Side feeding patterns and nuclear lifetime determinations by the Doppler shift attenuation method in ($\mathit{\alpha },n\gamma$) reactions

$\gamma$ rays were measured at several angles in both singles and coincidence mode in the ${}^{119}\mathrm{Sn}$($\alpha ,n\gamma$)${}^{122}\mathrm{Te}$ reaction at 15 MeV on a thick target. Lifetimes of excited states in ${}^{122}\mathrm{Te}$ were determined from a Monte Carlo Doppler shift attenuation method (DSAM) analysis of the Doppler broadened lines shapes of $\gamma$ rays de-exciting the levels. A comparison of several deduced lifetimes with recent results obtained with the ($n,n^{\prime }$) reaction allowed us to validate the choice of a parameter used to calculate the contribution of the side feeding times. The ingredients of the DSAM line-shape analysis (stopping power, description of instrumental line shapes, and side feeding evaluation) are presented in some detail. It is concluded that with proper treatment of side feeding, a DSAM line-shape analysis of peaks in singles or coincidence spectra obtained following the ($\alpha ,n\gamma$) reaction is able to provide rather accurate values for the lifetimes of levels with low and medium spins.

Figure 1

$\gamma \gamma$ coincidence spectra obtained following the ${}^{119}\mathrm{Sn}$$(\alpha ,n)$${}^{122}\mathrm{Te}$ reaction at 15-MeV beam energy. $\gamma$-ray peaks are labeled with their energies. Peaks assigned to decays of some of the newly assigned levels (Table ) are also labeled with the level energy.

Figure 2

(a) Probability distribution of the population of entry states in the ${}^{119}\mathrm{Sn}$$(\alpha ,n)$ reaction at 15.0 MeV, on a thick target. The yrast line and first few nonyrast states of each spin are shown. (b) Comparison between measured and calculated intensities for the yrast band $E2$ transitions.

Figure 3

Examples of Monte Carlo calculated probability distributions of side feeding times for different excited states.

Figure 4

(a) Illustration of the parametrization of the detector response line (or instrumental line shape). (b) Polynomial fit of the parameters of the instrumental line shape as a function of energy (here, for the mobile detector of this experiment).

Figure 5

Illustration of the description of some experimental peaks by the employed instrumental line-shape function.

Figure 6

Influence of $f_{\sigma }$ on the extracted lifetime. This graph refers to the transition 1844.4 keV (2408.0-keV level) and shows that the result of the present analysis coincides with that of the $(n,n^{\prime })$ reaction [4] for a value of $f_{\sigma }$ that is practically 1.

Figure 7

DSAM line-shape analysis of two transition $\gamma$ rays, 1844.4 and 1849.1 keV, de-exciting the levels at 2408.0 and 3030.5 keV, respectively (energies of both $\gamma$ rays and de-exciting levels are indicated). (a, c) Analysis performed at the forward and backward angles, respectively, from singles spectra; (b, d) ${\chi }^2$ analysis of the fit providing the extracted lifetime (indicated). Lifetimes measured with the $(n,n^{\prime })$ reaction [4] are also shown for comparison. The line-shape analysis was performed with a value $f_{\sigma }=1$. See discussion in Sec. 3d for other details.

Figure 8

Similar to Fig. 7, but for the line-shape analysis of the 1535.4 keV-line (from the 2099.2-keV state) from the singles spectra at the indicated angles. A small contaminant peak of lower energy had to be considered.

Figure 9

Similar to Fig. 7, for three overlapping transitions, 1747.1, 1750.5, and 1752.6 keV (from the decay of the 2310.7, 2930.7, and 1752.6 keV states, respectively), from singles spectra. The influence of the side feeding times is emphasized in each panel with the ${\chi }^2$ analysis.

Figure 10

Line-shape analysis of the 1267.3-keV transition from the 2448.5-keV level, from a summed coincidence spectrum.

Figure 11

DSAM analysis of the line shape of the 1345.6-keV transition from the 1909.5-keV state. Both side feeding and cascade feeding (see discussion in Sec. 3e) were considered in this analysis.

Figure 12

Same as Fig. 11 but for the line shape of the 1102.7-keV transition from the 2283.5-keV state.

Figure 13

Same as Fig. 11, for the 1226.2-keV line from the 2407.1-keV level. The small contamination from the singles spectra (a, c) disappeared in the coincidence spectrum (b). The lifetime measured with the $(n,n^{\prime })$ reaction [4] is also shown for comparison (d).

Figure 14

Same as Fig. 11, for the 1354.4- and 1357.3-keV lines from the levels at 2535.7 and 2538.6 keV, respectively.

Figure 15

Same as Fig. 11 for three lines, 1415.5, 1419.2, and 1422.4 keV, from the decay of the levels at 3166.4, 2600.8, and 2603.7 keV, respectively. Note that the 1422.4-keV line has a contribution from the 2679.4-keV level, for which the lifetime is known from Ref. [4]. See discussion in Sec. 3f.

Figure 16

Same as Fig. 11, for the 918.4-keV transition from the 2669.8-keV state. There are two contaminating transitions in the singles spectra; the one with 920.7-keV energy also presents a Doppler effect. The transition is clean in the coincidence spectrum. The lifetime was extracted from a combined analysis of all these spectra.

Figure 17

Same as Fig. 11, for the 2116.0-keV transition of the 2679.4-keV level, which is close to a contaminating transition of lower energy. The lifetime measured with the $(n,n^{\prime })$ reaction [4] is also shown for comparison (c).

Figure 18

Line-shape analysis of the 1049.3-keV transition from the 2800.8-keV level.

Figure 19

Same as Fig. 11, showing the analysis of a complicated multiplet of five lines. The transitions of 1632.9 keV (from the 2196.8-keV level) and 1639.8 keV (from the 2203.8-keV level) were calculated with their known lifetimes from Ref. [4], while the lifetimes of the 2810.0-keV level (de-exciting through the 1628.6-keV line) and the 2816.7-keV level (1635.9-keV line) were determined from the fit. The contaminating peak at the right had only instrumental shape.

Figure 20

Line-shape analysis of the 1127.4-keV transition from the 2878.3-keV state. This line could be seen cleanly only in the coincidence spectrum.

Figure 21

Line-shape analysis of the 1161.8-keV transition from the 2913.5-keV state. Two contaminating transitions were found, with only an instrumental line shape.

Figure 22

Line-shape analysis of the 1573.4-keV transition from the 3324.3-keV state. The line shape of the 1576.8-keV line could be calculated with the known lifetime of its 2758.3-keV level [4]. The other two, contaminating lines have only instrumental line shapes.

Figure 23

Illustration of the Monte Carlo simulations (Sec. 3f) of the probability distributions used to deduce the $B(\sigma ,\lambda )$ values (Table ). (a) Probability distribution for the lifetime of the $E_x=2816.7$ keV level, with and without uncertainty in the stopping power. (b, c) Probability distributions for the $B(M1)$ and $B(E2)$ transition rates of the 907.0-keV transition from the same state, which consider the asymmetric errors of both the lifetime and the mixing ratio (see Tables and ). The extracted $B(\sigma ,\lambda )$ values (listed in Table ) are also shown.