Superallowed Fermi -decays between the isobaric analogue states,
[
, provide the most precise values
of the vector coupling constant
and leading element
of
the Cabibbo-Kobayashi-Maskawa (CKM) flavour-mixing matrix, which are
critical for stringent tests of weak-interaction flavor-mixing sector
of the Standard Model of particle physics. In particular, these data
are needed for testing unitarity of the CKM matrix, violation of
which may signalize new physics beyond the Standard Model,
see [1] and refs. quoted therein.
In testing the Standard Model, precision is of utmost importance. Only
the -decays, for which the reduced life-times,
, are measured
with accuracy better than half a percent, can be used for that
purpose. At present, thirteen such cases are known in nuclei, ranging
in mass from
=10 to
=74. The extraction of
and
is not solely dependent on experimental data but also requires
theoretical input in the form of radiative and many-body
corrections to the experimental
values. The corrections are
small, of the order of a percent, but are critical for the applicability of
the entire method, because it relies on the so-called conserved vector
current hypothesis (CVC). The CVC hypothesis assumes independence of
the vector current on nuclear medium, and must be verified a
priori by investigating mass independence of the corrected reduced
life-times defined as:
Since the isospin symmetry is weakly broken, mostly by the Coulomb interaction that polarizes the entire nucleus, microscopic calculation of the ISB corrections is a challenging task. Capturing a delicate equilibrium between the hadronic and Coulomb effects is fully possible only within no core approaches. This, in heavier nuclei, reduces the possible choices to formalisms rooted in the density functional theory (DFT). However, as it was recognized already in the 70's [2], to determine the magnitude of isospin impurities, the self-consistent mean-field (MF) approaches cannot be directly applied, because of a spurious mixing caused by the spontaneous symmetry-breaking effects. This observation hindered theory from progress in the field for decades.
To overcome these problems, over the last few years we have developed
a no-core multi-reference DFT, which involves the isospin-
and angular-momentum projections of Slater determinants representing
the triplet states in mother and daughter
nuclei [3,4]. The formalism, dubbed static, was
specifically designed to treat rigorously the conserved rotational
symmetry and, at the same time, tackle the explicit breaking of the
isospin symmetry due to the Coulomb field. Recently, by allowing for
mixing of states that are projected from self-consistent Slater
determinants representing low-lying (multi)particle-(multi)hole
excitations, we have extended the model to the so-called dynamic
variant [5]. The model belongs to the class of the no core
configuration-interaction approaches, with the two-body short-range
(hadronic) and long-range (Coulomb) interactions treated on the same
footing. It is based on a truncation scheme dictated by the
self-consistent deformed Hartree-Fock (HF) solutions. The model can
be used to calculate spectra, transitions, and
-decay matrix
elements in any nuclei, irrespective of their mass and neutron- and
proton-number parities.
The aim of this work is to present this novel theoretical framework
along with preliminary results for the low-spin spectra and
-decay matrix elements in selected
nuclei. The
first applications of the model to the low-lying spectra in
Cl
and
S have been published in [5].
Hereafter, we focus on nuclei relevant to high-precision tests of the
weak-interaction flavor-mixing sector of the Standard Model. In this perspective,
we discuss the spectrum of
states in
Zn, which was
reassigned in a recent experiment [6], and is now posing a
challenge to theory. We also briefly overview preliminary attempts
and difficulties arising in determining the ISB correction to the
superallowed
Ga
Zn
-decay, which is strongly model dependent. We also
present preliminary results for the ISB correction to the Fermi
matrix element corresponding to the
Ca
K
transition. In our static calculations, the case of
=38 was
excluded from the canonical pool of superallowed data. This was
because of the anomalously large ISB correction, caused by
uncontrolled mixing of the
and
orbits, which for
the SV
Skyrme true interaction are almost
degenerate. The SV
interaction is the SV
functional [7] augmented with the tensor terms, see
discussion in [8].
The paper is organized as follows. In Sec. 2, the basics of
our dynamical model are briefly sketched. In Sec. 3,
preliminary numerical results concerning spectrum of states in
Zn and the ISB corrections for
Ca
K
Fermi transitions are presented. The paper is summarized in
Sec. 4.
Jacek Dobaczewski 2014-12-06