Study of ${\mathrm{Sc}}^{41}$ Levels by the ${\mathrm{Ca}}^{40}(p,\gamma ){\mathrm{Sc}}^{41}$ Reaction

The level structure of ${\mathrm{Sc}}^{41}$ produced in the ${\mathrm{Ca}}^{40}(p,\gamma ){\mathrm{Sc}}^{41}$ reaction has been studied by measuring the positron activity [$E_{max}\left({\beta }^{+}\right)=5.5\mathrm{}$ MeV, ${\tau }_{\frac{1}{2}}=0.6\mathrm{}$ sec] of the product nucleus. The measurements covered the range $0.6\le E_p\le 5.2$ MeV with a resolution width of about 5 keV. Forty-six resonances in the yield function were identified with states of ${\mathrm{Sc}}^{41}$. Absolute yields were also measured for each resonance with a $\beta$ detector of calibrated efficiency. Since all excited states of ${\mathrm{Sc}}^{41}$ are proton-unstable, these yields were attributed to transitions from the capture levels directly to the ground state. On this basis, and by assuming ${\Gamma }_{\gamma }<{\Gamma }_p$, values of the quantity $g{\Gamma }_{\gamma \mathrm{g}.\mathrm{s}.\mathrm{}}$ were determined for the ground-state transition from each level. By evaluating the statistical factor $g$ for various assumed values of the spin $J$, the radiative widths ${\Gamma }_{\gamma }$ were obtained. When expressed in Weisskopf single-particle units, these values fell within the ranges expected for $E1\mathrm{}$, $M1+E2\mathrm{}$, and $E2\mathrm{}$ transitions. Since the ground-state spin of ${\mathrm{Sc}}^{41}$ is ${\frac{7}{2}}^{-}$, these results eliminated from consideration assignments of $J^{\pi }={\frac{1}{2}}^{+},{\frac{1}{2}}^{-}, \mathrm{and} {\frac{3}{2}}^{+}$ for the radiating states. For 16 of the most strongly excited levels, specific evidence with respect to possible values of $J^{\pi }$ was obtained by measuring the angular distribution of the $\gamma$ radiation emitted in transitions to the ground state. For ten additional states, earlier studies of proton elastic scattering furnished values of the orbital angular momentum $l_p$ of the captured protons. These data permitted specific $J^{\pi }$ assignments in 14 favorable cases, and restricted assignments to two values of $J$ and either parity in ten cases. Eleven transitions are found to occur by means of either pure $E2\mathrm{}$ or mixed $M1\mathrm{}$ and $E2\mathrm{}$ radiation. The combined strength of these transitions exhausts 6-8% of the $E2\mathrm{}$ sum-rule limit. The present status of information on energies and values of $J^{\pi }$ of the states of ${\mathrm{Sc}}^{41}$ occurring at excitation energies up to 6.2 MeV is summarized.