PHYSICAL REVIEW C 89, 064315 (2014)
Multiparticle emission in the decay of 31Ar
G. T. Koldste,1 B. Blank,2 M. J. G. Borge,3 J. A. Briz,3 M. Carmona-Gallardo,3 L. M. Fraile,4 H. O. U. Fynbo,1 J. Giovinazzo,2
B. D. Grann,1 J. G. Johansen,1,* A. Jokinen,5 B. Jonson,6 T. Kurturkian-Nieto,2 J. H. Kusk,1 T. Nilsson,6 A. Perea,3 V. Pesudo,3
E. Picado,4,7 K. Riisager,1 A. Saastamoinen,5,† O. Tengblad,3 J.-C. Thomas,8 and J. Van de Walle9
1Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark
2Centre d’Études Nucléaire de Bordeaux-Gradignan, CNRS/IN2P3-Université Bordeaux I, F-33175 Gradignan Cedex, France
3Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain
4Grupo de Fı́sica Nuclear, Universidad Complutense, E-28040 Madrid, Spain
5Department of Physics, University of Jyväskylä, FIN-40351 Jyväskylä, Finland
6Fundamental Fysik, Chalmers Tekniska Högskola, S-41296 Göteborg, Sweden
7Sección de Radiaciones, Universidad Nacional, Heredia, Costa Rica
8GANIL, CEA/DSM-CNRS/IN2P3, F-14076 Caen Cedex 5, France
9CERN, CH-1211 Geneva 23, Switzerland
(Received 20 February 2014; published 25 June 2014)
A multihit capacity setup was used to study the decay of the dripline nucleus 31Ar, produced at the ISOLDE
facility at CERN. A spectroscopic analysis of the β-delayed three-proton decay of 31Ar is presented for the first
time together with a quantitative analysis of the β-delayed 2pγ decay. A new method for determination of the
spin of low-lying levels in the βp daughter 30S using proton-proton angular correlations is presented and used
to determine that the spin of the 5.2-MeV level is most likely 3+ with 4+ also possible. The half-life of 31Ar is
found to be 15.1(3) ms. An improved analysis of the Fermi β strength including the β3p-decay mode gives a
total measured branching ratio of 3.60(44)%, which is lower than the theoretical value found to be 4.24(43)%.
Finally, a previously unidentified γ transition from the isobaric analog state in the decay of 33Ar has been found.
DOI: 10.1103/PhysRevC.89.064315 PACS number(s): 23.40.Hc, 27.30.+t
I. INTRODUCTION detail in two experiments at ISOLDE in 1995 [4] and 1997 [5]
and found to be mainly sequential emission. A simultaneous
Because dripline nuclei have large β-decay Q values component is predicted [6], but there is still no experimental
and populate daughter nuclei with low particle-separation evidence for it. With the setup used in the experiment presented
energies, their decays are characterized by having many open here, which had a high efficiency for proton detection with a
channels [1]. This implies that decays at the dripline provide good energy and angular resolution, the decay of 31Ar can
unique possibilities to study exotic decay modes such as two- now be used to study another exotic decay mode; β-delayed
and even three-proton emission. The many decay channels 3p emission, which has previously only been observed in two
unfortunately also complicate the extraction of the decay other nuclei, 45Fe [7] and 43Cr [8,9], while this decay mode
strength. Here we show that by using a multihit detection only recently was discovered in the decay of 31Ar by Pfützner
setup it is possible to both map the β strength and study the
et al. [10]. The study of 31Ar can therefore now be used to
exotic decay modes for the dripline nucleus 31Ar. bring the same level of information on this decay mode as it
The proton-rich argon isotopes can be produced with brought to the β2p-decay mode roughly 15 y ago.
relative high yields and low contamination from CaO targets
A detailed mapping of the β3p-decay mode is needed to
using the Isotope Separation On-Line (ISOL) technique, which
31 evaluate the β strength at high energy. Precise measurement ofmakes Ar an ideal nucleus to choose for this type of study.
A schematic decay scheme of 31Ar is shown in Fig. 1. During the β3p channels will also make it possible to reassign decays
the past decades the decay of this isotope has been studied that have previously been wrongly assigned as β2p decays and
in several experiments at the ISOLDE radioactive ion beam thus the strength can be correctly placed in the decay scheme.
facility at the European research organization CERN. The first Correct assignment of 2p events also requires a good detection
interest in this nucleus arose from the possibility of detecting efficiency for γ rays, which enables detection of 2pγ events
ground state two-proton (2p) decay, but this decay mode has and correct identification of the final state of the 2p decay29
not yet been identified in this decay. However, 31Ar has been in P.
demonstrated to be a prolific β-delayed 2p emitter [2,3]. The Owing to the sequential nature of the 2p decay it can be used30
mechanism of the β-delayed 2p decay in 31Ar was studied in to study levels in S above the proton threshold, which are
relevant for nuclear astrophysics. Experimental limits on the
ratio between the proton and γ partial widths have been found
for low-lying levels in 30S using the β2p decay of 31Ar from
*Present address: Institut für Kernphysik, Technische Universität the same experiment discussed below [11]. As demonstrated
Darmstadt, D-64289 Darmstadt, Germany. here, the 2p decay mode can also be used to determine level
†Present address: Cyclotron Institute, Texas A&M University, spins by analyzing proton-proton angular correlations. Until
College Station, TX 77843-3366, USA. now only tentative spin assignments have been suggested by
0556-2813/2014/89(6)/064315(10) 064315-1 ©2014 American Physical Society
G. T. KOLDSTE et al. PHYSICAL REVIEW C 89, 064315 (2014)
18.38
31Ar
p 12.31 IAS
p p ?
