Level lifetimes in ${}^{32}\mathrm{P}$ obtained using the Doppler-shift attenuation method with thick molecular targets

Level lifetimes in the ${}^{32}\mathrm{P}$ nucleus have been determined using the Doppler-shift attenuation method (DSAM). Conventional DSAM measurements employ a thin target on a thick, high-$Z$ backing. An extension of the technique to thick molecular targets is presented. The necessary modifications in the standard analysis procedures, pertaining to the incorporation of stopping power estimations for molecular media and evolution of residue cross section in a thick target, have been implemented. Further, x-ray powder diffraction (XRD) and scanning electron microscopy (SEM) have also been carried out to probe the structural composition of the target. The lifetime results have been validated with respect to the previous measurements and upper limits on lifetimes of seven levels have been determined for the first time. Large-basis shell model calculations have been carried out and compared with the experimental measurements.

Figure 1

Angle dependent projection spectra exhibiting Doppler effects on the $\gamma$-ray peaks observed in the present work. The labels indicate the reported lifetimes in ps [12]. The inset illustrates the Doppler shifted 1526 keV and 1631 keV (from ${}^{29}\mathrm{Si})$ peaks at forward and backward angles from very short lived levels.

Figure 2

Stopping powers of ${}^{32}\mathrm{P}$ ions in ${\mathrm{Ta}}_2{\mathrm{O}}_5$ using srim (labeled srim in the legend), dechist with srim input and interpolation (dechist_srim) and dechist with effective $Z$ and effective $A$ for the ${\mathrm{Ta}}_2{\mathrm{O}}_5$ target (dechist_effective-z).

Figure 3

Cross-section of the residue as a function of beam energy. The original dechist program assigns a uniform cross section (red line) of the residue while the modified dechist program incorporates a beam-energy-dependent cross section (blue line) along the target thickness.

Figure 4

Least-square fitting of the 1631 keV peak from the ${}^{29}\mathrm{Si}$ nucleus, at $32{}^{\circ },90{}^{\circ }$, and $148{}^{\circ }$, using the lineshape package. The peak exhibits Doppler shifts at forward and the backward angles. The fits correspond to the target thicknesses 4.4 mg/${\mathrm{cm}}^2$ (effective) and 9.25 mg/${\mathrm{cm}}^2$ (total), respectively.

Figure 5

X-ray diffraction pattern obtained for ${\mathrm{Ta}}_2{\mathrm{O}}_5$ target. The intensity scale is linear. The monoclinic and the orthorhombic phases of crystalline ${\mathrm{Ta}}_2{\mathrm{O}}_5$ are identified by $\alpha$ and $\beta$ labels, respectively. The inset depicts the pattern at low angles. The observed hump at the low angles may be attributed to the presence of amorphous phase (see text).

Figure 6

Scanning electron micrograph images for ${\mathrm{Ta}}_2{\mathrm{O}}_5$ target. The upper panel illustrates the crystalline component while the bottom panel indicates the presence of amorphous component.

Figure 7

Variation of calculated lifetime for the 1755 keV state in the ${}^{32}\mathrm{P}$ nucleus as a function of the density of the ${\mathrm{Ta}}_2{\mathrm{O}}_5$ target. The red band indicates the reported lifetime of the level along with the uncertainties.

Figure 8

Schematic representation of the gating from transition above (GTA) procedure for determination of the level lifetime, as applied in the present work (see text).

Figure 9

Partial level scheme of ${}^{32}\mathrm{P}$ illustrating levels whose lifetimes have been measured in the present work. The lifetimes of the levels marked * have been measured for the first time in the present investigation.

Figure 10

Representative fits of the Doppler shapes of the 1677 and 2418 keV transitions from the ${}^{32}\mathrm{P}$ nucleus, obtained in the present work.