Prompt Response Function (PRF) of Lifetime Measurement in the 2 State of 192Os Nuclei Energy Levels from Triple-Gamma Coincidence Techniques

The effective prompt response function full width at half maximum, PRF FWHM of 637 ps (obtained from the prompt gamma pairs of 477 keV and 700 keV associated with the yrast 2 state in 206Po), and 1007 ps (obtained from the Compton gamma pairs of 189 keV and 237 keV associated with the 192Os(18O,16O)194Os 2 neutron transfer reaction) were used in fitting the time difference spectra obtained from the gamma coincident pairs of 206 keV and 374 keV in a symmetrised LaBr3(Ce) associated with the gamma transitions in 192Os, using the Half-life program. The values of half-life measured by fitting these PRF FWHM of 637 ps and 1007 ps separately show an excellent agreement of 282(16) ps and 272(21) ps, respectively, which correspond to the global half-life value of 282(4) ps for the 192Os. The mean value of 277(12) ps from these two measurements was used in calculating the B(E2; IL ÕIL-2) of 4233(114) e2fm4, which is equivalent to be 81(19) W.u. DOI:10.46481/jnsps.2020.98


Introduction
The atomic nucleus which forms the central part of the atom is made up of the protons together with the neutrons. In gen-257 eral, the atom consists of all these components together with the constant orbiting electrons. The nuclear size is estimated to be of the order of few Fermis, ranging from ∼ 1.6 fm (10 −15 fm) for light nuclei (for example Hydrogen, with only one proton) to ∼ 15 fm in heaviest elements, such as Uranium [1,2].
The nucleus of an atom is held together by the strong nuclear force, which is strong enough to overcome the proton repulsion (at short ranges of ∼ 1 fm). Figure 1 shows the entire nuclei chart with 283 stable or very long-lived nuclei [3] represented by the black squares. Their neutron-to-proton ratio is loosely grouped within the ranges 1.00 ¡ 1.40 for 2 ≤ Z ≤ 50 and 1.20 ¡ 1.60 for 50 < Z ≤94. The addition or removal of nucleons from stable nuclei obviously will alter the N/Z ratio, resulting in the formation of radioactive, unstable, neutron-rich systems [2,3,4]. The measurement of lifetimes of excited nuclear states can be regarded as a fundamental tool for nuclear spectroscopy [2,5]. These play a significant role in the determination of the reduced electromagnetic transition rates which are sensitive to the intrinsic properties of the nuclear levels between which the transition proceeds [5,6,7]. The excited states of nuclei can be produced in many ways including light particle evaporation following a heavy-ion fusion; multi-nucleon transfer, Coulomb excitation etc. [2].

Measurement of the Nuclear Excited States Lifetimes
The half-lives of the excited nuclear levels can be measured using the time profile of γ rays detected with (high-resolution) gamma-ray detectors. In this article, the Romanian array for γ ray SPectroscopy in HEavy ion REactions, RoSPHERE [5] was used. The lifetimes of the low-lying excited nuclear states typically range from femtoseconds to nanoseconds [7]. In this article, the convolution method was deployed for the measurement of the yrast halflife for the 2 + state in 192 Os were different PRF have been used in the determination of the halflife value for the state.
However, there are several techniques by which the lifetime of the nuclear excited states can be obtained apart from the approach stated above. These techniques are broadly classified based on the range of the lifetime of the excited state [6,7,8], and can be subdivided into two main categories; (a) the indirect methods which measure the energy width of the state, Γ, and (b) the direct methods which measure the mean decay lifetime, τ.

