Gamow-Teller transitions in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>A</mml:mi><mml:mo>=</mml:mo><mml:mn>40</mml:mn></mml:mrow></mml:math>isoquintet of relevance for neutrino captures in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Ar</mml:mi><mml:mprescripts/><mml:none/><mml:mn>40</mml:mn></mml:mmultiscripts></mml:math> (2014)

Background: The Gamow-Teller response of $^{40}\mathrm{Ar}$ is important for the use of liquid argon as a medium for neutrino detection. An ambiguity about the Gamow-Teller strength for the excitation of ${1}^{+}$ states at 2290 and 2730 keV in $^{40}\mathrm{K}$ results in a significant uncertainty for neutrino capture rates. This ambiguity is caused by the large discrepancy observed between strengths extracted from $^{40}\mathrm{Ar}$($p$, $n$) charge-exchange data and the transition strengths for the analog transitions studied in the $\ensuremath{\beta}$ decay of $^{40}\mathrm{Ti}$.Purpose: This study was aimed at resolving the ambiguity between the results from the $^{40}\mathrm{Ar}$($p$, $n$) charge-exchange and $^{40}\mathrm{Ti}$ $\ensuremath{\beta}$-decay data.Method: Shell-model calculations in the $sd\text{\ensuremath{-}}pf$ shell with a new interaction (WBMB-C) were used to study differences between the structure of the transitions from $^{40}\mathrm{Ar}$ and $^{40}\mathrm{Ti}$. Distorted-wave Born approximation reaction calculations were used to investigate uncertainties in the extraction of Gamow-Teller strength from the $^{40}\mathrm{Ar}$($p$, $n$) data. New high-resolution data for the $^{40}\mathrm{Ar}$($^{3}\mathrm{He}$,$t$) reaction were used to gain further insight into the charge-exchange reaction mechanism and to provide more information to test the validity of the shell-model calculations.Results: The shell-model calculations showed that interference between amplitudes associated with $pf$ and $sd$ components to the low-lying Gamow-Teller transitions, in combination with a difference in Coulomb energy shifts for $^{40}\mathrm{Ar}$ and $^{40}\mathrm{Ti}$, can produce the differences on the scale of those observed between the $^{40}\mathrm{Ar}$ charge-exchange and $^{40}\mathrm{Ti}$ $\ensuremath{\beta}$-decay data. In combination with the difference in nuclear penetrability of the ($p$, $n$) and ($^{3}\mathrm{He}$,$t$) probes, the different contributions from amplitudes associated with transitions in the $pf$ and $sd$ shells are likely also responsible for the observed discrepancy between the ratio of the cross sections for the low-lying ${1}^{+}$ states in the $^{40}\mathrm{Ar}$($p$, $n$) and $^{40}\mathrm{Ar}$($^{3}\mathrm{He}$,$t$) data.Conclusions: On the basis of this study, it is recommended to use Gamow-Teller strengths extracted from the $^{40}\mathrm{Ar}$($p$, $n$) data, not the $^{40}\mathrm{Ti}$ $\ensuremath{\beta}$-decay data, for the calculation of neutrino capture rates. Further theoretical studies are required to achieve a consistent quantitative description for the energy differences between low-lying ${1}^{+}$ states in $^{40}\mathrm{K}$ and $^{40}\mathrm{Sc}$ and the experimentally observed Gamow-Teller strengths.