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Register a new userA Nuclear Structure Model for Double Charge-Exchange Processes
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A new model, based on the BCS approach, is specially designed to describe nuclear phenomena $(A,Z)rightarrow (A,Zpm 2)$ of double-charge exchange (DCE). After being proposed, and applied in the particle-hole limit, by one of the authors (F. Krmpotic [1]), so far it was never been applied within the BCS mean-field framework, nor has its ability to describe DCE processes been thoroughly explored. It is a natural extension of the pn-QRPA model, developed by Halbleib and Sorensen [2] to describe the single $beta$-decays $(A,Z)rightarrow (A,Zpm 1)$, to the DCE processes. As such, it exhibits several advantages over the pn-QRPA model when is used in the evaluation of the double beta decay (DBD) rates. For instance, i) the extreme sensitivity of the nuclear matrix elements (NMEs) on the model parametrization does not occur, ii) it allows to study NMEs, not only for the fundamental state in daughter nuclei, as the pn-QRPA model does, but also for all final $0^+$ and $2^+$ states, accounting at the same time their excitation energies and the corresponding DBD Q-values, iii) together with the DBD-NMEs it provides also the energy spectra of Fermi and Gamow-Teller DCE transition strengths, as well as the locations of the corresponding resonances and their sum rules, iv) the latter are relevant for both the DBD and the DCE reactions, since the involved nuclear structure is the same; this correlation does not exist within the pn-QRPA model. As an example, detailed numerical calculations are presented for the $(A,Z)rightarrow (A,Z+ 2)$ process in $^{48}$Ca $rightarrow ^{48}$Ti and the $(A,Z)rightarrow (A,Z- 2)$ process in $^{96}$Ru $rightarrow ^{96}$Mo, involving all final $0^+$ states and $2^+$ states.
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The theoretical approach to a sequential heavy ion double charge exchange reaction is presented. A brief introduction into the formal theory of second-order nuclear reactions and their application to Double Single Charge Exchange (DSCE) reactions by distorted wave theory is given, thereby completing the theoretical background to our recent work [1]. Formally, the DSCE reaction amplitudes are shown to be separable into superpositions of distortion factors, accounting for initial and final state ion--ion interactions, and nuclear matrix elements. A broad space is given to the construction of nuclear DSCE response functions on the basis of polarization propagator theory. The nuclear response tensors resemble the nuclear matrix elements of $2 ubetabeta$ decay in structure but contain in general a considerable more complex multipole and spin structure. The QRPA theory is used to derive explicit expressions for nuclear matrix elements (NMEs). The differences between the NME of the first and the second interaction vertexes in a DSCE reaction is elucidated. Reduction schemes for the transition form factors are discussed by investigating the closure approximation and the momentum structure of form factors. DSCE unit strength cross sections are derived.
Spin-isospin transitions in nuclei away from the valley of stability are essential for the description of astrophysically relevant weak interaction processes. While they remain mainly beyond the reach of experiment, theoretical modeling provides important insight into their properties. In order to describe the spin-isospin response,vcthe proton-neutron relativistic quasiparticle random phase approximation (PN-RQRPA) is formulated using the relativistic density-dependent point coupling interaction, and separable pairing interaction in both the $T=1$ and $T=0$ pairing channels. By implementing recently established DD-PCX interaction with improved isovector properties relevant for the description of nuclei with neutron-to-proton number asymmetry, the isobaric analog resonances (IAR) and Gamow-Teller resonances (GTR) have been investigated. In contrast to other models that usually underestimate the IAR excitation energies in Sn isotope chain, the present model accurately reproduces the experimental data, while the GTR properties depend on the isoscalar pairing interaction strength. This framework provides not only an improved description of the spin-isospin response in nuclei, but it also allows future large scale calculations of charge-exchange excitations and weak interaction processes in stellar environment.
The role of the meson-exchange current correction to the nuclear charge operator is studied in electron scattering processes involving the excitation of medium and heavy nuclei to energies up to the quasi-elastic peak. The effect of these contributions in the quasi-free electron scattering process is a reduction of at most a 3% in the longitudinal response at the energy of the peak, a value which is below the experimental error and must not be taken into account in calculations in this energy region. On the other hand, the excitation of low-lying nuclear levels of neutronic character shows, with respect to the protonic ones, a considerable effect due to the inclusion of the two-body term in the charge operator. More realistic calculations, such as those performed in the random-phase approximation framework, give rise to a mixing of one particle-one hole configurations of both kinds which reduce these effects. However, it has been found that the excitation of some of these levels is sizeably affected by the meson-exchange contribution. More precise experimental data concerning some of these states, such as e.g. the high-spin states in 208Pb, could throw some light in the problem of a more feasible determination of these effects and, as a consequence, could provide an alternative procedure to obtain the charge neutron form factor.
To describe the double-charge-exchange (DCE) processes, we have designed recently the $(pn,2p2n)$-QTDA model which fully includes the pairing correlations and four quasiparticle excitations. It has been applied in $2 u$ double beta decays (DBDs), and the double charge-exchange resonances (DCERs). Here we extend it to $ 0 u $ DBD and discuss the relationship between the nuclear matrix elements (NMEs), and the DCE reaction matrix elements (RMEs) with the same spin-isospin structure. We do it for all final $0^+$ states, even in the region of DCERs, where the DBD is energetically forbidden. As an example, we evaluate the DBD $^{76}$Ge $rightarrow ^{76}$Se, both for $2 u$ and $0 u$ modes, as well as the associated DCE sum rules, excitation energies within the $Q$-value window for DBD, and the $Q$-value itself. We find that the $0 u$ NMEs are correlated with the RMEs, both at low energy, and in the DCER region where most of the transition strength is concentrated. These findings occur in other nuclei as well and suggest that measurements of $0^+$ DCERs could provide useful information regarding the $ 0 u $ DBD. An analogous comparison and conclusion cannot be made for the $2^+$ states, since the $0 u$ NMEs and RMEs transition operators are not similar to each other in this case.
Using an extended parity doublet model with the hidden local symmetry, we study the properties of nuclei in the mean field approximation to see if the parity doublet model could reproduce nuclear properties and also to estimate the value of the chiral invariant nucleon mass $m_0$ preferred by nuclear structure. We first determined our model parameters using the inputs from free space and from nuclear matter properties. Then, we study some basic nuclear properties such as the nuclear binding energy with several different choices of the chiral invariant mass. We observe that our results, especially the nuclear binding energy, approach the experimental values as $m_0$ is increased until $m_0=700$ MeV and start to deviate more from the experiments afterwards with $m_0$ larger than $m_0=700$ MeV, which may imply that $m_0=700$ MeV is preferred by some nuclear properties.
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