First beta-decay studies of the neutron-rich isotopes 53–55Sc and 56–59V

NUCLEAR PHYSICS A ELSEVIER

Nuclear Physics A 632 (1998) 205-228

First beta-decay studies of the neutron-rich isotopes 53-55Sc and 56-59V O. Sorlin a, V. Borrel a, S. Gr6vy a, D. Guillemaud-Mueller a, A.C. Mueller a, E Pougheon a, W. B6hmer b, K.-L. Kratz b, T. Mehren b, R M611er b'l, B. Pfeiffer b, T. Rauscher b'2, M.G. Saint-Laurent c, R. Anne c, M. Lewitowicz c, A. Ostrowski c,3, T. D6rfler d, W.-D. S c h m i d t - O t t d a lnstitut de Physique Nucliaire IN2P3-CNRS, F-91406 Orsay, France b lnstitutfiir Kernchemie, Universiti2"t Mainz, D-55099 Mainz, Germany c Grand Accil~rateur National d'hms Lourds (GANIL), BP-5027, F-14021 Caen, France d 11 Physikalisches Institut, Universitiit GOttingen, D-37073 G6ttingen, Germany

Received 27 June 1997; revised 23 October 1997; accepted 7 November 1997

Abstract The neutron-rich isotopes 5345Sc and 56-59V have been produced at GANIL in interactions of a 64.5 M e V / u 65Cu beam with a 9Be target. They were separated by the doubly achromatic spectrometer LISE3. Beta-decay half-lives and subsequent low-energy y-rays were observed for the first time. The present results are compared to QRPA model predictions. The quick drop of the half-life observed at N = 33 for 20Ca33 53 is weaker for 56 23V33 and absent for 54 215C33, indicating a vanishing of the N = 32 subshell north to 52Ca32. In an astrophysical context, these neutronrich isotopes represent r-process progenitors which, after//-decay, would produce the correlated isotopic over-abundances of 54Cr, 58Fe, 64Ni in certain refractory inclusions of meteorites. @ 1998 Elsevier Science B.V. PACS: 27.40.+z; 27.50.+e; 23.40.-s; 25.70.Mn Keywords: 53'54"555c, 56'57'58'59V(/~-) [from 9Be (65Cu, X), E = 64.5 MeV/nucleon]; measured E-/, 1~,, C/y-coin, T]/2; deduced r-process implications.

I Permanent address: Scientific Computing and Graphics, Inc., RO. Box 1440, Los Alamos, NM 87544. 2 Present address: lnstitut fiir Theoretische Physik, Klingelbergstrasse 82, Universitfit Basel, CH-4046 Basel, Switzerland. 3 Present address: Department of Physics and Astronomy, University of Edinburgh, James Clerk Maxwell building, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom. 0375-9474/98/$19.00 (~) 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 5 - 9 4 7 4 ( 9 8 ) 0 0 6 3 6 - 2

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O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

1. Introduction In previous papers [ 1,2], we have presented ,B-decay half-lives and delayed-neutron probabilities of neutron-rich isotopes from phosphorus to argon. These studies aimed at an understanding of the nuclear structure while crossing the N = 28 neutron closed shell far off stability. First evidence for a deformed region around ~$28 was established from the decay properties of 45 17C128, ~$28 and 43 jsP28. Meanwhile, an extensive theoretical and experimental work has been accomplished which definitely confirms our observation [ 36]. The present work is a continuation of those/3-decay studies for heavier nuclei in the region of the N = 32 subshell closure. Indeed, the very fast Gamow-Teller transition in the decay of 53Ca33 [7] and the large energy of the first 2+-state in 52Ca32 [8] indicate a rather strong subshell gap. On the other hand, 55Ti33 does not exhibit a fast Gamow-Teiler transition [9]. It is therefore of interest to investigate the decay of the neighbouring isotones 54Sc33 and 56V33. A better knowledge of the nuclear-structure properties of neutron-rich isotopes in the phosphorus to chromium region also serves as a basic starting point for an understanding of explosive nucleosynthesis of specific isotopic abundances in this mass-region. For example, an important consequence of the short half-lives of ~S2s and 45 17C128 was to weaken the constraint on the "mini r-process" duration of 7" ~< 100 ms discussed by Ziegert et al. [ 10]. Since now, the/3-turning points seem to occur closer to stability, this time constraint was relaxed to ~- ~ 1 s, and neutron densities of nn ~ 1019-102° cm -3 were invoked [ 1 ] in order to explain the particularly high abundance ratio 48Ca/46Ca 270 observed in the EK 1-4-1 inclusion of the Allende meteorite [ 11 ]. It is therefore of high interest to check whether a neutron-capture process, roughly equivalent to an r-process in a SNII supernova, can also account for the overabundances of 5°Ti, 54Cr, 58Fe, 64Ni and 66Zn in several CaAl-rich inclusions. By comparing/3-decay and neutroncapture times in the Sc-V region, a first rough idea of the potential r-process progenitors of the above isotopes may be obtained.

