Lifetime measurements of the yrast $8^{+}$ and $9^{+}$ states in ${}^{70}\mathrm{As}$

The lifetimes of the yrast $8^{+}$ and $9^{+}$ states of ${}^{70}\mathrm{As}$ have been measured via the $\gamma$-ray lineshape method following population by the ${}^9\mathrm{Be}{(}^{78}\mathrm{Rb},{}^{70}\mathrm{As})$ reaction at 101.6 MeV/nucleon. The strength of the $E18^{+}\to 7^{-}$ transition is found to be $B\left(E1\right)=1.3\left(5\right)\times {10}^{-5} e^2{\text{fm}}^2$ or $1.2\left(4\right)\times {10}^{-5}$ Weisskopf units (W.u.) while the $9^{+}\to 8^{+} M1$ transition is found to have a strength of $B\left(M1\right)=1.5\left(8\right) {\mu }_N^2$ or $0.85\left(42\right)$ W.u. The implications for the structure of these states is discussed and found to be consistent with an assignment to a $\pi g_{9/2}\nu g_{9/2}$ configuration.

Figure 1

Doppler-corrected $\gamma$-ray spectra obtained in coincidence with ${}^{70}\mathrm{As}$ fragments detected in the S800 for (a) the backward detectors and (b) the forward detectors, along with candidates for the most prominent $\gamma$ rays observed in these spectra. The insets show a closer view of the $8^{+}\to 7^{-}$ transition and the asymmetry in the associated 788.3-keV $\gamma$-ray peak due to the lifetime of the $8^{+}$ state. Also pictured in the insets is a simulation assuming a lifetime ${\tau }_{8^{+}}=0$ ps (dashed line). Comparison between the simulated backward and forward spectra shows that the backward spectrum already has a significant low-energy tail even with ${\tau }_{8^{+}}=0$ ps because of decays happening at different velocities inside the target, and so will not be as sensitive as the forward detectors to the lifetime.

Figure 2

A partial level scheme of ${}^{70}\mathrm{As}$ indicating the levels which are relevant to this study, with the transitions labeled by the vertical text (in keV). The transitions which were used as gates to determine the lifetimes of the $8^{(+)}$ and $9^{+}$ levels are indicated by the dashed boxes and are labeled I and II, respectively. Parentheses for tentative assignments are dropped in the text for simplicity. Data are from [15] except for the $J^{\pi }$ of the $\left({13}^{+}\right)$ state, which is from [6].

Figure 3

Fits to the Doppler-corrected $\gamma$-ray singles spectrum obtained with the forward ring of detectors for ${}^{70}\mathrm{As}$, where the lifetime of the $8^{+}$ state is fixed to 150 ps and only the amplitudes of the simulations are varied. The fit shown in (a) does not include the 791.3-keV $\gamma$ ray from the 2467.5-keV state, while (b) does contain the 791.3-keV $\gamma$ ray. Comparison between (a) and (b) makes it clear that the 791.3-keV $\gamma$ ray is necessary to reproduce the spectrum. Individual $\gamma$ rays included in the simulation in (b) can be seen in (c). The assumption for the exponential background is shown in (a) and (b) by the dashed curve. The vertical dashed lines indicate the area used to create gate I in Fig. 2 in order to generate the spectrum shown in Fig. 4.

