J. Nig. Soc. Phys. Sci. 2 (2020) 257–261

Journal of the
Nigerian Society

of Physical
Sciences

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

Coincidence Techniques

T. Daniela,b,∗, S. Kisyovc, P. H. Regana,d, N. Margineanc, Zs. Podolyaka, R. Margineanc, K.
Nomurae,f, M. Rudigiera, R. Mihaic, V. Wernerg, R. J. Carrolla, L. A. Gurgia, A. Opreac, T. Berrya,
A. Serbanc,h, C. R. Nitac, C. Sottyc, R. Suvailac, A. Turturicac, C. Costachec, L. Stanc, A. Olacelc,

M. Boromizac,h, S. Tomac, S. J. Gemanamb, F. Gbaorunb, I. Ochalai, E. C. Hembaj

aDepartment of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom
bDepartment of Physics, Benue State University, PMB 102119, Makurdi, Nigeria

cHoria Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), RO-077125 Bucharest, Romania
dAIR Division, National Physical Laboratory, Teddington TW11 0LW, United Kingdom

eDepartment of Physics, Faculty of Science, University of Zagreb, Bijenicka Cesta 32, HR-10000 Zagreb, Crotia
fCenter for Computational Sciences, University of Tsukuba, Tsukuba 305-8577, Japan

gInstitut fur Kernphysik, T.U. Darmstadt, 64289 Darmstadt, Germany
hUniversity of Bucharest, Faculty of Physics, Magurele-Bucharest, Romania

iDepartment of Physics, Kogi State University, Anyigba, Nigeria
jDepartment of Physics, Federal College of Education, Pankshin, Plateau State

Abstract

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

Keywords: Prompt response, Full width at half maximum, Lifetime, Scintillators

Article History :
Received: 21 April 2020
Received in revised form: 07 August 2020
Accepted for publication: 10 August 2020
Published: 15 November 2020

c©2020 Journal of the Nigerian Society of Physical Sciences. All rights reserved.
Communicated by: B. J. Falaye

∗Corresponding author tel. no: +2348167598988
Email address: tdaniel@bsum.edu.ng,

terrver.daniel@yahoo.co.uk (T. Daniel )

1. Introduction

The atomic nucleus which forms the central part of the atom
is made up of the protons together with the neutrons. In gen-

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Daniel et al. / J. Nig. Soc. Phys. Sci. 2 (2020) 257–261 258

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 nu-
clear force, which is strong enough to overcome the proton re-
pulsion (at short ranges of ∼ 1 fm). Figure 1 shows the entire
nuclei chart with 283 stable or very long-lived nuclei [3] rep-
resented by the black squares. Their neutron-to-proton ratio is
loosely grouped within the ranges 1.00 Õ 1.40 for 2 ≤ Z ≤ 50
and 1.20 Õ 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].

2. Measurement of the Nuclear Excited States Lifetimes

Figure 1. The chart of nuclides showing the stable nuclei in black squares with
the unstable ones on either side of the band of stability. The vertical and the
horizontal lines represent the magic numbers or closed shells [3].

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].

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 measure-
ment of the yrast halflife for the 2+ state in 192Os 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 ap-
proach 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.

3. 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 nu-
clear 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 tech-
niques.

Lifetime measurements within the picosecond to nanosec-
ond 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 LaBr3(Ce) scintillator material [15].

For almost three decades, the electronic timing technique
of β − γ − γ coincidence method using BaF2 crystals has been
used for picosecond lifetime measurements in neutron-rich nu-
clei [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 de-
veloped, where the time difference, ∆T, is obtained between the
coincident cerium-doped LaBr3 scitillators gated with a HPGe
energy coincidence [20, 21]. This has led to an improvement
compared to the previous BaF2 based analysis due to the supe-
rior energy resolution and fast decay time for LaBr3(Ce) detec-
tors [22, 23].

In this article, a triple-coincidence, γ1 − γ2 − γ3 technique
is adopted, based on the operation of both HPGe detectors and
LaBr3(Ce) scintillators. The time distribution spectrum from
the measured time difference between the two coincident LaBr3(Ce)
scintillators can be obtained either using a convolution of the
prompt (Gaussian) response function and the exponential de-
cay (see details in Figure 2) or alternatively by using the cen-
troid 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].

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Daniel et al. / J. Nig. Soc. Phys. Sci. 2 (2020) 257–261 259

Figure 2. The convolution function with the exponential and the Gaussian
prompt component as a function of t using arbitrary σ and τ, where τ is 5
times longer than σ [2].

Figure 3. Background subtracted time difference spectra for the yrast Iπ =2+

state in 192Os, obtained using the deconvolution method, showing the time dif-
ference between the 206 keV and 374 keV transitions. Time difference spectra
plotted with black lines are gated on (Eγ1 , Eγ2). The continuous line is the
Gaussian exponential convolution fit to the spectra.

4. Prompt Response Function (PRF) FWHM of 637 ps and
1000 ps in the Iπ = 2+ yrast state of 192Os

Here, we present the lifetime measurements of the yrast
state Iπ = 2+ from the 192Os isotope in the ground state band
obtained from the ’unsafe Coulombs Excitation’ from the bom-
bardment of the enriched (∼ 99%) 20 mgcm−2 192Os target with
a 80 MeV 18O beam which populates excited states associ-
ated with 194Os nucleus from ground state band of 374 keV
and 206 keV [2]. That is, for the time difference between the
LaBr3(Ce) at 374 keV (the feeding transition) of 4+ → 2+ and
the LaBr3(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 206Po 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

Figure 4. Time difference spectra for the yrast Iπ = 2 + state in 192Os, obtained
using (upper panel) the centroid shift method and (lower left and right panels)
deconvolution method, showing the time difference between the gamma pairs
of 206 keV and 374 keV transitions. Time difference spectra plotted with black
lines are gated on (Eγ1 , Eγ2 ), while the red lines show the reverse gating.
The continuous lines in lower panels are the Gaussian exponential convolution
fits to the spectra (the effective PRF FWHM value of 637 ps is taken from the
206Po [31]. This Figure is taken from Ref. [33] as Figure 6 (see details in cross
referencing, too).

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 192Os 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
192Os.

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.

5. Discussion of Results and Conclusion

Figures 3 and 4 present the time difference spectra obtained
between the gamma pairs of the 206 keV and 283 keV transi-
tions, whose extracted half-life values are 272(21) ps and 282(22)
ps, from fixing the FWHM value of 1007 ps and 637 ps, re-
spectively, constant in the Half-life program [33]. The weighted
mean of the extracted half-lives from the LaBr3(Ce)- LaBr3(Ce)
coincidence pairs of (206, 283) keV and (206, 374) keV tran-
sitions, 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

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Daniel et al. / J. Nig. Soc. Phys. Sci. 2 (2020) 257–261 260

Figure 5. Plot of the measured half-life values for the Iπ = 2+ yrast state in
192Os obtained from different approaches in the current work. The upper panel
shows the weighted mean obtained from the half-life values using an effective
PRF FWHM value of 1007 ps, while the lower panel presents the weighted
mean for an effective PRF FWHM value of 637 ps. The horizontal solid lines
indicate the weighted average of the half-life values from different decay paths,
while the red lines represent the associated uncertainty in the weighted mean.

the calculated error. This result agrees with the global half-life
value of 288(4) ps [32, 34] where other measured value for the
192Os 2+ state has been reported for the yrast state in 192Os.

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 192Os. This is an indication that once the time difference be-
tween 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.

Acknowledgement

T. D. would like to appreciates the Ph.D fellowship he en-
joyed from TETFund Nigeria for his research work in Exper-
imental Nuclear Physics at IFI-HH Bucharest, Romania, Na-
tional Argonne Laboratory, Chicago, USA and at the University
of Surrey, Guildford, UK. T. D also wishes to thank Prof. P.H.
Regan for introducing him to this novel and ’clean’ electronic
approach for the unveiling the intrinsic time information of the
nuclear structure using the coincidence technique.

References

[1] W. Gelletly, “Radioactive Ion Beams: A New Window on Atomic Nu-
clei”, Proceedings of the American Philosophical Society, 145 (2001)
519.

[2] T. Daniel, “Nuclear Structure Studies of Low-lying States in 194Os using
Fast-timing Coincidence Gamma-ray Spectroscopy”, Ph.D Thesis Sub-
mitted to the University of Surrey, Guildford, UK (2017).

[3] Segre Chart, “Nuclear Structure and Decay Data”, www.meta-
synthesis.com. Retrieved (2019).

[4] T. Daniel et al., “Review of the nuclear systematics for nuclei 140214”,
Journal of the Nigerian Association Of Mathematical Physics 49 (2019)
251.

[5] N. Marginean et al., “In-beam measurements of sub-nanosecond nuclear
lifetimes with a mixed array of HPGe and LaBr3:Ce detectors”, Eur. Phys.
Journ. A46 (2010) 329.

[6] H. Mach et al., “A Method for Picosecond Lifetime Measurements for
Neutron-rich Nuclei”, Nuclear Instruments and Methods in Physcis Re-
search, A280 (1989) 49.

[7] P. J. Nolan and J. F. Sharpey-Schafer, “The measurement of the lifetimes
of excited nuclear States”, Reports on Progress in Physics 42 (1979) 1.

[8] C. Mihai et al., “Side Feeding Patterns and Nuclear Lifetime Determi-
nations by the Doppler Shift Attenuation Method in (, n ) Reactions”,
Physical Review C81 (2010) 034314.

[9] T. K. Alexander, J.S. Foster, Advances in Nuclear Physics, edited by M.
Baranger, E. Vogt, Vol. 10 , 197 (Plenum Press, New York, London,
1978).

[10] B. Olsen and L. Boström, “Numerical Analysis of the Time Spectrum of
Delayed Coincidences, II”, Nuclear Instruments and Methods, 44 (1966)
65.

