English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Davidson potentials of the form $\beta^2 +\beta_0^4/\beta^2$, when used inthe E(5) framework, bridge the U(5) and O(6) symmetries, while they bridge theU(5) and SU(3) symmetries when used in the X(5) framework. Using a variationalprocedure, we determine for each value of angular momentum $L$ thevalue of$\beta_0$ at which the rate of change of various physical quantities (energyratios, intraband B(E2) ratios, quadrupole moment ratios) has a maximum, thecollection of the values of the physical quantity formed in this way being acandidate for describing its behavior at the relevant critical point. Energyratios lead to the E(5) and X(5) results (whice correspond to an infinite wellpotential in $\beta$), while intraband B(E2) ratios and quadrupole moments leadto the E(5)-$\beta^4$ and X(5)-$\beta^4$ results, which correspond to the useof a $\beta^4$ potential in the relevant framework. A new derivation of theHolmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.Comment: LaTeX, 29 pages plus 17 postscript figure

E(5) and X(5) critical point symmetries obtained from Davidson potentials through a variational procedure