Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions of the Bohr hamiltonian, a compendium   The Bohr hamiltonian, also called collective hamiltonian, is one of the
cornerstone of nuclear physics and a wealth of solutions (analytic or
approximated) of the associated eigenvalue equation have been proposed over
more than half a century (confining ourselves to the quadrupole degree of
freedom). Each particular solution is associated with a peculiar form for the
$V(\beta,\gamma)$ potential. The large number and the different details of the
mathematical derivation of these solutions, as well as their increased and
renewed importance for nuclear structure and spectroscopy, demand a thorough
discussion. It is the aim of the present monograph to present in detail all the
known solutions in $\gamma-$unstable and $\gamma-$stable cases, in a taxonomic
and didactical way. In pursuing this task we especially stressed the
mathematical side leaving the discussion of the physics to already published
comprehensive material. The paper contains also a new approximate solution for
the linear potential, and a new solution for prolate and oblate soft axial
rotors, as well as some new formulae and comments, and an appendix on the
analysis of a few interesting numerical sequences appearing in this context.
The quasi-dynamical SO(2) symmetry is proposed in connection with the labeling
of bands in triaxial nuclei.

22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph