Table Of ContentBeta decay of the exotic T = -2 nuclei 48Fe, 52Ni and 56Zn
z
S. E. A. Orrigo,1,∗ B. Rubio,1 Y. Fujita,2,3 W. Gelletly,1,4 J. Agramunt,1 A. Algora,1,5 P. Ascher,6
B. Bilgier,7 B. Blank,6 L. C´aceres,8 R. B. Cakirli,7 E. Ganio˘glu,7 M. Gerbaux,6 J. Giovinazzo,6
S. Gr´evy,6 O. Kamalou,8 H. C. Kozer,7 L. Kucuk,7 T. Kurtukian-Nieto,6 F. Molina,1,9
L. Popescu,10 A. M. Rogers,11 G. Susoy,7 C. Stodel,8 T. Suzuki,3 A. Tamii,3 and J. C. Thomas8
1Instituto de F´ısica Corpuscular, CSIC-Universidad de Valencia, E-46071 Valencia, Spain
2Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
3Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan
4Department of Physics, University of Surrey, Guildford GU2 7XH, Surrey, UK
5Inst. of Nuclear Research of the Hung. Acad. of Sciences, Debrecen, H-4026, Hungary
6Centre d’Etudes Nucl´eaires de Bordeaux Gradignan, CNRS/IN2P3 - Universit´e de Bordeaux, 33175 Gradignan Cedex, France
7Department of Physics, Istanbul University, Istanbul, 34134, Turkey
8Grand Acc´el´erateur National d’Ions Lourds, CEA/DSM - CNRS/IN2P3, BP 55027, F-14076 Caen, Cedex 5, France
6 9Comisio´n Chilena de Energ´ıa Nuclear, Casilla 188-D, Santiago, Chile
1
10SCK.CEN, Boeretang 200, 2400 Mol, Belgium
0
11Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
2
r The results of a study of the beta decays of three proton-rich nuclei with Tz =-2, namely 48Fe,
p 52Ni and 56Zn, produced in an experiment carried out at GANIL, are reported. In all three cases
A wehaveextractedthehalf-livesandthetotalβ-delayedprotonemissionbranchingratios. Wehave
measured the individual β-delayed protons and β-delayed γ rays and the branching ratios of the
4 corresponding levels. Decay schemes have been determined for the three nuclei, and new energy
1
levels are identified in the daughter nuclei. Competition between β-delayed protons and γ rays is
observed in the de-excitation of the T = 2 Isobaric Analogue States in all three cases. Absolute
]
x FermiandGamow-Tellertransitionstrengthshavebeendetermined. Themassexcessesofthenuclei
e under study have been deduced. In addition, we discuss in detail the data analysis taking as a test
- case 56Zn, where the exotic β-delayed γ-proton decay has been observed.
l
c
u PACSnumbers: 23.40.-s,23.50.+z,21.10.-k,27.40.+z,
n Keywords: β decay, decay by proton emission, β-delayed γ-proton decay, 48Fe, 52Ni, 56Zn, Gamow-Teller
[ transitions,isospinmixing,isospinsymmetry,massexcess,charge-exchangereactions,proton-richnuclei
2
v I. INTRODUCTION (∆S = 1 and ∆T = 1). For F transitions ∆S = 0
3 and ∆T = 0. Due to the simple nature of the oper-
8
ator, the GT transitions are an important tool for the
9 Theinvestigationofnuclearstructurefarfromtheval-
study of nuclear structure [2–5], providing information
3 ley of nuclear stability is a topic of the utmost impor-
0 on the overlap between the wave-functions of the parent
tance in contemporary nuclear physics. The experimen-
. groundstateandthestatespopulatedinthedaughternu-
1 tal challengeof exploringthis Terra Incognita demands
cleus. Moreover, they play an important role in nuclear
0 and has driven the construction of a new generation of
astrophysics, especially in stellar evolution, supernovae
6
facilities for the production and acceleration of radioac-
1 explosions and nucleosynthesis [6]. Since many heavy
tiveionbeams. Followingthesteadyimprovementinthe
: proton-richelementsareproducedintherp-processpass-
v range of beams available and their intensities, more and
ing through proton-rich fp-shell nuclei, the study of GT
i moreproton-richnucleicanbeproduceduptotheproton
X transitions starting from unstable proton-rich nuclei is
drip-line, enabling one to perform detailed decay studies
r also of crucial importance. Our knowledge of GT transi-
a and explore new and exotic decay modes [1].
tionswhenapproachingtheprotondrip-lineisstillrather
Beta-decay spectroscopy is a powerful tool to investi- incomplete [6], however, because the production of such
gate the structure of exotic nuclei. Beta decay is a weak nuclei becomes steadily more challenging.
interaction process mediated by the well-understood τ Normally in proton-rich nuclei proton decay is ex-
andστ operators,responsiblefortheobservedFermi(F) pected to dominate above the proton separation energy.
andGamow-Teller(GT)transitions,respectively. Itpro- In this context, proton-rich nuclei with the third compo-
vides direct access to the absolute values of the corre- nent of isospin T =-2 are of particular interest because
z
sponding transition strengths, B(F) and B(GT). their decay may present peculiarities related to the com-
The GT transitions are characterized by an angu- petitionbetweenβ-delayedprotonsandβ-delayedγ rays
lar momentum transfer ∆L = 0 and spin-isospin flip [7, 8]. Moreover recently a rare and exotic decay mode,
the β-delayed γ-proton decay, has been observed for the
first time in the fp-shell in the decay of 56Zn [7].
In this paper we present the results of a study of the
∗Electronicaddress: sonja.orrigo@ific.uv.es β decay of the Tz = -2 nuclei 48Fe, 52Ni and 56Zn. The
2
analysis of the data is described in detail using the 56Zn
56Zn
caseasanexample,expandingonsomeoftheprocedures
already presented in Ref. [7].
52Ni
The paper is organized as follows. Section II describes
the experiment performed at GANIL. Section III de-
scribesthedataanalysisprocedures. SectionIVpresents 48Fe
the experimental results for the β decays of 48Fe, 52Ni
and 56Zn. The determination of the mass excesses of
T =-2
thenucleiunderstudyisaddressedinSectionV.Finally, T =-3/2 Z
Section VI gives our conclusions. TZ = -1/2 TZ = -1 Z
FIG. 1: ∆E versus ToF identification plot for the dataset
II. EXPERIMENTAL SET-UP optimizedtoimplant56ZnclosetothemiddleoftheDSSSD.
Thepositionsofthe48Fe,52Niand56Znimplantsareshown.
The experiment to study the decay of 48Fe, 52Ni and
56Zn was performed at the LISE3 facility of GANIL 52Ni
(France) [9]. A 58Ni26+ primary beam, with an av-
erage intensity of 3.7 eµA, was accelerated to 74.5
MeV/nucleonandfragmentedonanaturalNitarget,200 48Fe
µmthick. TheLISE3separator[9]wasusedtoselectthe
fragments, which were implanted at a rate of approxi-
mately 200 ions/s into a Double-Sided Silicon Strip De-
T =-2
tector (DSSSD) of 300 µm thickness. The DSSSD had Z
16 X and 16 Y strips with a pitch of 3 mm, defining 256 TZ = -1/2 TZ = -1 TZ = -3/2
pixels. Two parallel electronic chains were used having
different gains to detect both the implanted heavy-ions
and subsequent charged-particle (betas and protons) de-
cays. TheDSSSDwassurroundedbyfourEXOGAMGe
FIG. 2: ∆E versus ToF identification plot for the dataset
clovers [10] used to detect the β-delayed γ rays.
optimizedfor48Fe. Thepositionsof48Feand52Niareshown.
The experiment was focused on the study of some
T =-2 proton-rich nuclei. The energy of the 58Ni beam III. DATA ANALYSIS
z
wasoptimizedtoimplant56Znclosetothemiddleofthe
DSSSD. Data were also taken by optimizing on 48Fe to The present section describes the analysis of the data
increasethestatisticsforthision. Furtherdatawerealso related to the β decays of 48Fe, 52Ni and 56Zn. Here we
recorded by focusing on the Tz =-1, 58Zn nucleus, of as- also expand on some of the details already presented in
trophysics interest since it constitutes a waiting point in Ref. [7]. The56Zncaseisusedasanexampleforthedis-
the rp-process. The results from this dataset were used cussion. The48Feand52Nicaseswereanalyzedfollowing
for comparison with a previous experiment and to esti- the same procedure; differences are also discussed.
mate the β detection efficiency in the DSSSD. The 48Fe, 52Ni or 56Zn ions were selected by setting
The Time-of-Flight (ToF) of the selected ions was de- gates off-line on the ∆E-ToF matrix (see Figs. 1 and 2).
fined as the time difference between the cyclotron radio- The total numbers of implanted nuclei detected, Nimp,
frequency and the signal they generated in a silicon ∆E were: 48Fe: 5.0x104, 52Ni: 5.3x105, 56Zn: 8.9x103.
detector located 28 cm upstream from the DSSSD. Si-
multaneous signals from both the ∆E detector and the
DSSSD defined an implantation event. The implanted A. Time correlations
ions were identified by combining the energy loss signal
inthe∆E detectorandtheToF.Anexampleofthetwo- In decay spectroscopy experiments performed with a
dimensionalidentificationmatrixobtainedforthesetting continuous beam, no unequivocal correlation between a
focused on 56Zn is shown in Fig. 1, where the positions given implantation event and its corresponding decay
of the T = -2 nuclei 48Fe, 52Ni and 56Zn are indicated. event can be established [8]. A widely-used approach
z
The identification matrix obtained for the dataset opti- [7, 8, 11] is to construct the correlations in time between
mized for 48Fe is shown in Fig. 2, where the positions all implantations and decay events. To this end, the 256
of 48Fe and 52Ni are indicated. A signal above threshold pixels of the DSSSD can be used as independent detec-
(typically 50-90 keV) in the DSSSD and no coincident tors. The correlation time t is defined as the time
corr
signal in the ∆E detector defined a decay event. difference between a decay event in a given pixel of the
3
DSSSDandanyimplantationsignalthatoccurredbefore B. Determination of the half-life
or after it in the same pixel that satisfied the conditions
required to identify the nuclear species. The correlation 1. Half-life fits
condition is |t | = |t −t | < T, where T is
corr decay implant
a chosen period of time. This means that a given de-
For each nucleus of interest, the correlation-time spec-
cay event will be correlated with all the implantations
trum can be constructed as explained in Section IIIA.
happening in the same pixel within the time T, and vice
This spectrum includes all the decays (betas and pro-
versa. Therewillbeatruecorrelationonlywhenthatde-
tons) correlated with a given implant. Thus all the pos-
cayeventbelongstotheimplantationeventunderconsid-
sible decays, from the parent nucleus or its daughters,
eration. Otherwise correlations will be random because
have to be taken into account in the fit of the half-life
thedecayeventwillbecorrelatedartificiallywithanim-
T with the Bateman equations [12].
plantation happening before or after the implantation to 1/2
The detection efficiency for a particular decay event
which it really belongs.
will depend strongly on the decay mode of that event,
This procedure ensures that the true correlations are
i.e., either by β-delayed proton or by β emission alone.
taken into account, at the price of including many ran-
Indeed the detection efficiency of the DSSSD is very dif-
domcorrelations. Thecorrelation-timespectrumandthe
ferent for protons (close to 100%) and for β particles
energy spectra resulting from this method will therefore
((cid:15) =13.6(6) %), see Section IIIC. Therefore for nuclei
contain both true and random correlations. β
where the decay mode is only by β emission, the inte-
In the correlation-time spectrum the random events
gration of the parent contribution and descendants will
willformaflatbackgroundwhichcaneasilybetakeninto
depend on the rather limited β detection efficiency.
account, while the true correlations will form the typical
48Fe, 52Ni and 56Zn all emit β-delayed protons. Thus
exponentialdecaycurve. Asanexample,thecorrelation-
an additional condition can be imposed to select only
time spectrum for 56Zn including all the decays (betas
the proton decays. This is achieved by setting an energy
and protons) is shown in Fig. 3.
threshold in the DSSSD spectrum (Section IIIE) which
Besidesthetruly-correlateddecays,theenergyspectra
removes the pure β decays while keeping the β-delayed
willcontaindecayeventscomingfromeitherthesameion
protons,andselectingcorrelatedimplantsforthedesired
but a different implantation event, or from different nu-
nuclear species. The advantage is that the daughter ac-
clei. These randoms have to be carefully removed. The
tivity(wherenoprotonsarepresent)isremovedfromthe
background subtraction procedure is described in Sec-
correlation-time spectrum. In this way the half-life can
tions IIIE and IIIF for the charged-particle and γ-ray
be fitted simply by using the parent activity A(t):
energy spectra, respectively.
We decided to correlate decays and implants in a pe-
A(t)=λN exp(−λ t), (1)
riod T = 50 s, i.e., in the interval [-50 s, +50 s]. This is p
differentfromRef. [8]wherethecorrelationswereformed
whereλ=ln2/T istheradioactivedecayconstantand
1/2
in the interval [0, 5000 ms]. There are two motivations
N is the total number of proton emissions. Thus the
p
for this choice. The correlations in the past, [-50 s, 0],
integration of the parent contribution does not rely on
clearly have no physical meaning but they are useful in
(cid:15) and directly yields N . The background is fixed by a
β p
thebackgroundsubtractionprocedure(seeSectionIIIE).
fit done on the left of the peak using a linear function.
The choice of a huge period T allows one to check the
Fig. 4 shows the correlation-time spectrum for 56Zn
shapeofthebackground,whichisexpectedtobeflat(see
correlated with the proton decays alone (DSSSD energy
Section IIIB2).
thresholdabove0.8MeV).Thehalf-lifeisdeterminedby
a least squares fit to the data with the function of Eq.
1. A value of T =32.9(8) ms is obtained for 56Zn [7].
s 1/2
m1600 A fit using a maximum likelihood minimization method
10 1400 gives a value of 32.8(8) ms. The result is not affected
s / by the choice of the range over which the fit was made.
nt1200 Changingtherangefrom10to1000half-lives(50s)made
u
Co1000 no difference to the results.
800 For comparison, if we use the Bateman equations [12]
600 to fit the 56Zn correlation-time spectrum containing all
thedecaymodes(Fig. 3),wehavetoinclude: theβdecay
400
of56Znto56Cu, whichpartiallygoestothegroundstate
200 of56Cuandpartiallyundergoesprotonemissionto55Ni;
the β decay of 56Cu to 56Ni; and the β decay of 55Ni to
-2000 -1500 -1000 -500 0 500 1000 1500 2000
Correlation time [ms] 55Co. As expected, we get a similar value, 31.2(11) ms.
We adopt the first method because it is more precise,
FIG.3: Spectrumofthetimecorrelationsbetweeneachdecay it relies only on our data and it allows us to extract N
event and all of the 56Zn implants (see text). p
independently of the β detection efficiency.
4
s Ideally the profile of the random-correlation background
m
0 1000 is expected to be a constant. However, there can be sit-
nts / 1 800 56Zn uaasthioanpse.whTehree tshheapbeacckagnrobuendaffpercotfiedle,ies.gn.o,tbflyapt,ublsuintghaosf
u the beam, or by the limited duration of the runs. In the
o
C 600
latter case the background assumes a triangular shape
T = 32.9(8) ms
1/2 centred at T =0 [13]. This effect is more pronounced
400 1/2
as the runs become shorter and it may affect the deter-
minationofT . Theeffectandtheproceduretocorrect
200 1/2
for it will be described in detail elsewhere.
Here we performed the time correlations over a huge
0
-200 -100 0 100 200 300 400 500 periodT tostudythebackgroundprofile. Inthepresent
Correlation time [ms]
case the duration of the runs is large enough that the
background profile is not affected. We verified that the
FIG. 4: Spectrum of the time correlations between each pro-
tondecay(DSSSDenergy>0.8MeV)andall56Znimplants. results for the half-life fit are the same both with and
without applying the correction for this effect.
2. Background from the random correlations
Variousmethodscanbeusedtodealwiththerandom- C. DSSSD detection efficiency
correlationbackground. AsinRef. [8],weincludedaflat
background in the half-life fit. This is a well-established A DSSSD detection efficiency of 100% has been as-
method to be used in simple cases such as the present sumedforbothimplantsandβ-delayedprotons. Arather
one, where the beam is continuous. If instead one sub- low efficiency value is expected for the β particles, also
tracts the background before fitting, there is an addi- reflectedintheβ-delayedγ emission,becauseofthecom-
tional source of uncertainty when fitting the final spec- bined effect of the small energy loss of the betas in the
trumbecauseofthelargerfluctuationsintroducedbythe DSSSD detector (about 100-200 keV) and the electronic
subtraction. threshold. In contrast, the β-delayed proton emission
Alternatively, a method that is very useful when the yieldsamuchhighersignalintheDSSSDsothatthepro-
beam is pulsed has been developed in Refs. [11, 13]. ton detection efficiency is not affected by the threshold.
There, a correlation-time spectrum for the background If the implantation occurs in the middle of the DSSSD,
isconstructedbyperformingthetimecorrelationsinthe theprotonefficiencyiscloseto100%,asexplainedbelow.
opposite pixel, i.e., between decays in the pixel [i,j] and A Monte Carlo simulation of the detection efficiency
implantsinthepixel[j,i]fori(cid:54)=j. Thebackgroundspec- for protons is shown as a function of their energy in Fig.
trum is then subtracted from the main correlation-time 5 of Ref. [8], where different implantation depths in a
spectrum. By applying this method in our case we get 300 µm thick DSSSD detector are considered. It was
consistentresultsbutalargeruncertaintyonT caused found that the detection efficiency was symmetric with
1/2
bythesubtraction. Besides,thebackgroundspectrumin- respect to the centre of the detector. If the 56Zn ions
troduces many fluctuations because of its low statistics. are implanted in the centre of the DSSSD (150 µm), the
Indeed in our case most of the ions produced were im- efficiency for protons of energy up to 3.5 MeV is 100%.
planted in the same region of the DSSSD as 56Zn, thus We simulated the implantation profile of the 56Zn ions
theoppositepixelcanhavefeweventswhenfarfromthe intheDSSSDinrealisticconditionsusingthesimulation
implantation region. This is not the case for the nuclei code LISE [14], obtaining a distribution centred in the
studied in Refs. [11, 13]. DSSSD and having a width of 30 µm FWHM. From pre-
In order to increase the statistics of the background vioussimilar works, suchasRef. [8], theGANILexperts
spectrum we have also considered an extended back- indicate that the differences in the implantation depth
ground spectrum created by correlating the decays in betweentheLISEsimulationsandthemeasurementsare
the pixel [i,j] with the implants in all the pixels of the of the order of 10 µm. If we adopt a reasonable system-
DSSSDexceptthe8pixelssurroundingthepixel[i,j]and atic error of 20 µm in the implantation depth, then the
thepixel[i,j]itself. Inthiswaythestatisticsoftheback- detection efficiency is 100% for all the protons with en-
groundspectrumareindeedimproved,howeverwhenthe ergy≤3.0MeV.Onlyforthe3.45MeVprotonseeninthe
beam is continuous we still prefer the first method be- decay of 52Ni is the efficiency slightly lower (≥ 98.5%).
causeitavoidstheintroductionofadditionalfluctuations Theβ detectionefficiencyoftheDSSSDisdetermined
due to the background subtraction procedure. by means of known βγ emitters, i.e., the T = -1 nuclei
z
In summary, as expected the three methods give con- populatedinthedatasetfocusedon58Zn[15]. Asdistinct
sistentresults. Thechoiceofthemethoddependsonthe from the T = -2 nuclei under study, β-delayed proton
z
details of the experiment carried out (beam properties emission is not present in the decay of these T = -1
z
and implantation pattern). isotopes. Indeedtheirdecayproceedsbyeitherβ-delayed
Finally,inRef. [13]apeculiareffecthasbeenobserved. γ emission or by β decay to the ground state, thus they
5
can be used to estimate the β detection efficiency from: E. Analysis of the charged-particle spectrum
N
(cid:15) = β , (2)
β N (1−τ) A 300 µm thick DSSSD detector was used to detect
imp
boththeimplantedheavy-ionsandthefollowingcharged-
whereN isthenumberofβdecaysobtainedbyintegrat-
β particle (betas and protons) decays (see Section II). The
ing the parent activity from the correlation-time spec-
strips of the DSSSD were calibrated and aligned using a
trum for these nuclei and τ is the dead time fraction,
triple-α-particle source and the peaks of known energy
which varies from ≈12% in the 58Zn dataset to ≈28% in from the decay of 53Ni [8]. The DSSSD spectrum was
the 56Zn+48Fe datasets. The number of implants N
imp obtainedasthesumofthespectrafromallthe256pixels.
is obtained by selecting the ion of interest in the identi-
The charged-particle spectrum measured in the
fication matrix (Section III). We obtain (cid:15) = 13.6(6) %.
β DSSSD for decays associated with implants of a given
MonteCarlosimulationsoftheemittedβ particles(done
nuclear species was formed as follows (the figures shown
as in Section IIIE for the β-p events) showed that the as examples are related to 56Zn). A DSSSD spectrum
differencesin(cid:15) between58ZnandtheT =-2nucleiun-
β z was created by selecting time correlations from 0 to 1
der study (48Fe, 52Ni and 56Zn) are of the order of 1%,
s (red-dashed zone in Fig. 5). This DSSSD spectrum,
hence well inside the quoted uncertainty for (cid:15) .
β shown in Fig. 6a, contains both true and random corre-
AsexplainedinSectionII,thedataacquisitionsystem
lations. AbackgroundDSSSDspectrum,containingonly
wastriggeredbyeitheranimplantationeventorbyade-
randoms and shown in Fig. 6b, was formed by setting a
cay event (β or proton). The γ rays were not included
gate from -40 to -10 s on the time correlation spectrum
in the trigger. The γ emissions were acquired in coinci-
(selectingtheblue-dottedzoneinFig. 5). Thetwospec-
dence with the decay events, which are affected by the
tra were then normalized to the time interval used and
correspondingDSSSDefficiency. Theβ efficiencyisused
the spectrum derived from Fig. 6b was subtracted from
to determine the absolute intensity I of each β-delayed
γ thespectruminFig. 6a. TheresultingDSSSDspectrum
γ ray observed in the decays of 48Fe and 52Ni from: associated with 56Zn is shown in Fig. 6c.
N
I(β−γ) = γ , (3)
γ (cid:15)γ (cid:15)β Nimp (1−τ) ms 1600
0 1500
γwhleinree Nanγdre(cid:15)preissenthtsetγhednetuemctbioernoeffficcoiuenntcsyinofththeegiEvXen- s / 1 1400
γ nt 1200
OGAM Ge clovers (see Section IIIF). For 56Zn, instead, u 500
the observed γ lines are in coincidence with the proton Co 1000
emission,thereforetheirintensitydoesnotdependon(cid:15)β: 800 0 1000
N 600
I(p−γ) = γ . (4)
γ (cid:15)γ Nimp (1−τ) 400
200
D. Total proton-emission branching ratio -50000 0 50000
Correlation time [ms]
The total proton branching ratio Bp is determined by FIG.5: Spectrumofthetimecorrelationsbetweeneachdecay
comparing the total number of protons, Np, with the eventandallthe56Znimplants. The0to1sand-40to-10 s
total number of implanted nuclei, N , according to: gatesareindicatedbythered-dashedandblue-dottedregions,
imp
respectively.
N
B = p . (5)
p N (1−τ)
imp Our procedure is similar to that of Ref. [8], but there
N is obtained, together with the half-life, from a fit thegatefor thebackgroundspectrumwas chosenfrom1
p
of the correlation-time spectrum after selection of the to 2 s. We chose a larger time gate, 30 s, to increase the
proton decays (see Section IIIB1). The selection of the statistics of the background spectrum. The advantage is
proton emission is achieved by setting an energy thresh- a reduction in the fluctuations coming from the subtrac-
old in the DSSSD spectrum just below the first proton tion of the two spectra. This is important in cases such
peakweidentify. AsdiscussedinRef. [8],thesystematic as 56Zn where the number of counts is limited. More-
errorofthisprocedurecanbeestimatedbyrepeatingthe over, we use the correlations in the past to define a time
determination of B using a DSSSD threshold differing interval on the left of the peak, which ensures that only
p
by±100keV.Sincethedeadtimefractionτ couldchange randoms are included in the background spectrum.
in the different measurements, we calculated a weighted- In general, a DSSSD spectrum shows a bump at low
average dead time in the same way as in Ref. [8]. The energy, due to the detection of β particles. The discrete
deadtimerecordedineachrunwasweightedbythenum- peaks visible above this bump are interpreted as being
ber of implants of a given ion in that run and divided by due to β-delayed proton emission. The proportion of β-
the total N of that isotope. delayedprotonstoβ decaydependsonthenucleusunder
imp
6
200 80
V s
0 ke (a) ount 70 (a)
s / 1 150 C 60
nt 50
u Monte Carlo
Co 100 40
simulations
30
50
20
10
0
0
0 1 2 3 4 5 1 1.5 2 2.5
Decay energy [MeV] Decay energy [MeV]
200 140
V V
Counts / 10 ke 110500 (b) Counts / 10 ke 11028000 1.691 2.661 3.423 3.508 (IAS) (b)
60
1 7
9 3
3 5
40 1. 2.
50
20
0 0
0 1 2 3 4 5 1 1.5 2 2.5 3 3.5
Decay energy [MeV] Decay energy [MeV]
200
eV (c) FIG. 7: (a) Monte Carlo simulations of β-p events with
k
0 Ep =1.1 MeV and a β end-point energy of 11.2 MeV. The
s / 1 150 phiegahk-einsefirtgtyedtabily. a(bG)auDsSsSiaSnDfucnhcatrigoend-hpaavritnigcleanspeexcptorunmentfioarl
unt decayeventscorrelatedwith56Znimplants. Thelineshapeof
Co 100 Fig. 7a was used for the fit shown here in dashed-red.
locatedinanextendedareainthemiddleofthedetector,
50
withanimplantationprofileobtainedfromLISEcalcula-
tions [14]. Protons of a given energy E were emitted at
p
0 the same time as β particles. The latter follow a distri-
0 1 2 3 4 5 bution determined by the Fermi function (β-decay event
Decay energy [MeV]
generator), with an end-point energy corresponding to
Q −E −S , where S is the proton separation energy
β p p p
FIG.6: DSSSDcharged-particlespectrafordecayeventscor-
in the daughter nucleus. A widening of 70 keV FWHM
relatedwith56Znimplants. Thespectrum(a)correspondsto
was imposed to simulate the DSSSD experimental reso-
time correlations from 0 to 1 s (red-dashed zone in Fig. 5)
lution.
and contains both true and random correlations. The back-
groundspectrum(b)iscreatedfortimecorrelationsfrom-40 Asanexample, Fig. 7ashowstheresultofthesimula-
to -10 s (blue-dotted zone in Fig. 5), normalized by the time tionoftheβ-pdecaywithEp =1.1MeV(corresponding
intervalusedandcontainsonlyrandoms. Peaksfromthe53Ni to the 56Cu level at 1.7 MeV, see Table V). A Gaus-
contaminant (T = 55.2(7) ms) [8] are seen between 1 and sian with an exponential high-energy tail describes the
1/2
2.5MeV.Theremovaloftherandomsisachievedinspectrum lineshape to a good approximation. This result is an
(c), obtained by subtracting the spectrum (b) from (a). additional justification for the procedure widely used in
Ref. [8]. The lineshape obtained from the simulations
study and it is reflected in the value of Bp (Eq. 5). For was also checked by us with the well isolated 57Zn pro-
example, for 56Zn the strength in Fig. 6c is dominated ton peak at E = 4.6 MeV. We used this lineshape to fit
p
by β-delayed proton emission and Bp = 88.5(26) % [7]. the experimental DSSSD spectra, by keeping the shape
The DSSSD experimental energy resolution is 70 keV fixed(i.e.,theGaussian+exponentialandtheslopeofthe
FWHM. The summing with the coincident β particles exponential) and fitting the parameters of the Gaussian
also affects the lineshape of the peak. To study the line- (height, mean, width) to the experimental proton peaks.
shape we performed Monte Carlo simulations for a sili- The result for 56Zn is shown in Fig. 7b. The subroutine
con DSSSD strip using the Geant4 code (version 4.9.6) [18], which allows the use of the same function in a more
[16,17]. Theradioactivesources(i.e.,theimplants)were automated way, was used to cross-check the fit of 56Zn
7
and to perform the fits for 48Fe and 52Ni, where many sources. An efficiency curve, shown in Fig. 8, was fitted
small peaks overlap. to the experimental data according to the efficiency en-
The procedures adopted allow for a proper determi- ergy dependence given in Ref. [19]. The γ efficiency was
nation of the proton centre-of-mass energy E and the ≈10% at 1 MeV γ-ray energy.
p
number of counts N in each proton peak i. The intensi- In order to create the γ spectrum correlated with im-
p
ties Ii of the proton peaks, which are important for the plants of a given nuclear species, one has first to define
p
extraction of the β-decay strengths, are then given by: a β(-p)-γ event. This is done by taking all the γ events
Ni
Ii = p . (6)
p Nimp (1−τ) V300
e (a)
k
TthheedeaxucgithatteironnuecnleeurgsyisEoXbtaoifneeadchbyleavdedliingpoEppulaantdedSipn. nts / 4 220500
It should be noted that in this kind of experiment both u
o
C
thekineticenergyoftheprotonandtherecoilenergyare
150
absorbed in the DSSSD.