1.78 p 4.083.45
3.11 p 5.85 p
28 2.75 2.42 5.39Si + 3p 1.95 5.221.38 p 4.81
4.69
29 4.40P + 2p 3.402.21
30 0.28S + p 31Cl
FIG. 1. Decay scheme for the β decay of 31Ar, not to scale. Selected proton and γ transitions are drawn.
reference to assignments in the mirror nucleus [12]. A separate The geometry and energy calibrations of the DSSSDs
analysis of the Gamow-Teller strength using the β3p decay of were made using a beam of 33Ar produced from the same
31Ar is in preparation [13]. target-ion source unit as 31Ar. A comprehensive description
In Sec. II the experiment is described. Section III A de- of the setup can be found in Ref. [11]. The pad detectors
scribes the determination of the half-life of 31Ar; an analysis of behind the DSSSDs were energy calibrated by using a standard
the spectroscopy of the β3p-decay mode follows in Sec. III B. α calibration source (containing 148Gd, 241Am, 239Pu, and
The analysis of the β2pγ events is presented in Sec. III C. 244Cm). The total proton detection efficiency, p, is taken as the
The new, improved results on the Fermi strength is given in total solid angle of the silicon Cube, which is 43(2)% of 4π .
Sec. III D. The new method for finding the spin of low-lying Two Miniball germanium cluster detectors [17] were
levels in 30S is presented in Sec. III E and applied to the case of situated outside the cube chamber behind detectors 3 and 4.
the 5.2-MeV level, which lacks firm spin assignment. Finally in Each Miniball cluster consists of three crystals, but
Sec. III F the γ transitions in the decay of 33Ar are discussed, unfortunately one of the crystals of the cluster behind
including identification of a previously unidentified γ line
from the isobaric analog state (IAS). In Sec. IV the main
results are summarized.
1
II. THE EXPERIMENT
The experiment was performed at the ISOLDE facility at 4
CERN, Switzerland, using the ISOL technique [14] with a
powder CaO target and a versatile arc discharge plasma ion 36
source [15]. The 60-keV ion beam was guided through the
General Purpose Separator [14] to separate the desired argon
isotope from other produced nuclei. However, a significant
background from nitrogen (as N2 and N2H) was present in
2 5
the final beam. An average yield of 31Ar of about 1 ion per
second was obtained for a run time of 7 days. The beam was
collected in a 50 μg/cm2 carbon foil situated in the middle of
the silicon cube detector setup [16]. The silicon cube consists FIG. 2. (Color online) The detector setup used for the experiment
of six double-sided silicon strip detectors (DSSSDs) in a cube consisting of a cube of DSSSDs and two Miniball Ge detectors. The
formation; see Fig. 2. For this experiment one detector with beam enters between DSSSDs 5 and 6 and is stopped in a carbon foil
thickness of 69 μm (No. 1), one detector with a thickness mounted on a small metal holder entering between DSSSDs 3 and 5.
of 494-μm (No. 5), and four detectors with a thickness close The top of the cube with three of the DSSSDs is lifted, following the
to 300 μm (Nos. 2, 3, 4, 6) were used, with 1500-μm-thick dotted black line, for better visualization. The two Miniball detectors
50×50-mm unsegmented silicon-pad detectors used for back- that were situated outside the cube behind DSSSDs 3 and 4 are not
ing behind four of the detectors (Nos. 1, 2, 3, 6). shown in the picture.
064315-2
MULTIPARTICLE EMISSION IN THE DECAY OF 31Ar PHYSICAL REVIEW C 89, 064315 (2014)
DSSSD 3 gave no signal. A preliminary energy calibration
was made using 137Cs and 60Co. This was supplemented by 3
a 152Eu source together with high energy γ lines from the
decay of 16,18N, 15C, and 32,33Ar recorded on-line. Together,
this gives an energy calibration up to an energy of 2.5 MeV 2
with an uncertainty of 1 keV, while above this energy, the
uncertainty is estimated to be 3 keV.
A total efficiency calibration was made for the two Miniball
detectors. First, an absolute efficiency calibration was made 1
using the low-lying γ lines from a 133Ba source with a known
activity of 17.0(3) kBq at the time of the experiment. The
detection efficiency for the γ lines from the 152Eu source, 0
corrected for emission probabilities using [18], is then scaled, 3 4 5 6 7 8Q  (MeV)
using the 302- and 356-keV points from 133Ba and placing the 3p
344-keV point from 152Eu on a straight line between these. The FIG. 3. (Color online) Q3p for three-particle events. The his-
absolute γ efficiency above 600 keV was then found by fitting togram shows all the events where the first two particles detected
the 152Eu points to a relative efficiency curve determined in have energies above 800 keV and the third has an energy above
a slightly different detector configuration [19] (that used four 500 keV unless it is in detector 5, where it also has to have an energy
different γ sources: 152Eu, 60Co, 207Bi, and 11Be). The result, above 800 keV. To obtain the histogram in green (gray), events that
using the formula in Re{f. [20], is ( ) are most likely not real 3p events were removed as described inthe text.
εγ (E) = E0.21 exp −2.669 − 1.457 log10
[ ( )] } MeV from noise and β particles the following energy gates are used:2
− E The energy of the first two particles detected should exceed0.231 log10 , (1)MeV 800 keV and the energy of the third 500 keV unless it is in the
thick detector (detector 5), where a β particle can deposit more
with an estimated uncertainty of 10%. energy. In the latter case the gate is set at 800 keV. The reason
For normalization of the total number of 31Ar collected for allowing the third particle to have an energy less than the
during the run, the largest one-proton peak at 2083 keV with others is that the 3p decay could go through the 3447.6(4)-keV
an absolute branching ratio of 26.2(29)% [21] is used. A small 7− level in 29P 699 keV above the proton threshold. In
fraction of the activity could only be seen from the beam 2 5+
entrance side. Furthermore, the target holder shadows several principle, the decay can also go trough the 3105.9(3)-keV 2
pixels in particular for detectors 1 and 2. These effects are all level only 357 keV above the proton threshold. However, the
included in the detailed Monte Carlo simulations discussed penetrability for this level is roughly a factor of 25 below the
7−
below to extract final branching ratios. It is estimated that penetrability for the 2 level. Furthermore, it is not possible
the total number of 31Ar collected during the experiment is with our setup to distinguish these low-energy protons from
5.6(6)×105. β particles. We thus first assume that there are no transitions+
through the 52 level. At the end of this section we return to
this issue and argue that this is a good assumption.
III. RESULTS AND DISCUSSION
The efficiency of detecting a β particle in coincidence with
A. Half-life of 31Ar a proton, using the same analysis cuts as for protons, can be
The half-life of 31Ar is found in the same way as in Ref. [5]. estimated to be 0.43(5)% from events with a single proton and a
Data were recorded continuously, but only events happening β particle. Using this efficiency we deduce from the measured
after the beam gate was closed 100 ms after each proton impact number of 2p event an expected number of β2p events of
on the production target were considered for the half-life deter- 29(4), roughly half of the total number of three-particle events
mination. Only the strongest 1p peak at 2083 keV, correspond- of 62. Some of these background events can be identified if
ing to an energy range between 2040 and 2120 keV, was used to the Q2p value of two of the particles corresponds to one of the
minimize background contributions. In this way the data could prominent two-proton transitions as was earlier demonstrated
be fitted using the maximum likelihood method to a single in Ref. [23]. Also, some of the three-particle events are all in
exponential component and a constant background. This gave the same detector or have a too high Q3p value. In this way
a half-life of 15.1(3) ms, which is consistent with previous 21 background events can be identified and removed, and only
determinations of 14.1(7) [5], 15(3) [3], and 15.1+1.3 ms [22]. the 41 remaining events are included in the following analysis.−1.1 These events are shown as the green (gray) histogram in Fig. 3.
A peak is seen in the green (gray) histogram of Fig. 3
B. β-delayed three-proton spectroscopy around 4.89(29) MeV containing 19 events (between 4.3 and
In the following we present the first spectroscopic analysis 5.5 MeV). To investigate the spread in Q3p owing to detection
of a β-delayed three-proton decay. A spectrum of the Q3p resolution a simulation was made, which showed that the
values calculated for the 3p events observed during the expected full width at half maximum is more than 300 keV. A
experiment is shown in Fig. 3. To eliminate contamination real peak of events from a given level in 31Cl is thus expected
064315-3
Counts / 40 keV
G. T. KOLDSTE et al. PHYSICAL REVIEW C 89, 064315 (2014)
to be as broad as the one at 4.89(29) MeV. This peak is most
likely attributable to the 3p decay of the IAS, because it 4
corresponds to a 31Cl level at an energy of 12.32(29) MeV.
It is interesting to note that it is only approximately half of 3
the 3p events that belong to the decay of the IAS. The other
half stems from transitions from levels in 31Cl above the IAS.
Owing to the large Q window for particle emission, many 2
decay channels are open; only a small fraction will therefore
decay by two-proton emission to the ground state in 29P. To
make a correct assignment, detection of 3p and 2pγ branches 1
is required. Using now the β3p decay a better determination of
the Gamow-Teller strength at high energy can be performed. 0
The 3p spectrum is discussed in detail separately in Ref. [13]. 3 4 5 6 7Q  (MeV)
The mechanism of the β-delayed 3p emission from the 2p
previously studied nuclides has not been determined. If
31 FIG. 5. (Color online) Q calculated from the two particles withsequential emission occurs in the case of Ar, it should be 2phighest energy. The histogram is from the 41 events in the green (gray)
possible to identify the known levels in both 30S and 29P from histogram of Fig. 3. The part that is green (gray) is the 19 events
the energy of the protons. However, owing to limited statistics around 4.84(29) MeV in the green (gray) histogram of Fig. 3.
and the considerable level density for high excitation energies
in 30S, it will not be possible to do this for 30S. If the decay
goes through levels in 29P, these can be identified via the suggests that the 3p emission is consistent with being fully
difference between the Q value and the Q value, because sequential, but owing to the large expected spread in the3p 2p
this difference corresponds to the energy of the level populated Q3p value a considerable simultaneous emission contribution
in 29P minus the proton separation energy. The reason for using cannot be excluded. When the energies of all three particles
the two Q values is that these can be extracted directly from are above 1.2 MeV, the particles are most likely all protons,
29
the experimental data and that a correction for the recoil of the but the density of states in P is then so high that it is easy to
daughter nucleus is included. The Q value can be calculated interpret a simultaneous decay as a sequential decay. This is3p
independently of the decay mechanism, while for theQ value not a problem for the level at 3447.6(4) keV (corresponding to2p
one must choose which particles should be considered to be a difference between Q3p and Q2p of 699 keV). The problem
the first two in the decay. In Fig. 4 this difference is plotted here is that one of the particles has an energy around 0.7 MeV
for two different choices together with lines indicating the and it is thus difficult to distinguish protons from β particles.
levels in 29P. For the black dots it is assumed that the first The majority of these events stem from the peak in the Q3p
two particles are the ones with the highest energy. This is, spectrum around 4.89(29) MeV (see Fig. 3), which most likely
however, not necessarily a reasonable assumption for all the belongs to the decay of the IAS. Their Q2p value can be seen
events. Instead, the first two particles can be chosen so that the in Fig. 5: More than half of them lie around 4.14(13) MeV.
difference between the Q and the Q Assuming they go through the 3447.6(4)-keV level in
29P, this
3p 2p values fits the known 31
levels in 29P (only the first five levels were included). This corresponds to a Cl energy at 12.27(13) MeV, in complete
choice is plotted as the green (gray) triangles. This analysis agreement with the value of 12.32(29) MeV from the Q3p
value. These events cannot be 2pβ events; if they were, one
would expect more than 2×103 events at this energy in theQ2p
spectrum made from 2p events. While there are indications
8 of small peaks around this energy, they contain less than 70
events. The IAS 3p decay can thus be assigned partly to go
7 through the level at 3447.6(4) keV in 29P, which supports the
assumption that the events lying close to 699 keV in Fig. 4
6 also are events going through this level.
