Spin differences in the ${}^{90}\mathrm{Zr}$ compound nucleus induced by $(p,p^{\prime })$, $(p,d)$, and $(p,t)$ surrogate reactions

The effect of the production mechanism on the decay of a compound nucleus is investigated. The nucleus ${}^{90}\mathrm{Zr}$ was produced by three different reactions, namely ${}^{90}\mathrm{Zr}(p,p^{\prime }){}^{90}\mathrm{Zr}$, ${}^{91}\mathrm{Zr}(p,d){}^{90}\mathrm{Zr}$, and ${}^{92}\mathrm{Zr}(p,t){}^{90}\mathrm{Zr}$, which served as surrogate reactions for ${}^{89}\mathrm{Zr}(n,\gamma )$. The spin-parity $\left(J^{\pi }\right)$ distributions of the states populated by these reactions were studied to investigate the surrogate reaction approach, which aims at indirectly determining cross sections for compound-nuclear reactions involving unstable targets such as ${}^{89}\mathrm{Zr}$. Discrete $\gamma$ rays, associated with transitions in ${}^{90}\mathrm{Zr}$ and ${}^{89}\mathrm{Zr}$, were measured in coincidence with light ions for scattering angles of ${25}^{\circ }–{60}^{\circ }$ and ${}^{90}\mathrm{Zr}$ excitation energies extending above the neutron separation energy. The measured transition systematics were used to gain insights into the $J^{\pi }$ distributions of ${}^{90}\mathrm{Zr}$. The ${}^{90}\mathrm{Zr}(p,p^{\prime })$ reaction was found to produce fewer $\gamma$ rays associated with transitions involving high spin states $\left(J=6–8\hslash \right)$ than the other two reactions, suggesting that inelastic scattering preferentially populates states in ${}^{90}\mathrm{Zr}$ that have lower spins than those populated in the transfer reactions investigated. The $\gamma$-ray production was also observed to vary by factors of 2–3 with the angle at which the outgoing particle was detected. These findings are relevant to the application of the surrogate reaction approach.

Figure 1

Total particle spectra as a function of excitation energy in ${}^{90}\mathrm{Zr}$ from (a) ${}^{90}\mathrm{Zr}(p,p^{\prime })$, (b) ${}^{91}\mathrm{Zr}(p,d)$, and (c) ${}^{92}\mathrm{Zr}(p,t)$ reactions.

Figure 2

Total $\gamma$-ray spectra in coincidence with particles from (a) ${}^{90}\mathrm{Zr}(p,p^{\prime })$, (b) ${}^{91}\mathrm{Zr}(p,d)$, and (c) ${}^{92}\mathrm{Zr}(p,t)$ reactions. The intense $\gamma$ rays from ${}^{90}\mathrm{Zr}$ are marked in red. The $\gamma$ rays labeled in blue are from ${}^{89}\mathrm{Zr}$.

Figure 3

Discrete $\gamma$-ray transitions from ${}^{90}\mathrm{Zr}$ and ${}^{89}\mathrm{Zr}$ studied in the present work. The energies are shown in keV. $J^{\pi }$ of levels are given in parentheses and double parentheses means that there are uncertainties in assignment. The levels marked by $*$ are isomeric states from which $\gamma$ rays are unobservable in the present measurements.

Figure 4

$\gamma$ decay probabilities as a function of ${}^{90}\mathrm{Zr}$ excitation energy for discrete $\gamma$-ray transitions from the ${}^{90}\mathrm{Zr}$. (a) $E_{\gamma }=2186$ keV, (b) 420 keV, (c) 561 keV, (d) 890 keV, (e) 1129 keV, and (f) 141 keV.

Figure 5

$\gamma$ decay probabilities as a function of ${}^{90}\mathrm{Zr}$ excitation energy for selected discrete $\gamma$-ray transitions between states of the ${}^{89}\mathrm{Zr}$. (a) $E_{\gamma }=863$ keV, (b) 1511 keV, (c) 1627 keV, (d) 769 keV, (e) 1943 keV, and (f) 177 keV.

Figure 6

(a) $\gamma$ decay probability ratios of ${}^{90}\mathrm{Zr}(p,p^{\prime })$ and ${}^{92}\mathrm{Zr}(p,t)$ to ${}^{91}\mathrm{Zr}(p,d)$ at $E_x=10.0–11.0$ MeV. (b) $\gamma$ decay probability ratios of ${}^{90}\mathrm{Zr}(p,p^{\prime }n)$ to ${}^{91}\mathrm{Zr}(p,dn)$ at $E_x=14.0–15.0$ MeV. Some other $\gamma$ transitions are displayed in addition to ones shown in Fig. 3: $E_{\gamma }=2222$ keV ($6^{+}\to 5^{-}$) and 1051 keV [$(7,8)\to 8^{+}$] from ${}^{90}\mathrm{Zr}$ for (a), and $E_{\gamma }=356$ keV ($5/2^{-}\to 3/2^{-}$), 1155 keV ($1/2^{-}\to 1/2^{-}$), 1833 keV ($5/2^{+}\to 9/2^{+}$), 2121 keV ($13/2^{-}\to 9/2^{+}$), and 2128 keV [$(7/2^{+})\to 9/2^{+}$] from ${}^{89}\mathrm{Zr}$ for (b) [27, 31]. Error bars in the $x$ axis come from uncertainties in $J^{\pi }$ assignment. Uncertainties of $L$ in $E_{\gamma }=1511$ and 2128 keV are assigned to $\pm 1\hslash$ for the present data analysis. Red dashed lines indicate unity.

Figure 7

(a) $\gamma$ decay probabilities as a function of ${}^{90}\mathrm{Zr}$ excitation energy for ${}^{90}\mathrm{Zr}(p,p^{\prime })$, (b) ${}^{91}\mathrm{Zr}(p,d)$, and (c) ${}^{90}\mathrm{Zr}(p,p^{\prime }n)$. Note these probabilities are normalized to 1, 1, and 0.5, respectively for convenience in comparison (see text for details). The $\gamma$-ray transitions shown are $E_{\gamma }=2186$, 890, 1129, and 141 keV for (a) and (b), and $E_{\gamma }=769$, 863, 1943, and 177 keV for (c).

Figure 8

Angular dependence of $\gamma$ decay probabilities for the six intense $\gamma$-ray transitions from ${}^{90}\mathrm{Zr}(p,p^{\prime })$, ${}^{91}\mathrm{Zr}(p,d)$, and ${}^{92}\mathrm{Zr}(p,t)$ reactions. The probabilities are averaged at $E_x=10.0–11.0$ MeV. (a) $E_{\gamma }=2186$ keV, (b) 420 keV, (c) 561 keV, (d) 890 keV, (e) 1129 keV, and (f) 141 keV.

Figure 9

Angular dependence of $\gamma$ decay probabilities for six intense $\gamma$-ray transitions from ${}^{90}\mathrm{Zr}(p,p^{\prime }n)$ reactions. The probabilities are averaged at $E_x=14.0–15.0$ MeV. $\gamma$-rays from levels with similar angular momentum are grouped in the same color (low $J$: red; high $J$: blue).