Systematic study of multi-quasiparticle<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>K</mml:mi></mml:math>-isomeric bands in tungsten isotopes by the extended projected shell model

Abstract

Background: The interplay between collective and single-particle degrees of freedom is an important structure aspect to study. The nuclei in the $A\ensuremath{\approx}180$ mass region are often denoted as good examples to study such problems because these nuclei are known to exhibit many rotational bands based on multi-quasiparticle $K$ isomers.Purpose: A large set of high-quality experimental data on high-$K$ isomeric states in the $A\ensuremath{\approx}180$ mass region has accumulated. A systematic description of them is a theoretical challenge as it requires a method going beyond the usual mean field with multi-quasiparticle configurations built in the shell-model basis. The $K$-isomer data provide an ideal testing ground for theoretical models.Method: The recently extended projected shell model (PSM) by the Pfaffian method is employed with a sufficiently large configuration space including up to 10 quasiparticles. The restoration of rotational symmetry which is broken in the deformed mean field is obtained by means of angular-momentum projection. With axial symmetry in the basis deformation, each multi-quasiparticle state, classified by a $K$ quantum number, represents the major component of a rotational $K$ band. Shell-model diagonalization in such a projected basis defines the $K$ mixing, which is the key ingredient of the present method.Results: Quasiparticle structure and rotational properties of high-$K$ isomers in even-even neutron-rich $^{174\ensuremath{-}186}\mathrm{W}$ isotopes are described. The rotational evolution of the yrast and near-yrast bands is discussed with successive band crossings. Multi-quasiparticle $K$ isomers and associated rotational bands in each W isotope are studied with detailed quasiparticle configurations given. Electromagnetic transition properties are also studied and the calculated $B(E2),B(M1)$, and $g$-factors are compared with experiment if data exist.Conclusions: Many nuclei of the $A\ensuremath{\approx}180$ mass region exhibit properties of an axially symmetric shape and $K$ is approximately a good quantum number. For such nuclei, the extended PSM assuming an axially symmetric basis but including $K$ mixing through diagonalization of the two-body Hamiltonian is an appropriate method to study multi-quasiparticle $K$ isomers and $K$ violations in these states. For special examples where one finds highly $K$-forbidden transitions the present model needs to be further improved.