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

We measured {sup 36}Ar({rvec p},p{sub 0}) cross sections and analyzing powers for E{sub p} between 3.22 and 5.98 MeV, and used these data to deduce spin, parity, and widths of 17 levels in {sup 37}K. Our results, combined with existing information on {sup 37}Ca {beta}{sup +} 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{sup {pi}}=3/2{sup +}, T=3/2 analog of the {sup 37}Ca ground state was found to have J{sup {pi}}=3/2{sup +}. The relative proton widths of the two levels imply an isospin-mixing matrix-element of 4.84{plus_minus}0.43 keV. This agrees with the value 5.93{sub {minus}0.65}{sup +0.23} keV extracted from the {beta}{sup +}-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 {sup 37}Ca decay into components feeding daughter levels with J{sup {pi}}=1/2{sup +}, 3/2{sup +}, or 5/2{sup +}, and compare the results to theory. None of the available shell-model calculations gives a satisfactory account of the data. {copyright} {ital 1997} {ital The American Physical Society}