Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sequence of Potentials Lying Between the U(5) and X(5) Symmetries   Starting from the original collective Hamiltonian of Bohr and separating the
beta and gamma variables as in the X(5) model of Iachello, an exactly soluble
model corresponding to a harmonic oscillator potential in the beta-variable (to
be called X(5)-$\beta^2$) is constructed. Furthermore, it is proved that the
potentials of the form $\beta^{2n}$ (with n being integer) provide a ``bridge''
between this new X(5)-$\beta^2$ model (occuring for n=1) and the X(5) model
(corresponding to an infinite well potential in the beta-variable, materialized
for n going to infinity. Parameter-free (up to overall scale factors)
predictions for spectra and B(E2) transition rates are given for the potentials
$\beta^2$, $\beta^4$, $\beta^6$, $\beta^8$, corresponding to E(4)/E(2) ratios
of 2.646, 2.769, 2.824, and 2.852 respectively, compared to the E(4)/E(2)
ratios of 2.000 for U(5) and 2.904 for X(5). Hints about nuclei showing this
behaviour, as well as about potentials ``bridging'' the X(5) symmetry with
SU(3) are briefly discussed.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
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The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg