content_image/412029.jpg content_image/412030.jpg
We take the GT to Fermi ratio from Ref. [11], where $^{it was determined to be 0.044}$±0.002. Adding this value to the Fermi matrix element and taking into account the ratio between the squares of the vector and the axial- vector coupling constants of 1.2695(29) [17], we derive a total f t value for the decay to the IAS of 1962(5) s. As we have neglected the corrections mentioned above, we add an additional uncertainty of 1% for this number which yields the final f t value for the IAS of 1962(20) s. 

<img src='content_image/412029.jpg'>

To determine the absolute branching ratio to the IAS, we now need the statistical rate function or Fermi function calculated from the β -decay Q EC value (11.6193(6) MeV [18]) from which we subtract the excita- tion energy of the IAS (5.5478(9) MeV) [14] and the half- life of $^{33}$Ar. For the half-life, we use the average of differ- ent literature values [4–8] for which we find 173.9(9) ms. The statistical rate function is calculated to be 3501(4). With these numbers, we determine a branching ratio to the IAS of 31.0(14)%. 

The branching ratio to the ground state of $^{33}$Cl could not be determined in our experiment. We therefore as- sume that mirror symmetry is a good approximation and calculate its feeding from the f t value of the mirror de- cay. $^{33}$P decays with a 100% branch to the ground state of $^{33}$S. The half-life (25.34(12) d) and the Q E C value (248.5(11) keV) [18] enables us to determine the f t value to be 107280(2250) s ( logf t = 5.03(1)). Using this f t value for the decay to the ground state of $^{33}$Cl, we deter- mine a branching ratio of 18.7(4)%. 

The difficulty is now to convert the branching ratios for the feeding of bound levels in $^{33}$Cl to absolute branch- ing ratios. We will test two ways of determining these branching ratios. In the first procedure, we use the to- tal proton branching ratio and the branching ratio to the ground state to deduce the feeding of bound excited lev- els as the three contributions should add up to 100%, as long as γ decay of proton-unbound levels is negligible. 

<img src='content_image/412030.jpg'>

In the second, we use the decay of $^{33}$Cl and the relative intensities of the γ transition in $^{33}$Cl to determine the feeding of bound levels. 

For the first procedure, we can obtain the total pro- ton branching ratio in two ways: i) by summing all pro- ton branching ratios in table II, ii) by integrating the β -gated proton spectrum assuming that it contains all proton events. However, in second this case, one has to cut the β particles by means of a threshold which we chose, somewhat arbitrarily, to be 1000 keV. We note that the final result changes by 0.8%, if we integrate the proton spectra starting at 900 keV. We include this in the final error. The total proton rate can then be nor- malized by means of the known absolute branching ratio of the IAS of 31.0(14)%. We determine a ratio between the number of counts for the IAS proton line and the to- tal proton intensity of 78(2)%. In the former procedure, where we sum the branching ratios from table II, we ob- tain a total proton branching ratio of 36.9(17)%. The latter procedure gives a value of 39.7(12)%. We adopt a final value of 38.8(13)% for this first procedure. 

With the branching ratio to the ground state of $^{33}$Cl of 18.7(4)% and the total proton branching ratio of 38.8(13)%, we derive a branching ratio to bound excited states in $^{33}$Cl of 42.5(17)%. From this number and the relative γ branching ratios (see figure 5 and table III), one can determine the absolute branching ratios for the feeding of the 810 keV level of 40.5(16) % and for the 2352 keV level of 2.0(3)%. 