5 We have also strong indications of events going through the
level at 4080.5(3) keV (corresponding to a difference between
4 Q3p and Q2p of 1332 keV). With the statistics available here
and the expected large spread in the Q3p, this is, however, not
3 conclusive. The sparsity of events with Q3p −Q2p between
0.9 and 1.1 MeV is a strong indication that there are no
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Q3p - Q2p (MeV)
simultaneous 3p decays with a low-energy proton.
We now return to the issue of possible involvement of the
5+
FIG. 4. (Color online) Q3p vs Q3p −Q2p . The lines indicate the 2 level at the 3105.9(3)-keV level 357 keV above the proton
levels in 29P. For the black circles Q is calculated assuming that threshold. By using measurements of the resonance strength,2p
pγ 7−
the first two particles are the ones with the highest energy and for the (2J + 1) , and the lifetime [24] one finds for the 2 level
green (gray) triangles it is calculated to best fit the five levels in 29P that  ∼ max = 51(31) meV and min = 0.038(10) meV,
shown. where max (min) refers to the largest (smallest) width of p
064315-4
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Counts / 40 keV
MULTIPARTICLE EMISSION IN THE DECAY OF 31Ar PHYSICAL REVIEW C 89, 064315 (2014)
+
and γ . For the 52 level one finds  ∼ max = 19(9) meV 5−
and min = 0.46(11) meV. If  7max = γ for the 2 level,
one would expect to see around 700 γ rays at 1493.6 keV, 4
corresponding to the decay of this level to the second excited
level, when gating on two protons. This we do not see in our 3
two-proton-gated γ spectrum; see Sec. III C and Fig. 7. We
therefore conclude that p = max. Looking now at the mirror 2
nucleus 29
− +
Si, where the 72 and
5
2 levels both lie below the
proton threshold, we see that the half-lives of these two levels 1
are 2.63(9) ps and 33(1) fs, respectively. The half-lives of the
two levels in 29P are 9(6) fs and 23(10) fs, respectively. By
comparison it is reasonable to assume that p = max for the 0 1 1.5 2 2.5 3
7− + E  (MeV)
2 level, as deduced above, and p =  for the 5 level. γmin +2
From this it is found that the proton width of the 52 level is FIG. 7. (Color online) The γ spectrum gated on two protons. For
7−111(72) times smaller than the proton width of the level the black spectrum both protons have energies above 800 keV. The2
and it is thus reasonable to assume that the 3p decay through extra events in green (gray) are γ rays where one of the protons has
+
the 5 level is suppressed. an energy between 500 and 800 keV and has not hit detector 5.2
C. β-delayed 2 pγ -decay to be above 800 keV [black + green (gray)]. In the following
all the levels in 29P up to 4.1 MeV are considered and the
The indications of a sequential 3p branch implies that the
29 number of 2pγ events is compared with the one expecteddecay populates higher-lying levels in P than previously from the 1p-gated γ spectrum. Because there is no reason
found. With our setup it was possible to detect γ rays in why the second emitted proton should have an energy above
coincidence with protons and we thus have a chance to see 800 keV instead of just 500 keV, the extra events in green
the γ transitions from these levels. However, the detection (gray) in Fig. 7 are also included.
efficiency is limited and the chance of detecting the γ ray in We now discuss in turn the evidence for the γ rays from
coincidence with both of the emitted protons is thus very small. 29 29 3+
For a real 2pγ event it is 2/ = 4.6 times more likely to detect the relevant states in P. The first excited state in P( 2 ) is atp
it as a 1pγ event than to detect it as a 2pγ event. We therefore 1383.55(7) keV [24]. The corresponding peak is clearly seen in
first search for the transitions from higher-lying levels in 29P both the 1p- and 2p-gated γ spectra. There are 64(11) events
in the one-proton-gated γ spectrum, which is shown in Fig. 6. above background in the 1p-gated spectrum. This implies that
(As previously, 800 keV is used as a lower energy cut on the there should be 14(2) events in the 2p-gated spectrum, which
proton). In this spectrum clear peaks are identified from the agrees very well with the 13(4) measured above background.
5+
lowest states of both 30S and 29P (see Ref. [11]), but owing The second excited state at 1953.91(17) keV ( 2 ) decays
to background in the spectrum there are no clear signatures primarily to the ground state. A peak at this energy is seen in
of levels above the second excited state in 29P. In Fig. 7 the the 1p-gated γ spectrum. It contains 59(15) events, but it is
two-proton-gated γ spectrum is shown. Two different gates are more than twice as broad as the other peaks in the spectrum.
used: one where both particles have energies above 800 keV This and the discussion in Ref. [11] indicates that there might
(black) and one where the second particle has an energy above be other contributions to the peak. From the 59(15) events in
500 keV unless it is in the thick detector 5, where it is required the 1p-gated spectrum one would expect 13(3) events in the
2p-gated spectrum. Only 7(3) events are observed in total, but
if there are other contributions to the peak in the one-proton-
30S gated spectrum the expected number would be smaller.
100 +The third excited state is a 32 state at 2422.7(3) keV,
and it decays also primarily to the ground state. There is
80 30S no significant signal above background in the 1p-gated γ
spectrum at this energy. In the 2p-gated spectrum there are
60 two events with no significant background at 2422(11) keV.
This would imply 9(7) events in the 1p-gated spectrum.
40 29P Considering the background level in this area in the 1p-gated
29P spectrum it is not possible to disprove this.30
20 S 30S The next level is the 3105.9(3)-keV level, which is just+
above the proton threshold. It is a 52 level and decays primarily
0 1 1.5 2 2.5 3 by a 1722.2-keV γ ray. Again there is no significant signal
Eγ (MeV) above background in the 1p-gated spectrum. There are a
maximum of 14(9) events above background, which implies
FIG. 6. (Color online) The γ spectrum gated on one proton with there should be 3(2) events in the 2p-gated spectrum, where
an energy above 800 keV. there are a total of 2.
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Counts / 4 keV
G. T. KOLDSTE et al. PHYSICAL REVIEW C 89, 064315 (2014)
7−The level at 3447.6(4) keV, which was identified in the Ref. [11] and in the results presented above for the IAS, there2
3p decay, has a total half-life of 9(6) fs. It decays primarily by are additional contributions. In addition to the 3p channel, all
a 1493.6-keV γ ray. There is a hint of a peak in the 1p-gated the levels up to the vicinity of the proton thresholds should,
γ spectrum at this energy containing 14(7) events. From this in principle, be included for both the 1p and the 2p channels.
one expects 3.0(15) events in the 2p-gated spectrum, where To get a precise determination of the branching ratios for the
there are a total of 2. different channels it is important to use spectra with a good+
The level at 4080.5(3) keV is a 7 level with a total half-life energy resolution and to precisely know the total number of2 31
of 11(1) fs. It decays primarily by a 2126.3-keV γ -ray. In the Ar collected and the detection efficiencies. For this reason
1p-gated γ spectrum, there is no indication of a peak at this only the 300-μm DSSSDs with backing are selected for this
energy. There are 5(5) events, which means that there should analysis. Of these, detector 2 had several broken strips and
be 1(1) event in the 2p-gated spectrum and there are a total of less accurate efficiency determination owing to shading from
2 events. the target holder. This leaves only detectors 3 and 6, which
In summary, the γ decays observed for the six lowest levels are used to determine the branching ratios for the two- and
in 29P give consistent results for the 1p- and 2p-gated γ one-proton decays in the following. The statistics is so low for
spectra, but only the feeding of the lowest two can be seen the three-proton decay that all the detectors are needed, and
directly in the γ spectra. the branching ratio is thus found using the data presented in
Sec. III B. It is listed in Table I together with the branching
D. The Fermi strength of the decay ratios found for the two- and one-proton decays. The branchingβ
ratio found here for the three-proton decay to the ground state
The Fermi strength in the β decay of 31Ar has been of 28Si is consistent with the 99% confidence level upper limit
measured previously [5] by considering the 1p and 2p decays of 0.11% found by Fynbo et al. [23].
of the IAS to the lowest states in 30S and 29P. As shown in The two-proton spectrum using only detectors 3 and 6 (with
E > 500 keV) is shown in Fig. 8. The peaks corresponding to
TABLE I. Branching ratios for the decay of the IAS. The 31Cl the decay to the ground state and the first and second excited
energies are found using the masses from Ref. [27] and a proton states of 29P are clearly visible in the spectrum at Q2p values
separation energy for 31Cl of 282.8(44) keV [28]. The decays of 7.6, 6.3, and 5.7 MeV. There is possibly a peak at 5.2 MeV
written in italic correspond to decays not uniquely identified in corresponding to the transition to the third excited state in 29P.
the spectra: There is marginal indication of the two-proton branch Transitions to higher-lying states cannot be identified. The
and the one-proton branches cannot be uniquely assigned to levels branching ratios in Table I are all lower than those reported by
in 30S. The total branching ratio is quoted with and without these Fynbo et al. [5]. The main reason for this is that our energy and
decays. The efficiencies used are different for each of the three decay angular resolution is better for this energy range, making our
modes and the uncertainties stemming from these are included in the
peaks significantly narrower. Reference [5] therefore included
uncertainties for each decay. The correlation is taken into account
for the uncertainty on the total branching ratio. Furthermore, there contributions from decays with Q2p values close to those
is a systematic error of 11% stemming from the normalization (see for the IAS decays. Furthermore, for the decays to excited29
Sec. II), which is not included in the uncertainties. states in P, the background from Gamow-Teller transitions is
estimated and subtracted here, which was not done in Ref. [5].
Three-proton branch The one-proton energy spectrum for detector 3 can be
Final state in 28Si(keV) J π Q3 (MeV) EIAS(MeV) B.R. (%) seen in Fig. 9 (the spectrum for detector 6 is similar). Thep
+ branching ratios are found separately for detectors 3 and 60 0 4.89(29) 12.32(29) 0.039(19) and the average is given in Table I. The large uncertainty
Two-proton branch
Final state in 29P(keV) J π Q2p(MeV) EIAS(MeV) B.R. (%)
0 1
+
2 7.633(4) 12.311(6) 1.47(23)+
1383.55(7) 32 6.251(4) 12.313(6) 0.88(15) 8 IAS → g.s.+
1953.91(17) 52 5.688(6) 12.320(8) 0.40(10)+ IAS → 1st ex.
2422.7(3) 32 5.22(8) 12.32(8) 0.075(50) 6 IAS → 2nd ex.
