$E0$ transition strength in stable Ni isotopes

Excited states in ${}^{58,60,62}\mathrm{Ni}$ were populated via inelastic proton scattering at the Australian National University as well as via inelastic neutron scattering at the University of Kentucky Accelerator Laboratory. The Super-e electron spectrometer and the CAESAR Compton-suppressed HPGe array were used in complementary experiments to measure conversion coefficients and $\delta (E2/M1)$ mixing ratios, respectively, for a number of $2^{+}\to 2^{+}$ transitions. The data obtained were combined with lifetimes and branching ratios to determine $E0,M1$, and $E2$ transition strengths between $2^{+}$ states. The $E0$ transition strengths between $0^{+}$ states were measured using internal conversion electron spectroscopy and compare well to previous results from internal pair formation spectroscopy. The $E0$ transition strengths between the lowest-lying $2^{+}$ states were found to be consistently large for the isotopes studied.

Figure 1

Schematic diagram (not to scale) of the superconducting electron (Super-e) spectrometer at the ANU. The spectrometer was developed for electron-positron pair spectroscopy, but here was used to collect electron singles events.

Figure 2

(a) Gamma-ray and (b) electron energy spectra collected for the ${}^{58}\mathrm{Ni}$ targets.

Figure 3

(a) Gamma-ray and (b) electron energy spectra collected for the ${}^{60}\mathrm{Ni}$ targets.

Figure 4

(a) Gamma-ray and (b) electron energy spectra collected for the ${}^{62}\mathrm{Ni}$ targets.

Figure 5

Peak fitting of the $2_2^{+}\to 2_1^{+}$ transitions in the electron spectra collected with Super-e for the (a) ${}^{58}\mathrm{Ni}$, (b) ${}^{60}\mathrm{Ni}$, and (c) ${}^{62}\mathrm{Ni}$ target. The background fit is shown by a black dashed line, each individual peak is shown by a grey dotted line and the total fit is shown by a full red line. For each transition, there are two peaks corresponding to the K and L electrons. Each fit has a reduced ${\chi }^2$ value of (a) 1.1, (b) 1.0, and (c) 1.2.

Figure 6

Gamma-ray energy spectrum of inelastic neutron scattering on a natural Ni target. A ${}^{207}\mathrm{Bi}$ source was placed near the HPGe detector during the measurements to provide an “online” energy calibration.

Figure 7

Doppler-shift data for the 1321 keV $\gamma$ ray from the 2775 keV $2_2^{+}$ level in ${}^{58}\mathrm{Ni}$. The line is a linear fit to the data.

Figure 8

Gamma-ray angular distribution of the 1321 keV $\gamma$ ray from the 2775 keV $2_2^{+}$ level in ${}^{58}\mathrm{Ni}$. The line is a Legendre polynomial fit to the data.

Figure 9

Example $\gamma$-ray angular distribution for the $2_2^{+}\to 2_1^{+}$ transition in ${}^{60}\mathrm{Ni}$ from the $\left(p,p^{\prime }\gamma \right)$ measurement. The inset shows the associated ${\chi }^2$ minimization curve.

Figure 10

The ${\chi }^2$ plots for the sensitivity to the mixing ratio in the $\gamma$-ray angular distribution for $2_{}^{+}\to 2_{}^{+}$ transitions observed in ${}^{58}\mathrm{Ni}$ (left) and ${}^{60}\mathrm{Ni}$ (right).

Figure 11

Ratio of experimental to theoretical K-shell internal conversion coefficients. For $E0+M1+E2$ transitions the theoretical values are only for $M1+E2$ multipolarities and the experimental uncertainty in the $\delta (E2/M1)$ mixing ratio is included in the error bar.

Figure 12

Experimental ${\rho }^2\left(E0\right)\times {10}^3$ values measured in this work, combined with previous literature values in ${}^{58,60}\mathrm{Ni}$ [16, 17]. Unfilled transitions indicate that an upper limit has been determined. Level energies are shown in keV. The levels are grouped by their value of $J^{\pi }$ so that $E0$ transitions where $\mathrm{\Delta }J=0$ appear vertically.

Figure 13

The known ${\rho }^2\left(E0\right)$ values for (a) $0_i^{+}\to 0_f^{+}$ and (b) $2_i^{+}\to 2_f^{+}$ transitions as a function of atomic mass. Upper/lower limits are shown as triangles with the error bar indicating the relevant limit. The data are from the most recent compilations by Kibédi [4] and Wood [2].