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Register a new userSuperdeformation and hyperdeformation in the $^{108}$Cd nucleus
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The superdeformation and hyperdeformation in $^{108}$Cd have been studied for the first time within the framework of the fully self-consistent cranked mean field theory, namely, cranked relativistic mean field theory. The structure of observed superdeformed bands 1 and 2 have been analyzed in detail. The bumps seen in their dynamic moments of inertia are explained as arising from unpaired band crossings. This is contrary to an explanation given earlier within the framework of projected shell model. It was also concluded that this nucleus is not doubly magic SD nucleus.
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The level lifetimes have been measured for a Shears band of $^{108}$Cd which exhibits bandcrossing. The observed level energies and B(M1) rates have been successfully described by a semi-classical geometric model based on shear mechanism. In this geometric model, the bandcrossing in Shears band has been described as the reopening of the angle between the blades of a shear.
The heaviest N=Z doubly-magic nucleus, $^{100}$Sn, and the neighboring nuclei offer unique opportunities to investigate the properties of nuclear interaction in extreme conditions. In particular, the Cd isotopes are expected to present features similar to those found in the Sn isotopic chain, since they have only two proton holes in the Z=50 shell. In this manuscript, the lifetime measurements of low-lying states in the even-mass $^{102-108}$Cd is presented. Thanks to the powerful detection capabilities of AGATA array and VAMOS++ spectrometer, the unusual employment of multi-nucleon transfer reactions permitted to investigate the first 2$^+$ and 4$^+$ states in all these nuclei, together with various deformed bands in $^{106}$Cd. The results were interpreted in the context of new state-of-the-art beyond-mean-field calculations, using the symmetry-conserving configuration-mixing approach. Despite the similarities in the electromagnetic properties of the low-lying states, there is a fundamental structural difference between the ground-state bands in the Z=48 and Z=50 isotopes. The comparison between experimental and theoretical results revealed a rotational character of the Cd nuclei, which have prolate-deformed ground states with $beta_2 approx 0.2$. At this deformation Z=48 becomes a closed-shell configuration, which is favored with respect to the spherical one.
We present a review of the mean-field approaches describing superdeformed states, which are currently used and/or being developed. As an example, we discuss in more details the properties of superdeformed A~60 nuclei, and present results of calculations for the rotational band in the doubly magic superdeformed nucleus 32S.
Superdeformed (SD) states in $^{40}$Ar have been studied using the deformed-basis antisymmetrized molecular dynamics. Low energy states were calculated by the parity and angular momentum projection (AMP) and the generator coordinate method (GCM). Basis wave functions were obtained by the energy variation with a constraint on the quadrupole deformation parameter $beta$, while other quantities such as triaxiality $gamma$ were optimized by the energy variation. By the GCM calculation, an SD band was obtained just above the ground state (GS) band. The SD band involves a $K^pi = 2^+$ side band due to the triaxiality. The calculated electric quadrupole transition strengths of the SD band reproduce the experimental values appropriately. Triaxiality is significant for understanding low-lying states.
The effect of nuclear superfluidity on antimagnetic rotation bands in $^{105}$Cd and $^{106}$Cd are investigated by the cranked shell model with the pairing correlations and the blocking effects treated by a particle-number conserving method. The experimental moments of inertia and the reduced $B(E2)$ transition values are excellently reproduced. The nuclear superfluidity is essential to reproduce the experimental moments of inertia. The two-shears-like mechanism for the antimagnetic rotation is investigated by examining the shears angle, i.e., the closing of the two proton hole angular momenta, and its sensitive dependence on the nuclear superfluidity is revealed.
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