One-proton branch
Final state in 30S(keV) J π Ep(MeV) EIAS(MeV) B.R. (%) 4
0 0+ 11.57(8) 12.24(8) 0.049(11)
2210.2(1) 2+ 9.46(8) 12.27(8) 0.104(18)
2
3404.1(1) 2+ 8.33(8) 12.30(8) 0.108(17)
3667.7(3) 0+ 12.30(8) 0.101(21)
8.08(8)
3677.0(3) 1+ 12.31(8) 0
+ 0 2 4 6 8 0 50 100 1504687.7(2) 3 12.22(8) 0.38(4) Ei (MeV) Counts / 4 keV7.01(8)
4809.0(3) 2+ 12.34(8)
Total 12.313(4) 3.05(42) FIG. 8. Two-proton spectrum made using only detectors 3 and 6
Total 3.60(44) with a lower cutoff of E > 500 keV. (Left) Q2p vs the energy, Ei , of
the two particles. (Right) The projection onto the Q2p axis.
064315-6
Q2p (MeV)
MULTIPARTICLE EMISSION IN THE DECAY OF 31Ar PHYSICAL REVIEW C 89, 064315 (2014)
of 2915 P(p,γ )
30S, which influences the silicon abundances that
can be directly studied from presolar dust grains believed to be
produced in classical novae. In the last few years the relevant
levels in 30S have been studied intensely [11,12,29–31], such
10 that the energies are now known for the relevant levels, while
some disagreements about the spin assignment remain. In this
section we present a new method for determining the spin of
these levels. The method is used to give the first determination
5 of the spin of the 5.2-MeV level populated in the 31Ar decay.
The method is based on using the sensitivity on spin of
proton-proton angular correlations in 2p decays going through
0 the level of interest. The distribution of angles, θ , between the7 8 9 10 11
E1 (MeV)
two protons can be written as [32]
∑νmax
FIG. 9. The one-proton energy spectrum for detector 3 for high W (cos θ ) = AνPν (cos θ ) ,
energies. ν=0
where Pν is the νth Legendre Polynomial and the sum extends
in the energy is attributable to limited statistics and a large to
uncertainty in the calibration of the back detectors for high
ν = min (2l ,2l ,2j ) ,
proton energies. Because the energy cutoff of the two-proton max 1 2
spectra is 500 keV the branching ratios are given up to the so that one obtains an isotropic distribution if the angular
30S level at 4809.0(3) keV [11] (413 keV above the proton momenta involved are small enough. Here j1(l1) and j2(l1) are
threshold) in the one-proton spectrum. The peaks at 8.1 and the spin (orbital angular momentum) of the first and second
7.0 MeV cannot be separated into two components, even emitted protons, respectively, and j is the spin of the 30S state
though they should both contain contributions from decays coupled with the first proton. The coefficient Aν is given by
to two different levels in 30S. The branching ratios are thus
A = F (l ,j ,j ) b (l ,l )F (l ,j ,j ) b (l ,l )
found for the total contribution from the two levels. ν ν 1 1 ν 1 1 ν 2 2 ν 2 2√
If we neglect isospin symmetry breaking the β strength to ( ′) = 2 l(l + 1)l′(l′ + 1)the IAS isBF = 5. Using the Coulomb displacement energy of bν l,l l(l + 1) + ′ ,l (l′ + 1) − ν(ν + 1)
32,33,34,35Ar extracted from Ref. [25] we estimate the Coulomb
displacement energy of 31Ar to be 6.85(10) MeV, giving where Fν can be found from the tabulation in Ref. [32].
QEC =
31
18.38(10) MeV. With this and our improved half-life In the β2p decay of Ar we expect the excess protons to be
of 31Ar (see Sec. III A) we obtain a total theoretical branching mainly in the sd shell and shall therefore make the assumption30
ratio of 4.24(43)%, where the large uncertainty stems from the that only positive parity states in S will be populated. The
uncertainty on the QEC value. Without this the uncertainty
possible values for A2 in the decay are given in Table II. In
of the total theoretical branching ratio is only 0.09%. A many cases there are two possible values for j and the table
better determination of the mass of 31Ar would thus be very indicates the range spanned by the two extreme situations in
beneficial. The theoretical branching ratio is larger than the which only one j value contributes.
experimental value of 3.60(44)%, but the discrepancy is within To use this method, transitions from distinct levels in31
one standard deviation. The uncertainty on the experimental Cl must be identified with sufficient statistics. This is only30
value cited does not include the relatively large uncertainty possible for the strongest fed level in S at 5.2 MeV. This+
stemming from the normalization of the number of 31Ar ions level has previously been assigned either as 0 [12] based on
in the experiment determined by using the absolute branching levels in the mirror nucleus or as a 3
+ state based on its γ
ratio of the main 1p peak (see Sec. II). The results here decay [29]. To have sufficient statistics all detectors are used
constitute an improvement over the earlier result by Fynbo with a low-energy cutoff on the first particle of 800 keV and
et al. [5], but note that the uncertainties on both the total the second of 500 keV, except for the thick detector 5, where
experimental and theoretical branching ratios quoted there are
underestimated. However, there remain levels in 29P below the TABLE II. The A2 coefficients for 2p transitions calculated for
proton threshold and one above to which two-proton decays the different initial states, J πi (in
31Cl), through five positive parity
could not be extracted. We could also not identify any π 30 1 +γ states, Jm (in S), to a 2 final state (ground state of
29P).
rays corresponding to transitions in 31Cl from the IAS, but
a contribution from these cannot be excluded. Note that γ π π 3 + + +J J 5 7m i 2 2 2
transitions from the IAS have been found in the decay of both
32 +Ar [26] and 33Ar (see Sec. III F). 0 0 0 0
1+ 0 0 0
+
E. Spin of low-lying levels of 30S 2 0 0 [−0.70;−0.25]
3+ [0.15; 0.87] 0 0
A detailed knowledge of the levels just above the proton 4+ [0.76; 1.00] [0.13; 0.95] 0
threshold in 30S is important for determining the reaction rate
064315-7
Counts / 20 keV
G. T. KOLDSTE et al. PHYSICAL REVIEW C 89, 064315 (2014)
2
8 IAS → g.s. 100
IAS → 1st ex.
