced a renewed interest in recent years due to the possibility of performing these measurements with rare isotopes, using inverse kinematics. Several theoretical models are being used for the interpretation of these new data, such as the distorted-wave impulse approximation (DWIA), the transition amplitude formulation of the Faddeev equations due to Alt, Grassberger and Sandhas (FAGS) and, more recently, a coupled-channels method here referred to as transfer-to-the-continuum (TC). [Purpose] Our goal is to compare the momentum distributions calculated with the DWIA and TC models for the same reactions, using whenever possible the same inputs (e.g. distorting potential). A comparison with already published results for the FAGS formalism is performed as well. [Method] We choose the $^{15}$C($p$,$pn$)$^{14}$C reaction at an incident energy of 420 MeV/u, which has been previously studied with the FAGS formalism. The knocked-out neutron is assumed to be in a $2s$ single-particle orbital. Longitudinal and transverse momentum distributions are calculated for different assumed separation energies. [Results] For all cases considered, we find a very good agreement between DWIA and TC results. The energy dependence of the distorting optical potentials is found to affect in a modest way the shape and magnitude of the momentum distributions. Moreover, when relativistic kinematics corrections are omitted, our calculations reproduce remarkably well the FAGS result. [Conclusions] The results found in this work provide confidence on the consistency and accuracy of the DWIA and TC models for analyzing momentum distributions for $(p,pn)$ reactions at intermediate energies.
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