100
50
F. Analysis of the gamma spectrum
0
0 1000 2000
Four EXOGAM Ge clovers were used to detect the β-
g energy [keV]
delayed γ rays. Each clover comprised four Ge crystals,
300
giving a total of 16 Ge crystals. Two parallel electronic V
e (b)
chainswithdifferentamplifierswereusedtodetectγ rays 4 k250
up to 2 MeV and γ rays of higher energy. The first elec- s /
tronic chain was used in the analysis of all the γ rays up nt200
u
to 2 MeV. In the spectra obtained by using the second Co
electronic chain a problem was detected during the data 150
analysis. As seen from known peaks, a regular deforma-
100
tion pattern was observed, i.e., a distortion of each peak
inaintervalof≈60keV.Thisaffectedtheanalysisofthe 50
higher-energyγ rays,particularlyfor48Febecauseofthe
poor statistics. 0
0 1000 2000
TheGecrystalswerecalibratedinenergybyusingthe g energy [keV]
γ lines from 60Co, 137Cs and 152Eu sources. The align-
300
V
mentbetweenthespectrameasuredinthe16crystalswas e (c)
k
cross-checked and a summed spectrum was constructed. 4 250 511
Theenergyresolutionwas4keVFWHMforthe60Coline s /
at1.33MeV.Theγ detectionefficiencywascalibratedby unt200
o
using the γ lines from the 60Co, 137Cs, 133Ba and 207Bi C
150
100
y
c
n 50 1835
e
ci
effi 00 1000 2000
γ 10-1 133Ba g energy [keV]
207Bi FIG. 9: γ-ray spectra for decay events correlated with 56Zn
207Bi implants. The spectrum (a) corresponds to time correlations
60Co from 0 to 1 s (red-dashed zone in Fig. 5) and contains both
137Cs trueandrandomcorrelations. Thebackgroundspectrum(b)
iscreatedfortimecorrelationsintheblue-dottedzoneinFig.
10-2 102 103 5,normalizedbythetimeintervalusedandcontainsonlyran-
γenergy[keV] doms. Theremovaloftherandomsisachievedbysubtracting
thespectrum(b)from(a)anditisshowninthespectrum(c).
FIG. 8: Calibration of the efficiency for γ detection. Data In addition to the 511 keV γ line associated with the annihi-
points from the 60Co, 137Cs, 133Ba and 207Bi sources are lation of the positrons emitted in the decay of 56Zn, a peak
shown, together with a fit by the function from Ref. [19]. belonging to the daughter 56Cu is seen at 1835 keV [7].
8
in coincidence with the β(-p) decays. Then the β(-p)-γ inferred from the intensities of the proton peaks. How-
eventsarecorrelatedwiththeimplantationsignals,inthe ever, the de-excitation of the T = 2, IAS via proton de-
same way as was done in Section IIIA. The background cay is isospin-forbidden and it can only happen because
subtraction procedure is analogous to that adopted to of a T = 1 isospin impurity in the IAS. In such cases
create the DSSSD spectrum (Section IIIE). An example competition between β-delayed proton emission and β-
of the resulting γ spectra is shown in Fig. 9 for 56Zn. delayed γ de-excitation from the IAS becomes possible,
Aγ spectrumwascreatedbyselecting(β(-p)-γ)-implant alsobecauserelativelylowprotonenergiesareusuallyin-
time correlations from 0 to 1 s, which contains both true volved. Weindeedobservesuchcompetitioninthedecay
andrandomcorrelations(Fig. 9a). Abackgroundγspec- of 48Fe, 52Ni and 56Zn. 56Zn is a special case where the
trum, containing only randoms, was formed by setting a competitionbecomespossibleevenatenergieswellabove
gate on the correlations in the past (Fig. 9b). The two S . Thus for all three nuclei the intensities of the pro-
p
spectra were then normalized to the time interval used ton and γ transitions from the IAS have to be added to
andthespectruminFig. 9bwassubtractedfromthatin get the correct β feeding to the IAS, and hence the right
Fig. 9a to produce Fig. 9c. amount of Fermi strength. Furthermore, in the case of
Theγ spectrumcoincidentwithdecayscorrelatedwith 56Znweobserved theexotic β-delayedγ-protondecayin
agivenionisthenanalyzed. Theγ linesofthisspectrum three cases [7]. Therefore for a proper determination of
are good candidates for β-delayed γ transitions belong- B(GT) of a given level the intensity deduced from the
ing to the ion of interest. The half-life associated with proton transition has to be corrected for the amount of
each γ line is determined from the fit of a correlation- indirect feeding coming from the γ de-excitation.
time spectrum gated on that line, after subtraction of a The measured T and I were used to determine the
1/2 β
background correlation-time spectrum obtained by set- B(F) and B(GT) values according to the equations:
tinganenergygateonthetwosidesoftheγ line(mainly
Compton background). This half-life is compared to the IIAS(E )
B(F)=K β IAS , (7)
half-life of the nucleus. Such a procedure allowed the f T
IAS 1/2
association of the 1835 keV γ line with 56Zn [7].
Gamma-proton coincidences are also obtained either
bspyepctlarucimngocronbdyitpiounttsinogn tghaetepsrootnonthpeeaγkslionfest.heIDnScSaSseDs B (GT)= K Iβj(Ej) , (8)
such as 56Zn, where most of the γ decay is followed by a j λ2 fj T1/2
proton emission, the γ-proton coincidences allow for the
where the index j indicates the daughter state at en-
identification of weak γ lines and further confirm that
ergy E , f = f(Q − E ,Z) is the Fermi factor [20],
these transitions belong to the decay of 56Zn. j j β j
K = 6143.6(17) [5] and λ = -1.2701(25) [21].
EachγlinewasfittedbyaGaussianwithalinearback-
ground to extract the energy centroid E and number of
γ
counts N . The intensity of the line, I , was obtained
γ γ IV. EXPERIMENTAL RESULTS
according to either Eq. 3 or 4 depending on the case.
