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تسجيل مستخدم جديدThe subtle connection between shape coexistence and quantum phase transition. The Zr case
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Background: Zr region is characterized by very rapid changes in the ground state structure of the nuclei. In particular, the onset of deformation when passing from $^{98}$Zr to $^{100}$Zr is one of the fastest ever observed in the nuclear chart. It has been probed both experimental and theoretically that certain low-lying excited states of Zr isotopes own different shapes than the ground state. Purpose: We intend to disentangle the interplay between the sudden changes in the ground state shape, i.e., the existence of a quantum phase transition, and the presence in the spectra of coexisting states with very different deformation, i.e., the presence of shape coexistence. Method: We rely on a previous calculation using the Interacting Boson Model with Configuration Mixing (IBM-CM) which reproduces in detail the spectroscopic properties of $^{96-110}$Zr. This IBM-CM calculation allows to compute mean-field energy surfaces, wave functions and any other observable related with the presence of shape coexistence or with a quantum phase transition. Results: We obtain energy surfaces and the equilibrium value of the deformation parameter $beta$, the U(5) decomposition of the wave functions and the density of states. Conclusions: We confirm that Zr is a clear example of quantum phase transition that originates from the crossing of two configurations with a very different degree of deformation. Moreover, we observe how the intruder configuration exhibits its own evolution which resembles a quantum phase transition too.
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The goal of this contribution is to analyze the connection between shape coexistence and quantum phase transition, two seemingly unrelated phenomena that share common aspects, namely, the rapid change in the ground state structure along an isotope ch
ain or the presence of several minima at the mean-field level. To illustrate the similarities and differences between both phenomena, we will focus in the Pb region, in particular in Pt and Hg isotopes, as well as in Zr isotopes.
The rapid shape change in Zr isotopes near neutron number $N$=60 is identified to be caused by type II shell evolution associated with massive proton excitations to its $0g_{9/2}$ orbit, and is shown to be a quantum phase transition. Monte Carlo shel
l-model calculations are carried out for Zr isotopes of $N$=50-70 with many configurations spanned by eight proton orbits and eight neutron orbits. Energy levels and B(E2) values are obtained within a single framework in a good agreement with experiments, depicting various shapes in going from $N$=50 to 70. Novel coexistence of prolate and triaxial shapes is suggested.
The mass region with A~100 and Z~40 is known to experience a sudden onset of deformation. The presence of the subshell closure $Z=40$ makes feasible to create particle-hole excitations at a moderate excitation energy and, therefore, likely intruder s
tates could be present in the low-lying spectrum. In other words, shape coexistence is expected to be a key ingredient to understand this mass region. The aim of this work is to describe excitation energies, transition rates, radii, and two-neutron separation energies for the even-even 94-110Zr nuclei and, moreover, to obtain information about wave functions and deformation. The interacting boson model with configuration mixing will be the framework to study the even-even Zr nuclei, considering only two types of configurations: 0particle-0hole and 2p-2h excitations. On one hand, the parameters appearing in the Hamiltonian and in the E2 transition operator are fixed trough a least-squares fit to the whole available experimental information. On the other hand, once the parameters have been fixed, the calculations allow to obtain a complete set of observables for the whole even-even Zr chain of isotopes. Spectra, transition rates, radii, $rho^2(E0)$, and two-neutron separation energies have been calculated and a good agreement with the experimental information has been obtained. Moreover, a detailed study of the wave function has been conducted and mean-field energy surfaces and deformation have been computed too. The importance of shape coexistence has been shown to correctly describe the A~100 mass area for even-even Zr nuclei. This work confirmed the rather spherical nature of the ground state of 94-98Zr and its deformed nature for 100-110Zr isotopes. The sudden onset of deformation in 100Zr is owing to the rapid lowering of a deformed (intruder) configuration which is high-lying in lighter isotopes.
The goal of this study is to find an observable that could distinguish between both phenomena, shape coexistence and quantum phase transitions. The selected observable to be analyzed is the two-neutron transfer intensity between the 0+ states in the
parent and daughter nuclei. The framework in which the study is done is the Interacting Boson Model (IBM), including its version with configuration mixing (IBM-CM). In order to generate the wave functions of the isotope chains of interest, needed for calculating transfer intensities, previous systematic studies with IBM and IBM-CM are taken without changing the parameters. Results for two-neutron transfer intensities are presented for Zr, Hg and Pt isotopic chains using IBM-CM and, moreover, the same is done for Zr, Pt and Sm isotopic chains using IBM with just a single configuration, i.e., without using configuration mixing. In the case of Zr, the two-neutron transfer intensities between the ground states provide a clear observable indicating that normal and intruder configurations coexist in the low-lying spectrum and that they cross at A=98->100, and this could allow to disentangle whether or not shape coexistence is inducing a given QPT. In the case of Pt, where shape coexistence is present and the regular and the intruder configurations cross for the ground state, there is almost no influence in the value of the two-neutron transfer, neither in the case of Hg where the ground state always has regular nature. For the Sm isotope chain that is one of the quantum phase transition paradigms, the value of the two-neutron transfer is strongly affected.
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ambiguity. Starting from the spinless scattering case, we demonstrate how an unknown overall phase depending on energy and angle mixes the structures seen in the associated partial-wave amplitudes making the partial wave decomposition non-unique, and illustrate it on a simple toy model. We then apply these principles to pseudo-scalar meson photoproduction and show that the non-uniqueness effect can be removed through a phase rotation, allowing a consistent comparison with model amplitudes. The effect of this phase ambiguity is also considered for Legendre expansions of experimental observables. 5 pages,
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