Proton decay from the isoscalar giant dipole resonance in ${}^{58}\mathrm{Ni}$

Proton decay from the $3\hslash \omega$ isoscalar giant dipole resonance (ISGDR) in ${}^{58}\mathrm{Ni}$ has been measured using the ($\alpha ,{\alpha }^{\text{'}}p$) reaction at a bombarding energy of 386 MeV to investigate its decay properties. We have extracted the ISGDR strength under the coincidence condition between inelastically scattered $\alpha$ particles at forward angles and decay protons emitted at backward angles. Branching ratios for proton decay to low-lying states of ${}^{57}\mathrm{Co}$ have been determined, and the results compared with predictions of recent continuum-RPA calculations. The final-state spectra of protons decaying to the low-lying states in ${}^{57}\mathrm{Co}$ were analyzed for a more detailed understanding of the structure of the ISGDR. It is found that there are differences in the structure of the ISGDR as a function of excitation energy.

Figure 1

Differential cross sections of the ${}^{58}\mathrm{Ni}$($\alpha ,{\alpha }^{\text{'}}$) reaction at $E_{\alpha }=386$ MeV for exciting isoscalar giant resonances in ${}^{58}\mathrm{Ni}$. The distorted-wave Born approximation (DWBA) calculations have been obtained by assuming $100\%$ exhaustion of the energy-weighted sum rules (EWSR). The resonance energies have been assumed to be at $E_x=19$, 29, 15 and 26 MeV for the $L=0$, 1, 2 and 3 resonances, respectively. The regions used for the difference-of-spectra (DOS) analysis are indicated.

Figure 2

Inelastic $\alpha$-scattering spectra at ${1.8}^{°}<{\Theta }_{\mathrm{c}.\mathrm{m}.}<{2.5}^{°}$ and ${3.1}^{°}<{\Theta }_{\mathrm{c}.\mathrm{m}.}<{3.8}^{°}$. The resonance structures were separated from the background with functions fitted in the continuum regions at $E_x=23\text{−}40$ MeV (see text for more details); the subtracted backgrounds are shown by the solid lines. The difference of the two spectra (DOS) after subtracting the assumed backgrounds is also shown.

Figure 3

Angular distribution of the cross sections for the resonance structure observed in the $3\hslash \omega$ region. The cross sections for the resonance at $E_x=23\text{−}40$ MeV were fitted with the DWBA calculations for $L=1$ and $L=3$. The $L=1$ and $L=3$ cross sections used in the fit are plotted.

Figure 4

Double-differential cross sections as function of the final-state energy in ${}^{57}\mathrm{Co}$ projected for the $3\hslash \omega$ region in ${}^{58}\mathrm{Ni}$. (a) Final-state spectra extracted for the scattering angles ${1.8}^{°}<{\Theta }_{\mathrm{c}.\mathrm{m}.}<{2.5}^{°}$ and ${3.1}^{°}<{\Theta }_{\mathrm{c}.\mathrm{m}.}<{3.8}^{°}$. (b) DOS showing the feeding pattern to the low-lying states in ${}^{57}\mathrm{Co}$ by emitting protons from the ISGDR. Individual final states are partly identified and fitted. Some yield corresponding to the ${}^{16}\mathrm{O}$($\alpha ,{\alpha }^{\text{'}}p$)${}^{15}\mathrm{N}$${}_{\mathrm{g}.\mathrm{s}.}$ reaction is also observed due to oxygen contamination in the target.

Figure 5

(a) Double-differential cross sections at ${1.8}^{°}<{\Theta }_{\mathrm{c}.\mathrm{m}.}<{2.5}^{°}$ and ${3.1}^{°}<{\Theta }_{\mathrm{c}.\mathrm{m}.}<{3.8}^{°}$ plotted as a function of excitation energy in ${}^{58}\mathrm{Ni}$. The data points have been obtained with a gate on the proton decay to the ground state in ${}^{57}\mathrm{Co}$. (b) DOS representing the $L=1$ strength populating the ground state in ${}^{57}\mathrm{Co}$.

Figure 6

Strength distributions expressed in differential exhaustion factors defined as fractions of the EWSR of ISGDR. The spectra represent the $L=1$ strengths identified with DOS analysis of (a) coincidence data gated with proton-decay to the ground state in ${}^{57}\mathrm{Co}$ (Fig. 5) and (b) singles data (Fig. 2). Fit functions and parameters are also indicated.

Figure 7

Difference final-state spectra plotted as function of the excitation energy in ${}^{57}\mathrm{Co}$. Coincidence conditions are set for (a) low- and (b) high-energy components of the ISGDR strength in ${}^{58}\mathrm{Ni}$. Fits of individual final states are plotted.