Inthissectionweshowtheexperimentalresultsforthe
T = -2 nuclei 48Fe, 52Ni and 56Zn. The total numbers
G. Determination of B(F) and B(GT) z
of implantation events N , the half-lives T and the
imp 1/2
total proton-emission branching ratios B are given in
For the even-even T = -2 nuclei discussed here, two p
z Table I.
kinds of state are expected to be populated in β decay:
the T = 2, Jπ = 0+ Isobaric Analogue State (IAS), fed
bytheFermitransition,andanumberofT =1,Jπ =1+ TABLE I: Total numbers of implantation events, half-lives
states due to Gamow-Teller transitions. In the present and total proton-emission branching ratios for the decays of
section we describe the procedure used for the determi- 48Fe, 52Ni and 56Zn. In the lower half of the table results
from Refs. [8, 22, 23] are shown for comparison.
nation of the Fermi and GT transition strengths, B(F)
and B(GT), respectively. The peculiarities observed in
Isotope N T (ms) B (%) Ref.
imp 1/2 p
thedecayofeachnucleuswillbeaddressedinSectionIV.
48Fe 49763(268) 51(3) 14.4(7) this work
Foreachnucleus,fortheprotonandγ peaksidentified
52Ni 532054(729) 42.8(3) 31.1(5) this work
in the DSSSD and γ spectra respectively, we determined
the energies of the peaks (from the centroids obtained 56Zn 8861(94) 32.9(8) 88.5(26) this work
in the fits) and the intensities of the transitions (from 48Fe 154241 45.3(6) 15.9(6) [8]
the areas of the peaks). The β feeding I to the states 44(7) [22]
β
populated in the daughter nucleus is then deduced. 52Ni 272152 40.8(2) 31.4(15) [8]
In proton-rich nuclei the proton decay is expected to 38(5) [23]
dominateforstateswellabove(>1MeV)theprotonsep- 56Zn 630 30.0(17) 86.0(49) [8]
aration energy S and so usually the β feeding is readily
p
9
Our T values are larger than those in the litera- s
1/2 m1000
ture, nevertheless using the same analysis procedure we 0
footuhnerdnaugcoleoid, saugcrheeamse4n9tFewiatnhdR5e3fN. i[.8]Inforcotmhepharailsfo-lnivwesitohf nts / 1 800 48Fe
the previous study [8], the present experiment achieved u
o
a higher energy resolution for protons, 70 keV FWHM, C 600
T = 51(3) ms
thankstotheuseofathinnerDSSSDdetectorandbetter 1/2
preamplifiers. The improved resolution, together with 400
the increased statistics, allowed us to establish for the
first time the decay scheme of 56Zn and to observe the 200
exotic β-delayed γ-proton decay [7].
New and detailed spectroscopic information has also -200 -100 0 100 200 300 400 500
been obtained on the β decays of 48Fe and 52Ni be- Correlation time [ms]
cause of the improved experimental conditions. The de-
FIG. 10: Spectrum of the time correlations between all
cay schemes of 48Fe and 52Ni have been enriched with the 48Fe implants and each proton decay (DSSSD energy
manynewstatesidentifiedinthecorrespondingdaughter E > 0.94 MeV,withtheadditionalconditionE ∈/[1.85,2.23]
p p
nuclei, and the β-decay strengths have been extracted. MeV to remove the 49Fe contaminant).
Thedetailsforeachofthethreenucleiunderstudyare
discussed in the following sections. V
e (a)
k
0 800
2
s /
A. Beta decay of 48Fe nt 600
u
o
C
The 48Fe nucleus was first detected at GANIL [24]. 400
S
ResultsfromdecaystudieswerepresentedinRefs. [8,22]. IA
Fig. 10 shows the correlation-time spectrum for 48Fe 200
obtained in our experiment, where proton decays with
energyabove0.94MeVhavebeenselectedintheDSSSD 0
and the region corresponding to the 49Fe impurity (see 0 1 2 3 4 5 6
Decay energy [MeV]
below) has been removed. The half-life is determined by
fitting the data including the β decay of 48Fe (Eq. 1) eV S) (b)
and the random correlation background (Section IIIB). k A
A half-life T = 51(3) ms is obtained. The maximum 20 200 6 (I 2
likelihood an1d/2least squares minimization methods gave nts / 150 3.03 8 3.63 6 2 0
theTshaemechraesrugeltd.-particle spectrum measured in the Cou 16 3.50 3.72 e 4.31 12 4.53 68
DSSSD for decay events correlated with 48Fe implants is 100 3.2 49F 4.4 4.7
shown in Fig. 11a. The large bump observed at low en-
ergy is due to the detection of β particles not coincident 50
with protons. Nine discrete peaks are identified above
thisbumpandinterpretedasbeingduetoβ-delayedpro- 0
1 1.5 2 2.5 3
ton emission. They are fitted as explained in Section
Decay energy [MeV]
IIIE. The fit is shown in Fig. 11b where the peaks are
labelled according to the corresponding excitation ener-
FIG. 11: (a) DSSSD charged-particle spectrum for decay
gies in 48Mn, obtained as EX = Ep + Sp with Sp = events correlated with 48Fe implants. (b) Fit of the peaks
2018(10) keV (see Section V). The proton decay of the related to the proton emission following the β decay of 48Fe.
IAS is identified at E = 3.036(2) MeV as in Ref. [8]. Peaks are labelled according to the corresponding excitation
X
The additional peak visible at E ≈ 2 MeV (in blue) energies in the β-daughter 48Mn. The peak labelled as 49Fe
p
is due to a residual contribution (3.0(3)%) of the 49Fe (inblue)isduetoaresidualcontaminationfromthisisotope.
contaminant. As explained in Ref. [8], the background
subtraction procedure cannot remove completely the ac- from 48Fe below the 49Fe peak. Hence in the construc-
tivityofverystronglyproducedisotopessuchas49Fe. By tion of the correlation-time spectrum, besides imposing
imposing an increasingly restricted identification cut on a DSSSD threshold of 0.94 MeV, we have also removed
48Fewecanprogressivelygetridofthe49Fecontaminant, the energy region corresponding to the 49Fe peak by im-
but at the price of poorer statistics. We have chosen the posing E ∈/[1.85,2.23] MeV. In this way we get a B =
p p
reasonable compromise of obtaining a good separation 14.4(7)%. Since in Ref. [8] the residual 49Fe impurity is
between the residual 49Fe peak and the 48Fe peaks. We notremoved,theygetaslightlydifferentvalue,15.9(6)%.
have also checked that there is no visible contribution If we include the 49Fe peak we also get 15.1(7)%.