Figure 4

Fits to the Doppler-corrected $\gamma \gamma$ coincidence data, with all panels showing the $\gamma$ rays in the forward ring. In each panel the solid curve is the best fit to the data while the short-dashed line indicates the assumption of the background. The long-dashed curve shows a simulation with a lifetime of 0 ps for comparison. Also shown in each panel is the ${\chi }^2$ distribution for that fit. Panel (a) shows the fit to the experimental spectrum gated on the 903.8-keV $\gamma$ ray from the ${10}^{+}$ state along with simulations in which the lifetime of the $8^{+}$ state is varied. ${\chi }^2$ analysis yields a lifetime of ${\tau }_{8^{+}}=80\left(28\right)$ ps. Panel (b) shows the experimental data gated on the 76.1-keV $\gamma$ ray from the $9^{+}$ state but attempts to fit these data with simulations which do not account for the $9^{+}$ lifetime. These simulations fail to reproduce the experimental lineshape and result in a poor ${\chi }^2$ distribution. Panel (c) shows the same data, but the simulations include feeding from the $9^{+}$ state (with ${\tau }_{8^{+}}=80$ ps fixed), as well as allowing for coincidence from above with the 827.7- and 980.7-keV $\gamma$ rays which populate the $9^{+}$ state. This fit reproduces the lineshape of the $8^{+}$ state, and ${\chi }^2$ analysis yields a lifetime for the $9^{+}$ state of ${\tau }_{9^{+}}=85\left(30\right)$ ps.

Figure 5

(a) Doppler-corrected spectra from the forward ring generated for the gate on the 903.8-keV $\gamma$ ray from the ${10}^{+}$ state and a gate of the same width placed at approximately 1200 keV in order to show the contribution from the background. There is a clear peak at 788.3 keV from the $8^{+}$ state in the gate on the 903.8-keV $\gamma$ ray while there is no obvious contribution in the background gate. (b) Doppler-corrected spectra from the forward ring generated by placing a gate on the 76.1-keV $\gamma$ ray from the $9^{+}$ state and a gate of the same width placed immediately above it in energy in order to show the background contribution. As in (a), there is a clear peak from the $8^{+}$ state in the gate on the 76.1-keV $\gamma$ ray, but no evidence for a peak in the background spectrum. The peak at approximately 300 keV in the spectrum gated on 76.1 keV can be explained by coincidence with the 81.2-keV $\gamma$ ray from the $5_1{}^{(-)}$ state, which can be populated from the $6^{(-)}$ and ${\left(5\right)}_1$ states [15].

Figure 6

(a) The fit to the Doppler-corrected $\gamma$-ray singles spectrum from the forward detector ring. The fit pictured was generated assuming the lifetimes ${\tau }_{8^{+}}=100$ ps and ${\tau }_{9^{+}}=80$ ps. The background was assumed to be exponential in shape and is indicated by the dashed line. (b) The individual components that went into the fit in (a). In contrast to Fig. 3, each component's feeding into the $8^{+}$ state is included in the simulations, with the exception of the 944.9-keV $\gamma$ ray which does not feed the $8^{+}$ state. Shown in the inset is the ${\chi }^2$ surface generated by varying the lifetimes of the $8^{+}$ and $9^{+}$ states, with the projections of the minimum value for each grid line shown along each axis. To provide a sense of scale, the red area in the lower left of the ${\chi }^2$ distribution corresponds to a value of ${\chi }^2/N\approx 2$, while the minimum value is approximately ${\chi }^2/N\approx 1.15$. Although the $1\sigma$ uncertainty limits lie outside the search area, the minimum can be clearly seen at ${\tau }_{8^{+}}\approx 100$ ps and ${\tau }_{9^{+}}\approx 80$ ps, in agreement with the results from the $\gamma \gamma$ coincidence fits.

Figure 7

$B\left(M1\right)$ values for several $9^{+}\to 8^{+}$ transitions in nuclei in the vicinity of ${}^{70}\mathrm{As}$, along with a particle-vibration coupling model prediction indicated by the horizontal dashed line. The solid line is intended to emphasize the relative differences among the data points. The values for the selected nuclei with mass $A>70$ are known, while the value for ${}^{66}\mathrm{Ga}$ is tentative in that it is not certain whether the decay is of $E1$ or $M1$ character. If it is $M1$, then the drastic reduction from ${}^{70}\mathrm{As}$ to ${}^{66}\mathrm{Ga}$ suggests a sudden change in the nuclear structure. $B\left(M1\right)$ (or lifetime) data for other nuclei are taken from [25, 26, 27, 28].