6 1IAS → 2nd ex.
4 50 4
3
2 5 6
00 2 4 6 8 0 200 400 600 800 0 1 2 3 4 5 6 7
Ei (MeV) Counts / 4 keV E1 (MeV)
FIG. 10. Two-proton spectrum with lower cutoff, E1 > 800 keV FIG. 12. (Color online) Energy of the first particle for transitions
and E2 > 500 keV, except for detector 5, where E2 > 800 keV. (Left) going through the 5.2-MeV level in 30S. The peaks containing most
Q2p vs the energy, Ei , of the two particles. (Right) The projection counts are marked by numbers.
onto the Q2p axis.
uniform. The conclusion for peaks 2 and 3 is less clear: The
800 keV is used. The resulting data are shown in Fig. 10. Kolmogorov test shows with 97.5% confidence that the events
The 30S levels calculated from these events can be seen in in peak 2 are not consistent with a uniform distribution [33],
Fig. 11. The energy of the first particle (the one with the highest but the deviations do not correspond to a standard angular
energy) of the events passing through the 5.2-MeV level are correlation shape because the fit does not give a value for
shown in Fig. 12. Each peak in this spectrum corresponds A2 that is significantly different from 0 (fits including an
to population of the 5.2-MeV level from specific states in
31Cl. The most intense peaks are numbered and are used in
the following analysis. In Fig. 13 the angular correlation for
two of the peaks are shown together with a simulation of Peak 1
the same decay that assumes a uniform angular distribution 12
(i.e., A2 = 0). The simulated curves are fitted to the data for 10
all numbered peaks of Fig. 12 with and without an A2 term.
The resulting A2 values are shown in Table III along with the 8
difference in χ2 for the two fits. Also shown are the results
of a Kolmogorov test (essentially the maximum difference in 6
cumulative distributions scaled with the square root of the 4
number of counts; the 5% significance level then corresponds
to a value of 1.36 [33]) for a comparison between the data and 2
a uniform distribution.
Both the χ2 difference and the Kolmogorov test indicate
12
that the events in peaks 1, 5, and 6 are consistent with being Peak 4
10
8
600
6
4
400
2
0
200 -1 -0.5 0 0.5 1
cosΘ2p
FIG. 13. (Color online) Angular distribution of the two protons
0 5 5.5 6 forming peaks 1 and 4 in Fig. 12 compared with the corresponding
Excitation energy in 30S (MeV) fitted 2p simulations for either isotropic (green solid curve) or
nonisotropic (red dashed curve) distributions. For better visualization
FIG. 11. Energy spectrum for 30S calculated for the events from data are here shown using 45 bins, while the fits are made using
Fig. 10. 90 bins.
064315-8
Counts / 20 keV Q2p (MeV)
Counts / bin Counts / bin Counts / 20 keV
MULTIPARTICLE EMISSION IN THE DECAY OF 31Ar PHYSICAL REVIEW C 89, 064315 (2014)
TABLE III. The A2 coefficients for different 2p transitions from TABLE IV. The relative branching ratios of the γ transitions in
31Cl through the 5.2 MeV level in 30S, together with the difference in the decay of 33Ar (above the line) and 33Cl (below the line). The peak
χ 2 compared to a uniform fit and the result D of a Kolmogorov test identifier corresponds to Fig. 14. The intensities of the γ transitions
to a uniform distribution. The peak numbers correspond to Fig. 12. from the 33Ar decay are normalized to peak 1 and compared to the
results of Ref. [34]. The transition marked by a * is compared to
Peak E(31Cl) (MeV) A 22 χ D Ref. [35], as suggested in Ref. [34]. The intensities of the γ transitions
− from the decay of
33Cl are normalized to peak III and compared to
1 6.674(6) 0.12(14) 0.67 0.79 the results of Ref. [36].