2. Experiment

2.1. Set-up The isotopes 53-55Sc and 56-59V w e r e produced by fragmentation of a 64.5 MeV/u 65Cu beam impinging onto a 90 mg/cm 2 Be target. A low-Z target was chosen in order to favour the production of completely stripped nuclei. The desired fragments were selected by a magnetic analysis (Bpl) in the doubly achromatic spectrometer LISE3 [ 12,13]. The large number of species transmitted was reduced by means of a wedge-shaped degrader in the intermediate focal plane. Analyzed by a second magnet (Bp2), the unwanted nuclei were stopped in the thick jaws of the slits mounted in the focal plane. This energy-loss selection is roughly proportional to A3/Z 2. It suppresses also

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

207

Table 1 Main Bp settings. The number of isotopes implanted (N) during the collection time (7~) of each setting is also indicated Bpl (Tm) = 2.706 Bp2 (Tm) = 2.580 T,(h) ~ 10.3 Isotope 53Sc 54Sc 55Ti 56Ti 56V 57 V 5SV 5SCr 59Cr

N 47 27 453 102 20 3696 74 31 891

Bp~ (Tin) = 2.7652 Bp2(Tm) = 2.6511 T~(h) ,~ 10.0 Isotope 52Sc 53Sc 54Ti 55Ti

56V 57V 58Cr 59Cr

N 324 682 2200 1336 1746 3189 92 215

Bpl (Tm) = 2.8190 Bp2(Tm) = 2.7052 Ts(h) ~ 20.2 Isotope 54Sc 55Sc 55Ti 56Ti 57Ti 57V 5SV 59V 6°Cr

N 363 42 1810 1429 42 1999 1347 55 115

incompletely stripped fragments which have passed the first selection. The main magnetic rigidity settings, given in Table 1, correspond to a careful optimisation to isotopes of different neutron-richness. The aluminium wedge-degrader in the intermediate focal plane had a thickness of 221.5 /zm for the central trajectory. Consecutive to the focal plane, LISE3 features a WIEN-type velocity filter used to eliminate long-lived nuclei, which would have enhanced the fl-background in the first two settings. In the third one, all transmitted nuclei were of interest. Table 1 also contains the measuring times 7",. and the number of observed nuclei. They were identified by means of two consecutive 300 and 5 0 0 / z m silicon detectors. The first served for the determination of the energy loss and also gave a time-of-flight signal referenced to the cyclotron radiofrequency. Fig. 1 shows an energy-loss versus time-of-flight spectrum with the Bp setting of Table l, column 2. The nuclei were implanted in the second Si detector, consisting of twelve 2 mm-wide strips (24 x 2 x 0.5 mm). Four electronic chains were connected to each strip in order to measure the energy and time for the heavy ions and for the/3-particles from their decay. A momentum acceptance of the spectrometer of +0.5% was chosen to avoid a too broad implantation profile. For the two higher magnetic rigidity settings, a 200 # m aluminium foil was inserted between the silicon detectors in order to match the longer range of the nuclei. The Si telescope was surrounded by a 4~-y-detection system. It consisted of a ring of eight BGO crystals. Such a system allows a very high fl-ycoincidence efficiency, gp x gz, ~ 0.25 x 0.66, g~ and gz, being the average total/3- and y-efficiencies respectively. The BGO detectors also allowed to investigate the strongest y-transitions. Energy levels could be tentatively assigned, for implantation rates as low as a few per minute. In the case of the most strongly produced 57V isotope, the signal of a Ge detector mounted in the rear part of the BGO ring was exploitable.

