Isospin mixing in $^{37}$ K and spin decomposition of Gamow-Teller strength in $^{37}$ Ca decay

Authors:

We measured

^{36}

(p \to {, p}_{0})

cross sections and analyzing powers for

E_{p}

between 3.22 and 5.98 MeV, and used these data to deduce spin, parity, and widths of 17 levels in

^{37}

K. Our results, combined with existing information on

^{37}

β^{+}

decay, yield information on the distribution of Fermi and Gamow-Teller strength in this decay. A

T = 1 / 2

level lying 31 keV below the

J^{π} {= 3 / 2}^{+}

T = 3 / 2

analog of the

^{37}

Ca ground state was found to have

J^{π} {= 3 / 2}^{+}

. The relative proton widths of the two levels imply an isospin-mixing matrix-element of

4.84 \pm 0.43

keV. This agrees with the value

{5.93}_{- 0.65}^{+ 0.23}

keV extracted from the

β^{+}

-decay intensities to the two levels, plus the Gamow-Teller to Fermi strength ratio for the 5018 keV level. We decompose the Gamow-Teller strength in

^{37}

Ca decay into components feeding daughter levels with

J^{π} {= 1 / 2}^{+}

{3 / 2}^{+}

, or

{5 / 2}^{+}

, and compare the results to theory. None of the available shell-model calculations gives a satisfactory account of the data.

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Isospin mixing in37K and spin decomposition of Gamow-Teller strength in37Ca decay