Ground State Bands of the E(5) and X(5) Critical Symmetries Obtained from Davidson Potentials through a Variational Procedure

Details Ground State Bands of the E(5) and X(5) Critical Symmetries Obtained from Davidson Potentials through a Variational Procedure Ground State Bands of the E(5) and X(5) Critical Symmetries Obtained from Davidson Potentials through a Variational Procedure

2003-12-29

arxiv.org/abs/nucl-th/0312121v1

Phys.Lett. B584 (2004) 40-47

Physics

Nuclear Physics

Nuclear Theory

LaTeX, 12 pages, 4 postscript figures

Scientific paper

10.1016/j.physletb.2004.01.018

Davidson potentials of the form $\beta^2 +\beta_0^4/\beta^2$, when used in the original Bohr Hamiltonian for $\gamma$-independent potentials bridge the U(5) and O(6) symmetries. Using a variational procedure, we determine for each value of angular momentum $L$ the value of $\beta_0$ at which the derivative of the energy ratio $R_L=E(L)/E(2)$ with respect to $\beta_0$ has a sharp maximum, the collection of $R_L$ values at these points forming a band which practically coincides with the ground state band of the E(5) model, corresponding to the critical point in the shape phase transition from U(5) to O(6). The same potentials, when used in the Bohr Hamiltonian after separating variables as in the X(5) model, bridge the U(5) and SU(3) symmetries, the same variational procedure leading to a band which practically coincides with the ground state band of the X(5) model, corresponding to the critical point of the U(5) to SU(3) shape phase transition. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

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