O. Sorlin et al./Nuclear Physics A 632 (1998)205-228

208

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of flight

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I. Energy-loss vs time-of-flight plot using a degrader foil selection for magnetic rigidities of

Bp] = 2.7652 Tm and Bp2 = 2.6511 Tm (see Table 1, column 2).

2.2. Determination of decay properties Each time a fragment hits the first Si-detector, the primary beam is switched off for about five times the expected/3-half-life of the implanted nucleus. This time is chosen to be Tc = 3.3 s for the two first magnetic settings and 1.6 s for the third one. During the cut-off time, the data-acquisition system recorded the following fl and fl-3, parameters: the /3-energy in a strip, the time elapsed since the detection of the implanted nucleus, and the ?'-energy in the eight BGO crystals and in the Ge detector. A fl-event was only recorded as valid if occurring in the same strip # i as the precursor nucleus or in one of the neighbouring strips # i - 1 and i -t- 1. Generally, the energy loss of the electrons, corresponding to their path in the strips, was rather small. It was about 100 keV for the shortest trajectories if the implantation occurred in the middle of a strip. About 15% of the beta rays were detected in the adjacent strips. In this case, the path of the/3-particles may be considerably longer, and energy losses of up to 1 MeV were observed. An energy threshold of 70 keV was set for a safe level above background. As a consequence, the detection efficiency in the strips adjacent to the implantation strip was enhanced. A rough fl-energy calibration was made by means of a 137Cs source. A time-to-amplitude converter using the/3-signal in a given strip as start and a 3,-signal in one of the BGO segments as stop served to determine the prompt/3-3' coincidences. The half-lives were deduced from the time histogram of the /3-3' coincidences which were detected after the identification of the corresponding nuclei. This triple-coincidence requirement of the implanted nucleus, and the consecutive /3- and 3,-ray detection led to a very low background. In case of sufficient statistics, as for 56-58V, half-lives were also determined

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

209

from the time analysis of events detected in the full-energy y-peaks. For nuclei with a very l o w / 3 - y coincidence rate, only the 3-events were used. Even though this increased the background, very good agreement for the half-lives of 56-58V was obtained with and without the y-coincidence. The number N#r of/3-9' coincidences represents events where at least one y-ray followed the/3-decay. In the case of y-cascades, when a few y's per decay were emitted, the measured number NBTto t is larger than Ntis,. The number N3~, can be compared to the number Np of y-rays in a full-energy line in coincidence with /3-events. The relative y-ray intensity 1~, can be defined as the ratio Nt,/N~. The total-energy efficiency of the BGO crystals e~, (including photopeak ep and Compton diffusion ecompt) is lower than given in Refs. [14,15] due to the necessity of a high 100 keV threshold. It was chosen in order to eliminate the X-rays that are emitted by the Wien filter. Values of the y-detection efficiencies ep and e~, of the BGO ring were estimated to be 0.75(3), 0.75(3) at 400 keV; 0.65(3), 0.70(3) at 600 keV; 0.45(3), 055(3) at 1 MeV; 0.33(3), 0.51(3) at 1.5 MeV, respectively. The relative intensity 1~, and the probability p of feeding an excited state in the daughter nucleus can be defined as follows:

N pe~ , ~t, Nfl~

Iv - - -

p -

N 3~ g~" × N3

(1)

The decay of an excited state may occur by the emission of y' (s) in a large energy-range. Therefore the probability p is determined using an average y-efficiency of g~, = 66(4)%, adopted from the measured efficiencies e~, mentioned above. A y-energy resolution of 18% was determined using 22Na and 137Cs calibration sources.