10
V800
e 90 TABLE II: Correction of the intensity of the 48Fe β-delayed
k700
2 proton emission due to the coincidences with the 98 keV γ
s/600 ray (see text). Centre-of-mass proton energies Ep, excita-
nt 313 tionenergiesE in48Mn,theintensitiesbeforecorrectionIi
u500 X p
Co 98 (normalized to 100 decays), the corrections derived from the
400 spectrum in coincidence with the 98 keV γ ray, ∆I (%) (see
p
300 49Fe Fig. 13 and text), and the intensities after correction Ipf.
200 E (keV) E (keV) Ii(%) ∆I (%) If(%)
p X p p p
100 2499(10) 4517(14) 1.2(5) +0.1 1.3(5)
0 2381(10) 4399(14) 0.8(4) +0.2 -0.1 0.9(4)
100 150 200 250 300 350
2281(10) 4299(14) 1.3(3) +0.1 -0.2 1.2(3)
γenergy[keV]
1695(10) 3713(14) 0.7(2) +0.6 1.3(2)
FIG. 12: γ-ray spectrum for decays correlated with 48Fe. 1601(10) 3619(14) 1.5(2) -0.6 0.9(3)
1018(10) 3036(2)b 4.5(3) +0.3 4.8(3)
eV S) b IAS.
k A
unts / 20 125000 3.036 (I 3.6193.713 299399517 ctthhomee 3efis.r6sf1tr9oemxacntidhtee3dd.7se1tc3aatyMeooefVfth4p7eCeoarbk.sseHrhveaenvdcee3b.t7ehe1en3iMcnotereVrnesclietteviedeslbtoyof
Co 100 4.4.4. shifting this 0.6% intensity from the lower energy level
to the upper one, as indicated in Table II. At higher
energy a triplet of peaks is observed (4.299, 4.399 and
50
4.517 MeV), the first two of which are also separated by
around 100 keV, for which a small amount of intensity
0
is also observed in coincidence with the 98 keV γ ray
0 0.5 1 1.5 2 2.5 3 (dashed-redhistograminFig. 13). Thustheintensitiesof
Decay energy [MeV]
this tripletof peakshavebeen corrected ina similar way
(see Table II). Finally, in the γ-gated spectrum a small
FIG. 13: DSSSD charged-particle spectrum correlated with
peak (of intensity 0.3%) is seen at E ≈ 0.9 MeV, which
48Feimplants. Theblack-emptyhistogramisthefullDSSSD p
is attributed to the decay of the IAS to the first excited
spectrum. The dashed-red histogram is gated on the γ line
statein47Cr,thusthisintensityisaddedtotheIASone.
at 98 keV and scaled up to account for the γ efficiency.
Table II shows the corrections and the intensities, before
The γ-ray spectrum measured in coincidence with all and after correcting.
the decays correlated with the 48Fe implants is shown in The weight of evidence outlined above supports the
Fig. 12. Threeγlinesareobservedat90,98and313keV. decay scheme shown in Fig. 14. There is an alternative
The fourth line visible in Fig. 12 at 261 keV comes from explanation, namely that the levels at 3.619 and 4.299
the residual 49Fe contaminant. A further γ ray of 2634 MeV do not exist and the corresponding proton peaks
keV is expected in the decay of 48Fe [8], which we can are due to transitions from the 3.713 and 4.399 MeV
only partially observe because of the problem affecting levels, respectively, to the first excited state in 47Cr. To
thelow-amplificationelectronicchain(seeSectionIIIF). indicate this possibility we show the levels at 3.619 and
Thus for this γ ray we took I = 30(5)% from Ref. [8] 4.299 MeV with dashed lines in Fig. 14.
γ
to calculate the β-decay strength. The coincidence with the 98 keV γ ray selects proton-
Gamma-protoncoincidenceswereperformedforallthe decay events only. The half-life associated with the γ
γ rays observed. As expected, the γ lines at 90 and 313 lineat98keVagreeswellwiththe48Fehalf-lifeobtained
keVarefoundtobecoincidentwiththeβ bump. The98 in Fig. 10. This is an additional confirmation that the
keV line comes from the decay of the first excited state fit in Fig. 10 is not affected by some possible residual
to the ground state in the proton-daughter 47Cr [8]. contributionfromtheβtailintheregionE >0.94MeV.
p
It is worth noting that the pair of proton peaks at Our observations are summarized in the 48Fe decay
3.619 and 3.713 MeV differs in energy by approximately scheme in Fig. 14 and in Table III, which gives the en-
100 keV, close to the energy of the first excited state ergies and intensities of the proton and γ peaks, the β
in 47Cr. The DSSSD spectrum gated on the γ line at feedings, the B(F) and B(GT) strengths (where we used
98 keV, corrected by the corresponding γ efficiency, is Q = 11202(19) keV determined in Section V). Fig. 14
β
shown in Fig. 13 (dashed-red histogram) and compared also shows the half-lives of the daughter nuclei [25].
with the full DSSSD spectrum (black-empty histogram). The IAS decays by both proton emission and γ de-
The98keVγ rayisfoundtobeincoincidencewithpart excitation, via the γ cascade at 2634, 90 and 313 keV.
ofthe3.619MeVprotonpeak,indicatingthatthispartof Indeedbarrier-penetrationcalculationsgiveapartialpro-
the intensity (0.6%), given in Table II as ∆I in percent, ton half-life of t ∼ 10−17 s, two orders-of-magnitude
p 1/2
