High-K isomers: some of the questions
EPJ Web of Conferences
High-K isomers: some of the questions
P. M. Walker 0
0 Department of Physics, University of Surrey , Guildford GU2 7XH , United Kingdom
High-K isomers exemplify the coexistence of individual-particle and collective motion in atomic nuclei. Here, the topic is briefly outlined, and some open questions are discussed. These include violations of the K quantum number; the high-spin limit to K isomerism; the fission stability of K isomers; possibilities for manipulation and control of K-isomer decay rates; and access to K isomers in neutron-rich nuclei.
1 Introduction
This conference celebrates the scientific life and work of
George Dracoulis, who sadly passed away in 2014. I was
privileged to be his first PhD student. During my PhD, we
made an experimental study of high-spin states in 172Hf
[
1, 2
], and we thus embarked on a life-long journey
exploring long-lived, excited states in deformed nuclei, the
so-called K isomers. Amongst our many joint publications
are a 1999 Nature review of isomers [3]; a 2001 review
focussed on high-K isomers [
4
]; and finally an in-depth
isomer review, soon to be published [
5
], that Dracoulis
worked on until shortly before he died. He also published
other related reviews, notably his recent Nobel symposium
paper [
6
], and a new and comprehensive K-isomer
tabulation [
7
].
The present paper introduces a selection of open
questions relating to K isomers, where much research remains
to be done. As we develop our understanding and push
towards the outer reaches of the nuclear chart, one of the
experimental issues that needs to be kept in mind was stated
by Dracoulis [
6
]: “There is always a problem to be aware
of with the study of isomers ... and that is that the popular
techniques for their identification can be compromised if
the lifetimes become very long, as might occur,
paradoxically, in the more interesting cases.”
First, though, some terminology needs a brief
explanation. The K quantum number represents the
projection of the nuclear angular momentum onto its
deformation axis (symmetry axis) with the deformed shape being
prolate in the vast majority of cases. High K values can
be made by broken-pair, deformation-aligned excitations,
with each broken pair increasing the number of
quasiparticles (unpaired nucleons) by two units. Electromagnetic
transitions from (multi-)quasiparticle states are called “K
forbidden” if the change in K exceeds the multipole order
of the transition, i.e. if ΔK > λ. However, due to K-mixing
mechanisms (rotational, vibrational or statistical [
4
]) such
transition are hindered, rather than strictly forbidden. The
degree of forbiddenness is defined as ν = ΔK − λ, and
the reduced hindrance is expressed as fν = (FW )1/ν, where
FW is the Weisskopf hindrance factor [
4, 7
]. In this way,
fν represents the hindrance per degree of K forbiddenness,
giving some measure of the effect of K-mixing processes,
with large fν values corresponding to little K mixing.
2 Erosion of the K quantum number
There is no strict definition of the half-life needed for a
nuclear excited state to be termed an “isomer”.
Nevertheless, it is clear that short half-lives generally correspond
to low fν values. With germanium γ-ray detectors, it
becomes difficult to determine half-lives of less than about
10 ns. One such case from the early work of Dracoulis
and Walker [
1, 2
], alluded to above, is the half-life of the
two-quasiproton, Kπ = 6+ isomer in 172Hf. The curve
fitting necessary to obtain the 5 ns value is illustrated in Fig.
1.
Perhaps surprisingly, after nearly four decades, this
172Hf isomer is still at the edge of accessibility, with
regard to having a measureable half-life: the corresponding
state in the lighter adjacent even-even isotope, 170Hf, only
has a half-life limit, measured to be <5 ns [
9
]. The
advent of fast-timing LaBr3, γ-ray detectors (see, for
example, Ref. [
10
]) may well remove this impasse, and open the
door to a range of shorter-lived K isomers.
Nevertheless, as of now, there are five even-even
hafnium isotopes with Kπ = 6+ isomers that have known
half-lives, as given in Table 1. The most recently
determined value is for 180Hf, now listed in the 2015 review of
Kondev et al. [
7
]. As seen in Table 1, the half-lives range
over almost four orders of magnitude, and the fν values for
the E2 decay branches vary by a factor of six. Clues to the
observed behaviour come from inspection of the
dependence of fν on the product of the valence nucleon numbers,
NpNn, revealing a strong correlation [
11, 12
], as illustrated
in Fig. 2. (Note that the new fν value for 180Hf is in good
accord.) Qualitatively, the behaviour seems to be
reasonably simple: small values of NpNn correspond to weak
collectivity, which can reasonably be associated with poor K
conservation, hence small fν values. However, a
quantitative understanding of this relationship remains elusive. In
contrast, a recent analysis by Chen et al (...truncated)