The Concept of Convolution
Apart from the fact that these techniques are classified based on the range of lifetime information associated with the energy levels, convolution and the centroid shift methods can widely be employed in the measurement of these lifetimes of the nuclear levels [10,11,12,13,14,15]. In these approaches, two or more γ ray transitions are used; the populating transition(s) to an energy level and the depopulating transition(s) out of the energy levels [2]; bringing about the gamma coincidence techniques.
Lifetime measurements within the picosecond to nanosecond region where the decaying γ rays are measured directly are obtained using the direct method [16]. Among these direct methods is the electronic timing technique, which in this article is based on the use of fast (time) response γ-ray detectors, made from LaBr 3 (Ce) scintillator material [15].
For almost three decades, the electronic timing technique of β − γ − γ coincidence method using BaF 2 crystals has been used for picosecond lifetime measurements in neutron-rich nuclei [17]. In this method, the desired decay path/cascade can be selected with the use of a high-resolution Ge detector. More recently [13,14,15,18,19], the use of triple coincidences for lifetime measurements in the picosecond region has been developed, where the time difference, ∆T, is obtained between the coincident cerium-doped LaBr 3 scitillators gated with a HPGe energy coincidence [20,21]. This has led to an improvement compared to the previous BaF 2 based analysis due to the superior energy resolution and fast decay time for LaBr 3 (Ce) detectors [22,23].
In this article, a triple-coincidence, γ 1 − γ 2 − γ 3 technique is adopted, based on the operation of both HPGe detectors and LaBr 3 (Ce) scintillators. The time distribution spectrum from the measured time difference between the two coincident LaBr 3 (Ce) scintillators can be obtained either using a convolution of the prompt (Gaussian) response function and the exponential decay (see details in Figure 2) or alternatively by using the centroid shift method [24,25,26]. Both methods of analysis can be used when the half-life of the nuclear state is long enough to be measured by fitting the exponential nature of its decay [27] while the centroid shift method is particularly useful in cases where the half-life is of the same order or smaller than the full width at half maximum, FWHM prompt time response [27,28,29,30,31]. 258  Here, we present the lifetime measurements of the yrast state I π = 2 + from the 192 Os isotope in the ground state band obtained from the 'unsafe Coulombs Excitation' from the bombardment of the enriched (∼ 99%) 20 mgcm −2 192 Os target with a 80 MeV 18 O beam which populates excited states associated with 194 Os nucleus from ground state band of 374 keV and 206 keV [2]. That is, for the time difference between the LaBr 3 (Ce) at 374 keV (the feeding transition) of 4 + → 2 + and the LaBr 3 (Ce) at 206 keV (depopulating transition) of 2 + → 0 + ground state with fixed PRF FWHM of 1007 ps (see Figure 4.1 for details) and 637 ps (see Figure 4.2) [32] using the Halflife program [33].
The choice of these PRF FWHM is necessitated from the fact that the ∆T obtained from the gamma pairs of 477 keV and 700 keV associated to 206 Po for the 637 ps [31] and 1007 ps as obtained from the ∆T between the Compton gamma pairs of the 189 keV and 237 keV transitions are actually very 'prompt' or Gaussian in nature because the time difference between them is very small as compared with a normal time difference obtained in a fit to the exponential slope. The relevance of this work here is to see whether there is a significant difference in the half-life measurement with these PRF values.
In each approach stated above, the lifetime measurements for the yrast state in 192 Os with fixed PRF FWHM at either 637 ps [32] or 1007 ps are in agreement with each other. This points to the fact that the time difference spectra presented in either case is prompt in which the time information from them does not contribute 'significantly' to the measured yrast state in 192 Os.
The weighted means of the two results obtained from fixing either PRF FWHM at 637 ps [32] or 1007 ps for the ∆T of 206 keV and 374 keV gamma pairs are presented in Figure reff5 with each result having the calculated error associated with the FWHM used and from the transitions employed here. The error bars in the stated results are mostly attributed to the fact that there is limited counts in all the measurements.  (22) ps, from fixing the FWHM value of 1007 ps and 637 ps, respectively, constant in the Half-life program [33]. The weighted mean of the extracted half-lives from the LaBr 3 (Ce)-LaBr 3 (Ce) coincidence pairs of (206, 283) keV and (206, 374) keV transitions, fixing FWHM values at either 1007 ps or 637 ps, is plotted in Figure 5. Both results agree excellently with each other approach even as the PRF FWHM was varied and within 259 the calculated error. This result agrees with the global half-life value of 288(4) ps [32,34] where other measured value for the 192 Os 2 + state has been reported for the yrast state in 192 Os.

Discussion of Results and Conclusion
In conclusion, the results obtained from the PRF values of 637 ps and 1007 ps have shown a great similarity, which in turn is in agreement with the global half-life value for the 2 + state in 192 Os. This is an indication that once the time difference between two gamma energies is "prompt", there is an insignificant presence of the time information (that is, in the half-life value) for such a state.