[11] E. Ye Berlovich and V. V. Lukashevich, “On Lifetime Measurements in
the Picosecond Range Using Coincidence Technique”, Nuclear Instru-
ments and Methods, 55 (1967) 323.

[12] R. S. Weaver and R. E. Bell, “Method of Evaluating Delayed Coincidence
Experiments”, Nuclear Instruments and Methods, 9 (1960) 149.

[13] P. J. R. Mason et al., “Half-life of the Iπ = 4− Intruder State in 34P:
M2 Transition Strengths Approaching the Island of Inversion”, Physical
Review C 85 (2012) 064303.

[14] P. J. R. Mason et al., “Half-life of the Yrast 2+ State in 188W: Evolu-
tion of Deformation and Collectivity in Neutron-rich Tungsten Isotopes”,
Physical Review C 88 (2013) 044301.

[15] M, Rudigier, “Fast Timing Measurement Using an LaBr3(Ce) Scintilla-
tor Detector Array Coupled with Gammasphere”, Acta Phys. Pol. B 48
(2017) 351.

[16] P. J. Nolan and J. F. Sharpey-Schafer, “The Measurement of the Lifetimes
of Excited Nuclear States”, Reports on Progress in Physics 42 (1979) 1.

[17] H. Mach et al., “A Method for Picosecond Lifetime Measurements for
Neutron-rich Nuclei:(1) Outline of the Method” Nuclear Instruments and
Methods in Physics Research A 280 (1989) 49.

[18] O. J. Roberts et al., “E3 and M2 Transition Strengths in 209Bi” Physical
Review C 93 (2016) 014309.

[19] T. Alharbi et al., “Electromagnetic Transition Rates in the N = 80 Nucleus
138Ce” Physical Review. C 87 (2013) 014323.

[20] D. Bucurescu et al., “The ROSPHERE -ray Spectroscopy Array”, Nuclear
Instruments and Methods in Physics Research A 837 (2016) 1.

[21] I. Deloncle et al., “Fast Timing: Lifetime Measurements with LaBr3 Scin-
tillators”, Journal of Physics: Conference Series 205 (2010) 012044.

[22] Lanthanum Bromide Scintillation Detectors, www.LaBr3(Ce) detectors.
Retrieved (2016).

[23] E. V. D. van Loef et al., “Scintillation Properties of LaBr3:Ce3+ Crystals:
Fast, Efficient and High-energy-resolution Scintillators”, Nuclear Instru-
ments and Methods in Physics Research A486 (2002) 254.

[24] B. Olsen and L. Boström, “Numerical Analysis of the Time Spectrum of
Delayed Coincidences, II”, Nuclear Instruments and Methods, 44 (1966)
65.

[25] E. Ye Berlovich and V. V. Lukashevich, “On Lifetime Measurements in
the Picosecond Range Using Coincidence Technique”, Nuclear Instru-
ments and Methods, 55 (1967) 323.

[26] R. S. Weaver and R. E. Bell, “Method of Evaluating Delayed Coincidence
Experiments”, Nuclear Instruments and Methods, 9 (1960) 149.

[27] H. J. Kim and W. T. Milner, “Short Nuclear Lifetime Measurements via
the Pulse Beam Delayed-Coincidence Technique”, Nuclear Instruments
and Methods 95 (1971) 429.

[28] E. de Lima et al., “Tests of the Methods of Analysis of Picosecond Life-
times and Measurement of the Half-life of the 569.6 keV Level in 207Pb”,
Nuclear Instruments and Methods 151 (1978) 221.

260



Daniel et al. / J. Nig. Soc. Phys. Sci. 2 (2020) 257–261 261

[29] T. Alharbi, “Electromagnetic Transition Rates in 34P, 138Ce and 140Nd
Using the Fast Timing -Ray Coincidence Technique”, Ph.D Thesis Sub-
mitted to the University of Surrey, Guildford, UK (2012).

[30] P. Petkov et al., “Lifetime Determination in Delayed-coincidence Exper-
iments using the Differential Decay-curve Approach”, Nuclear Instru-
ments and Methods in Physics Research, Section A 500 (2003) 379.

[31] T. Daniel et al., “Gamma-ray Spectroscopy of the Low-lying Energy-
States Populating the 0.64 ms 13/2+ Isomeric State in 205Po nuclei using
the Coincidence Techniques”, Nigerian Journal of Pure and Applied Sci-

ences, 8 (2017) 281.
[32] P. H. Regan et al., “Applications of LaBr 3 (Ce) Gamma-ray Spectrometer

Arrays for Nuclear Spectroscopy and Radionuclide Assay”, Journal of
Physics: Conference Series 763 (2016) 012004.

[33] C. Wheldon, www.wheldon.talktalk.net/files/halflife.c.
[34] C. M. Baglin, “Nuclear Data Sheets for A = 192”, Nuclear Data Sheets

113 (2012) 1871.

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