2.3. Background estimation During one spectrometer setting of about I0 hours, approximately 10000 nuclei are implanted. A typical implantation profile N(i) is shown in Fig. 2a. Since correlated fl-particles can only be present in strips # i - 1, i or i + 1,/3's detected in all other strips are counted as background with a frequency fB(i). Fig. 2b represents the distribution fB (i) for each strip #i. The background contribution B(i) can be written as follows: i+1

B(i) = N(i)Tc Z

fB(k),

(2)

k=i-- 1

where Tc is the opening time of the/3-detection after implantation. In Eq. (2), the sum reflects that all three strips are valid for correlated /3's after an implantation in a strip #i. Strip # 8 was excluded from the analysis since it had been damaged prior to the experiment. Fig. 2c shows the decay spectrum of 57V. The total background contribution, given by the sum of B(i) over all strips, is deduced from Fig. 2a, b and Eq. (2). Its value is 44 + 2 counts per 100 msbin. In an analysis of the data of Fig. 2c by a xZ-fit containing the background as free parameter, a completely coherent value of 43.3 ± 1.8 counts per bin is obtained. The fitted decay curve is shown as a solid line. Similar

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

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t (ms) Fig. 2. (a) Implantation profile of 57V in the 12-strips detector. The central position was set with the WIEN filter. (b) Background frequency fB in each strip. It is obtained by the B-events detected in all strips except the three taken for correlated B-decay following the implantation of a precursor nucleus. (c) Time spectrum of the decay of ~Tv. The solid curve shows the result of a X 2 minimization using the background as a free parameter.

211

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

agreement was obtained for the isotopes 56V and 58V, reinforcing the confidence in the absolute determination of the background. For longer-lived species (53Sc) or weakly produced isotopes (55Sc, 59V), this background determination is indeed essential since it can no longer be determined by a parameter-fit. The same procedure of background determination was applied to t h e / 3 - y coincidences.

3. Results The measured half-lives for the isotopes 53-55Sc and 56-59V are given in Table 2 within one standard deviation. The corresponding decay curves are shown in Figs. 3a-b and Figs. 4a-h for the scandium and vanadium isotopes, respectively. Gamma-energy spectra are depicted in Figs. 5a-e. The intensities for these y-rays are given in Table 3. In the following, we will comment on the analysis of each nuclide. Table 2 Measured half-lives for scandium and vanadium isotopes by means of fl-singles or fl-y coincidence decaycurves Isotope

53Sc 54Sc 55Sc 56V 57V 58V 59V

TI~2 (ms) >3 s 225(40) 120(40) 233(20) 330(30) 195(20) 70(40)

TI~~ (ms)

225(25) 316(25) 214(20)

Adopted TI/2 (ms)

225(40) 120(40) 230(25) 323(30) 205(20) 70(40)

Table 3 Probability p of feeding an excited state in the daughter nuclei and relative intensity 1~, from subsequent decay for the studied scandium and vanadium isotopes. The definition of p and I~, is given in Eq. ( 1), Section 2.2 Isotope

p (%)

53Sc 54Sc

0(10) 130(25)

55Sc 56V

45(10)

57V

45(5)

58V 59V

80(10)

* Unresolved peaks.

E~, (MeV)

Iz, (%)

0.50(5) 1.00(5) 1.70(5)

40(20) 50(20) 40(20)

0.34(5) 0.70(5) 1.00(5) 0.30(5) 0.60(5) 0.80(10) 0.90(10)

40(15) 50(20) 30(10) 60(10) 30(10) 30(10) 80(20)*

212

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228 20

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t (ms) Fig. 3. (a),(b) Half-life spectra of 54'55Sc isotopes. The solid curves show the results of X2 minimizations using a fixed background value and the known daughter activities of 54Ti (1.5(4) s [9]) and 55Ti (0.59(5) s [91). The background contributions (not shown on the pictures) have been deduced by the method described in Section 2.3. They amount to 3.78 counts per 120-ms bin in the case of 5nSc, and 0.166 counts per 60-msbin for 55Sc. For the latter isotope, the resulting decay curve is indicated by a dashed line.