2 7.380(6) 0.16(11) 1.97 1.57
3 7.512(7) 0.35(19) 3.51 0.88 Peak E (keV) I Eref(keV) I refγ γ
4 7.919(8) 0.48(19) 6.69 1.40 γ γ
5 9.434(9) 0.04(19) 0.05 0.72 1 811.2(10) 100(10) 810.6(2) 100(1)
6 (IAS) 12.313(4) 0.03(18) 0.03 0.65 2 1541.0(10) 3.2(3) 1541.4(6) 3.6(2)
All 0.18(5) 13.18 7.95 3 2342.3(11) 1.10(13) 2352.5(6) 1.3(2)
4 4734(3) 0.46(9)
∗ 2230.4(19) 3.9(4) 2230.6(9) 1.7(5)
A4 term do not change this conclusion). The fit for the I 841.3(10) 109(16) 841 118.6(36)
events of peak 3 points to an A2 parameter different from II 1966.9(12) 132(18) 1966 104.2(16)
0, but the Kolmogorov test does not find the distribution to III 2867(3) 100(15) 2866 100.0(18)
be significantly different from uniform. Finally, the events of
peak 4 have a distribution significantly different from uniform +peak 4 corresponds to a 52 level the spin of the
30S level must
with more than 95% confidence [33] using the Kolmogorov be 4+ +, and if it is a 32 level it most likely must be 3
+ while
test and the value for A2 is different from 0 with more than 4+ is less likely. Considering in a similar way all the data in
2σ . This is also the case if all events of the 5.2-MeV peak are Table III, the preferred value for the spin of the 5.2-MeV level
considered, which implies that there must be components that
+ is 3
+, because several of peaks 1–6 give a uniform distribution,
are nonuniform. With reference to Table II this excludes the 0 + + +
and 1+ assignments for the 30S level. Spin 2+ is also excluded which for a 3 level would be consistent with both
5
2 and
7
2
because it can only give deviations to negative A values. levels in
31Cl. One would expect at least one of peaks 1–6 to
2
The spins of the states in 31
+
Cl corresponding to the come from a 32 level in
31Cl and therefore a 4+ assignment
numbered peaks in Fig. 12 are only known for the case of of the 5.2-MeV level would produce an angular correlation
+
the IAS (peak 6), where it is 5 . The other observed states significantly different from uniform. Assuming that the spin
3+ 5+
2
7+ of the 5.2-MeV level is 3
+, one can infer that the spin of
can be either 2 , 2 , or 2 assuming that only allowed +
decays are populated. The value for the IAS indicates a the 7.919(8)-MeV level in
31Cl (peak 4) is 32 and that of theβ A2 + +
uniform distribution. By comparing the value of A2 with the 6.674(6)-MeV level (peak 1) is either
5 or 72 2 . The spin of the
A2 values in Table II it can be concluded that the 5.2-MeV level remaining three levels (excluding the IAS) cannot be restricted
in 30S has spin 0–3+, while the 4+ assignment is less likely. By owing to the uncertainty on the A2 values.
comparing the value of A2 for peak 4 with Table II we can only+ +
conclude that this peak stems from a 32 or
5
2 level in
31Cl. If F. γ -transitions in the decay of 33Ar
To obtain a good calibration of the particle detectors
several runs with 33Ar were made during the experiment. The
10 6 A γ spectrum from these, i.e., in the decay of
33Ar, can be
seen in Fig. 14. The peak marked with numbers corresponds
5 1 to transitions in the β-daughter
33Cl, the ones marked with
10 Roman numbers to transitions in the β-granddaughter 33S and
the one marked by a * to a transition in the β-proton daughter
10 4 32S. A, B, C, and D are peaks from annihilation, pileup, and
I
B 2 γ -transitions from decays of
40K and 18N, respectively. The
*
10 3 C IID 3 assignment is supported by the half-life found for the peaks.
III The relative intensities of the γ lines observed in the decay of
4 33
10 2 Ar are given in Table IV. They are compared to results from
three different experiments [34–36]. The line at 4734(3) keV
1 2 3 4 from the transition between the IAS in 33Cl and the first excited
Eγ (MeV) state in 33Cl has not previously been observed in the decay of
33Ar.
FIG. 14. (Color online) The γ spectrum of 33Ar. The numbers
corresponds to transitions in the β-daughter 33Cl, the Roman numbers IV. SUMMARY
to transitions in the β-granddaughter 33S and the * to a transition in
the β-proton daughter 32S. The letters corresponds to background An improved half-life of 31Ar of 15.1(3) ms has been
lines. determined. For the first time a spectroscopic analysis of
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G. T. KOLDSTE et al. PHYSICAL REVIEW C 89, 064315 (2014)
the decay mode of β-delayed three-proton emission has been used for the level at 5.2 MeV, which is found to be either a 3+
presented, showing that in the case of 31Ar roughly half of or 4+ level, with the data favoring the 3+. In previous studies
the 3p decays stem from the IAS in 31Cl, while the rest stem this level has been suggested to be a 0+ level [12] based on a
from higher-lying levels. It is shown that the 3p emission is comparison with the mirror nucleus, or as a 3+ level based on
mainly sequential through the lowest levels above the proton its γ decay [29]. It is currently not known if there might be
threshold in 29P, but a component of simultaneous emission two levels around this energy, but we can conclude that a 3+
cannot be excluded. level at 5.227(3) MeV is populated in the decay of 31Ar. We
A quantitative analysis of β2pγ events has been performed see no indications that this peak may consist of two separate
and used to search for γ transitions from excited states in 29P. contributions in the present data.
Only γ rays from the two lowest excited states in 29P could be Finally, the γ transitions in the decay of 33Ar are measured
clearly identified. and their relative intensities are given and compared to
Analysis of all identified decay channels of the IAS previous measurements. A new γ line from the decay of the
including the β3p decay and contributions from decays to IAS is found at 4734(3) keV.
higher-lying states in 30S than previously observed has led to
an improved determination of the Fermi strength. The total
measured branching ratio to the IAS is 3.60(44)%, which
ACKNOWLEDGMENTS
is lower than the theoretical value of 4.24(43)%, but the
discrepancy is less than one standard deviation. This leaves We thank Marek Pfützner for helpful discussion and
room for contributions from decays to excited states in 29P input on the analysis of the β3p-decay of 31Ar. This work
(above 1.96 MeV) and for a possible γ -decay channel of the was supported by the European Union Seventh Framework
IAS in 31Cl. through ENSAR (Contract No. 262010). This work was partly
A new method to determine the spin of low-lying levels supported by the Spanish Funding Agency under Projects No.
in 30S is presented. It uses angular correlations between the FPA2009-07387, No. FPA2010-17142, and No. AIC-D-2011-
two protons in the β2p decay passing through the level of 0684, by the French ANR (Contract No. ANR-06-BLAN-
interest. Because the spin of the populated levels in 31Cl is not 0320), and by Région Aquitaine. A.S. acknowledges support
known an ensemble of states in 31Cl is used. The method is from the Jenny and Antti Wihuri Foundation.
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064315-10