In this article a method for lifetime measurements in the sub-picosecond regime via the Doppler-shift attenuation method (DSAM) following the inelastic proton scattering reaction is presented. In a pioneering experiment we extracted the lifetimes of
30 excited low-spin states of $^{96}$Ru, taking advantage of the coincident detection of scattered protons and de-exciting $gamma$-rays as well as the large number of particle and $gamma$-ray detectors provided by the SONIC@HORUS setup at the University of Cologne. The large amount of new experimental data shows that this technique is suited for the measurement of lifetimes of excited low-spin states, especially for isotopes with a low isotopic abundance, where $(n,n^{prime}gamma$) or - in case of investigating dipole excitations - ($gamma,gamma^{prime}$) experiments are not feasible due to the lack of sufficient isotopically enriched target material.
Background: Excitations with mixed proton-neutron symmetry have been previously observed in the $N=52$ isotones. Besides the well established quadrupole mixed-symmetry states (MSS), octupole and hexadecapole MSS have been recently proposed for the nu
clei $^{92}$Zr and $^{94}$Mo. Purpose: The heaviest stable $N=52$ isotone $^{96}$Ru was investigated to study the evolution of octupole and hexadecapole MSS with increasing proton number. Methods: Two inelastic proton-scattering experiments on $^{96}$Ru were performed to extract branching ratios, multipole mixing ratios, and level lifetimes. From the combined data, absolute transition strengths were calculated. Results: Strong $M1$ transitions between the lowest-lying $3^-$ and $4^+$ states were observed, providing evidence for a one-phonon mixed-symmetry character of the $3^{(-)}_2$ and $4^+_2$ states. Conclusions: $sdg$-IBM-2 calculations were performed for $^{96}$Ru. The results are in excellent agreement with the experimental data, pointing out a one-phonon hexadecapole mixed-symmetry character of the $4^+_2$ state. The $big< 3^-_1||M1||3^{(-)}_2big>$ matrix element is found to scale with the $<2^+_{mathrm{s}}||M1||2^+_{mathrm{ms}}>$ matrix element.
The influence on $gamma$-ray spectra of differential nonlinearities (DNL) in subranging, pipelined analog-to-digital converts (ADCs) used for digital $gamma$-ray spectroscopy was investigated. The influence of the DNL error on the $gamma$-ray spectra
, depending on the input count-rate and the dynamic range has been investigated systematically. It turned out, that the DNL becomes more significant in $gamma$-ray spectra with larger dynamic range of the spectroscopy system. An event-by-event offline correction algorithm was developed and tested extensively. This correction algorithm works especially well for high dynamic ranges.
