β−γ(Circularly Polarized) Correlation Measurements inF20andAl28

A new measurement of the asymmetry parameter $A$ characterizing the $\beta -\gamma$ (CP) correlation (CP ≡ circularly polarized) for the decays of ${\mathrm{F}}^{20}$ and ${\mathrm{Al}}^{28}$ is reported herein. The spin sequence of ${\mathrm{F}}^{20}$ was already known to be $2^{+}\left({\beta }^{-}\right)2^{+}\left(\gamma \right)0^{+}$ from the work of Freiburg and Soergel. The purpose of the present experiment was to reduce the error on $A$ in order to get a more accurate value for the isospin impurity coefficient ${\alpha }_0\mathrm{}\left(1\right)\mathrm{}$ characterizing the 1.63-MeV state ($2^{+}$, $T\approx 0$) in ${\mathrm{Ne}}^{20}$. Our result is $A=0.174\mathrm{}\pm 0.014$. This agrees with Freiburg and Soergel, but represents an improvement in accuracy of a factor of 5. ${\alpha }_0\mathrm{}\left(1\right)\mathrm{}$ is found to be (1.5±2.9) × ${10}^{-3\mathrm{}}$, using the present value for $A$. By methods described elsewhere, the effective Coulomb matrix element $\left|〈H_c〉\right|$ is found to be 14±28 keV. A comparison of this value with the values for four other states in ${\mathrm{Ne}}^{20}$ ($E_x=7.2, 13.7, 14.1, \mathrm{and} 14.2$ MeV), computed by Wilkinson using the $E1\mathrm{}$ prohibition rule in self-conjugate nuclei, indicates that $\left|〈H_c〉\right|$ tends to be ≲30 keV regardless of excitation (so long as the state is particle-stable). This result also lends support to the surmise expressed earlier that for mixing of states of the type being observed here this upper limit is independent of atomic weight; the bulk of other similar measurements have been made in the atomic weight range of 40 to 150 (with the single exception of ${\mathrm{Na}}^{24}$). The result for ${\mathrm{Al}}^{28}$ is $A=-0.315\mathrm{}\pm 0.024$. This establishes the $3^{+}$ assignment for the ground state of ${\mathrm{Al}}^{28}$ and corresponds to a pure Gamow-Teller $\beta$ decay ($3^{+}$ → $2^{+}$). It also rules out the possibility of a Bouchiat-type comparison of the asymmetry parameters for ${\mathrm{Al}}^{28}$ and ${\mathrm{P}}^{28}$ (as has been done for the cases of ${\mathrm{Na}}^{24}$ and ${\mathrm{Al}}^{24}$) in order to check the conserved-vector-current hypothesis. In addition, the ${\mathrm{Al}}^{28}$ measurement was of important practical value in verifying the polarimeter calibration, since the single $\gamma$ ray of 1.77 MeV in the ${\mathrm{Al}}^{28}$ decay is so close in energy to the ${\mathrm{F}}^{20}$ $\gamma$ energy.