Recently, Park et al. [50] performed high-precision
measurement of the superallowed
Fermi decay
of
Ca
K, see also [51]. The
reported
value of 3062.3(68)s was measured with a relative
precision of
0.2%, which is sufficient for testing and
determining the parameters of electroweak sector of the Standard
Model. This piece of data is the first, after almost a decade,
addition to a set of canonical
Fermi
transitions, which are used to determine
. Moreover, being
a mirror partner to superallowed
Fermi
transition
K
Ar, it allows for sensitive
tests of the ISB corrections and, in turn, for assessing quality of
nuclear models used to compute the ISBs [50].
Unfortunately, using the DFT with the SV Skyrme functional, which
gives a strong mixing between the and
orbits,
it is difficult to determine the ISB corrections to the
K
Ar and
Ca
K
superallowed transitions. In particular, in our previous static DFT
calculations, the ISB corrections turned out to be of the order of
9%, and thus were disregarded [14,15].
In Ref. [18], we presented preliminary results of the
NCCI study of Ca and
K. Here we extend them to
calculations that include three low-lying antialigned reference
configurations in
K and four configurations in both
Ca
and
Ar. Basic properties of these reference states are listed
in Table 4.
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1 |
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0.000 | 0.083 | 60![]() |
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0.50 | Y |
2 |
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1.380 | 0.035 | 0![]() |
0.50 | ![]() |
Z |
3 |
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1.559 | 0.042 | 0![]() |
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1.50 | Z |
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1 |
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0.000 | 0.088 | 60![]() |
0 | 0 | - |
2 |
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0.762 | 0.006 | 0![]() |
0 | 0 | - |
3 |
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1.669 | 0.045 | 0![]() |
0 | 0 | - |
4 |
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2.903 | 0.015 | 60![]() |
0 | 0 | - |
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1 |
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0.000 | 0.088 | 60![]() |
0 | 0 | - |
2 |
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0.651![]() |
0.002 | 46![]() |
0 | 0 | - |
3 |
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1.600 | 0.045 | 0![]() |
0 | 0 | - |
4 |
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2.754 | 0.017 | 60![]() |
0 | 0 | - |
Results of our NCCI calculations, including the binding energies of the
lowest states, excitation energies of the first excited
states, and the ISB corrections to superallowed
-decays, are visualized in Fig. 4. The total
binding energies of the
states in these three nuclei are
underestimated by circa 1%. Concerning the first excited
states, our model works very well in
Ca. In this nucleus, the
measured excitation energy,
keV, is
only 186keV larger than the calculated one,
keV. Note, however, that the calculated excitation
energies of the
states are predicted to decrease with increasing
, at variance with the data. In turn, the difference between
experimental and theoretical excitation energies of the
in
Ar grows to approximately 0.7MeV.
The ISB corrections
to the
Ca
K transitions between the
and
states are
equal to 1.7% and 1.5%, respectively. As compared to our previous
static model, which for the
states was giving an unacceptably
large correction of 8.9%, the NCCI result is strongly reduced.
Nevertheless, it is still almost twice larger than that of Towner and
Hardy [27], who quote the value of 0.77(7)%.
Similar results were obtained for the K
Ar
transitions, where the calculated corrections are 1.3%
(
) and 1.4% (
).
Again, as compared to the static variant of our model, the value for
the
transition is strongly reduced, but it
is considerably larger than the Towner and Hardy result of 0.66(6)%.
Nevertheless, we see that the NCCI model removes, at lest partially, pathologies
encountered in the static variant.
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Jacek Dobaczewski 2016-03-05