Electron capture strength for ${}^{60,62}\mathrm{Ni}$ and ${}^{58,60,62,64}\mathrm{Ni}$($p$, $n$)${}^{58,60,62,64}\mathrm{Cu}$ reactions at 134.3 MeV

Background: The strength of electron capture for medium mass nuclei has a significant effect on the evolution of supernovae. There is insufficient knowledge of these strengths and very little data for important radioactive nuclei. Purpose: Determine whether it is feasible to obtain EC strength from studies of $T_o+1$ excitations in ($p$, $n$) reactions, and whether this might yield information for radioactive nuclei. Methods: Cross sections for the ${}^{58,60,62,64}\mathrm{Ni}$($p$, $n$)${}^{58,60,62,64}\mathrm{Cu}$ reactions were measured over the angular range of $0.3{}^{\circ }$ to $11.6{}^{\circ }$ at 134.3 MeV using the IUCF neutron time-of-flight facility. Results: The $T_o+1$ excitations in ${}^{60,62}\mathrm{Ni}$ were identified by comparison with inelastic proton scattering spectra, their $B$(GT) were extracted, and the corresponding electron capture rates in supernovae were calculated. Data from the TRIUMF ($n$, $p$) experiments at 198 MeV were reanalyzed; the electron capture rates for the reanalyzed data are in moderately good agreement with the higher resolution ($p$, $n$) results, but differ in detail. The possibility of future measurements with radioactive nuclei was considered. Conclusions: It may be possible to obtain low-lying electron capture strength for radioactive nuclei by studying ($p$, $n$) reactions in inverse kinematics.

Figure 1

Diagram of transitions via ($p$, $n$), ($n$, $p$), and ($p$, $p^{\text{'}}$) interactions. More intense transitions are shown by darker lines. With the exception of the transition to the isobaric analog state, those shown involve transfer of total angular momentum, spin, and isospin $\Delta J=\Delta S=\Delta T=1$. States labeled with the same quantum numbers are isobaric analogs. The symbols $T_{>}$, $T$, and $T_{<}$ stand for $T_o+1$, $T_o$, and $T_o-1$. We are concerned here with the relatively weak ($p$, $n$) transitions to the $1^{+}$, $T_{>}$ states.

Figure 2

Spectra for ${}^{58,60,62,64}\mathrm{Ni}$ ($p$, $n$) reactions at 134.4 MeV. There are about ${10}^4$ counts per channel for a channel width of about 150(115) keV for the ${}^{60}\mathrm{Ni}$(${}^{62}\mathrm{Ni}$) spectrum in the region of the $T_{o+1}$ peaks. This is sufficient to observe the weak $T_o+1$ states as described in the text. The numbers above the peaks in the spectra are excitation energies. Spectra observed in ($p$, $p^{\text{'}}$) reactions [18] on the target nuclei are plotted on the energy axis. The sharp peak toward the left of each ($p$, $p^{\text{'}}$) spectrum is the lowest-lying $T_o+1$ state.

Figure 3

Angular distributions for the $T_o+1$ excitations in ${}^{60}\mathrm{Ni}$ (upper points) and ${}^{62}\mathrm{Ni}$ (lower points); the points are the cross sections above the smooth background for the lowest lying $T_o+1$ peak in Fig. 2. The ${}^{60}\mathrm{Ni}$ cross sections have been multiplied by 10 for display purposes. The curves are the DWBA calculations described in the text.

Figure 4

$B$(GT) for ${}^{58,60,62,64}\mathrm{Ni}$ to ${}^{58,60,62,64}\mathrm{Cu}$ from the shell model calculations described in the text.

Figure 5

(a) Spectrum for ${}^{60}\mathrm{Ni}$($p$, $n$)${}^{60}\mathrm{Cu}$ ($T=3$) at 134.3 MeV, in the region of the $T_o+1$ states. The black and gray (black and green on-line) curves are two- and three-Gaussian fits, respectively. (b) Spectrum for ${}^{60}\mathrm{Ni}$($n$, $p$)${}^{60}\mathrm{Co}$ at 198 MeV. The black and gray (black and green on-line) curves are two- and three-Gaussian fits, respectively. (c) Spectrum for ${}^{62}\mathrm{Ni}$($p$, $n$)${}^{62}\mathrm{Cu}$ ($T=4$) at 134.3 MeV, in the region of the $T_o+1$ states. (d) Spectrum for ${}^{62}\mathrm{Ni}$($n$, $p$)${}^{62}\mathrm{Co}$ at 198 MeV. The 198 MeV data are from Ref. [4] and the 134.3 MeV data are from the present work. Spectra are fitted with a second order polynomial background and two or three Gaussian peaks. For details see the text.

Figure 6

Values of $B$(GT) for ${}^{60}\mathrm{Ni}$ obtained from the present 134.3 MeV ($p$, $n$) data and the 198 MeV TRIUMF ($n$, $p$) data. (a) and (b) show the results of the fits to the ($p$, $n$) and the ($n$, $p$) cross sections as described in the text and shown in Fig. 5. (c) shows $B$(GT) from the multipole decomposition analysis (MDA) performed in Williams [4], and shown in their Fig. 12. The results from large scale shell model calculations [2] are shown in (d). For details see the text.

Figure 7

Reaction rates obtained from the $B$(GT) of Fig. 6. The upper two panels show the absolute rates and the lower two panels the results compared to those for the 134.3 MeV ($p$, $n$) data. For details see the text.