53Sc: N o clear decay was seen in t h e / 3 - d e c a y spectrum within the 3.3 s observation window. Also very few y - r a y s were observed. This indicates a rather long half-life and, presumably, a small population o f excited states in the daughter nucleus 53Ti (Fig. 5a). We therefore only could derive a lower limit Tl/2 /> 3 s. A r e m e a s u r e m e n t of this isotope with a l o n g e r t i m e - w i n d o w is necessary. 54Sc: Fig. 3a shows the decay curve for/3-singles. The full curve shows a fit in which the contribution from the decay o f the daughter, 54Ti with T1/2 = 1 . 5 ( 4 ) s [ 9 ] , was taken into account. Two y - l i n e s o f similar intensities 40 and 50% were found at 5 0 0 ( 5 0 ) and 1 0 0 0 ( 5 0 ) keV, respectively, in the B G O detector (Fig. 5 b ) . Possibly, the 1 M e V line

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

213

56v 100 -T

T1/2 = 233 ± 20 ms

counts

(a)

J

counts

T n/ 2 = 225 + 25 ms

!

10

800

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~

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Fig. 4. ( a ) - ( d ) Half-life spectra of 56 59 V isotopes. In the case of 5 9 V , the daughter activity of 5 9 C r 0.46(5) s [91 was subtracted. ( e ) - ( g ) Half-life spectra of 56-58V isotopes from the fl-y coincidences. For the 56-58V isotopes, the background was taken as a free parameter. The values were found to be consistent with the ones deduced by the method described in Section 2.3. (h) Time spectra of f l - y coincidences in the decay of 58V with the additional condition that the y-energy spectrum of Fig. 5e is in the range 700 keV < E~, < 1100 keV.

214

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228 25

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14

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E [keV]

l

!

1500

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E [keV] Fig. 5. (a)-(e) BGO energy-spectra of 53Sc, 54Sc, 56V, 57V, and 5Sv. The small dashed lines represent the experimental background of fl-'y coincidences. In the case of 58V, ~,-rays with energies in the range of 700 to 1100 keV were selected to measure their half-life in Fig. 4h.

corresponds to the 2 + ~ 0 + transition in S4Ti, a rather typical E(2 +) energy in this mass region. At the limit of statistical significance, a third line is located at 1.7 MeV. 55Sc: The decay of 55Sc populates the daughter nucleus 55Ti [9], which has a half-life of Tile = 590(50) ms. This contribution has been subtracted in the solid curve (Fig. 3b) showing a fit to the fl-singles. 56V: Its decay curve could be derived from the fits of both fl-singles and /3- 3, coincidences (Figs. 4a and e). The decay of the daughter nucleus 56Cr was neglected because of its long half-life 7"1/2 = 5.9 min [16,17]. Three T-rays have been observed (Fig. 5c) at 340(50), 700(50) and 1000(50) keV with comparable intensities of 40,

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

215

50 and 30%, respectively. 57V: Beta-singles a n d / 3 - y coincidences were obtained for this nucleus. The daughter decay of 57Cr, with T~/2 = 21 s [ 18], was neglected. Since this nucleus was present in all three magnetic rigidity settings (see Table 1), it was studied under different background conditions. Consistent values could be derived. Figs. 4b and f arise from the second Bp setting which has the highest statistics. Three y-rays have been observed (see Fig. 5d) at 300(50), 700(50) and 900(50) keV with efficiencies of 60, 30, and 30%, respectively. The first y-line is also seen in the /3-gated Ge-detector at an energy of 267(4) keV. 58V: Agreement was found between the half-lives deduced from the/3-singles and the fl-y coincidences (Figs. 4c and g), in both cases neglecting the decay of the daughter SSCr, with T1/2 -- 7 s [ 19]. The large peak at 900(100) keV from the BGO counter (Fig. 5e) certainly corresponds to two unresolved transitions possibly containing the cascade 4 ~ --+ 2 + ~ 0 +. Fig. 4h shows a decay curve gated on the y-energy range of 800-1100 keV, again confirming the reliability of the background determination. 59V: For this weakly produced isotope, only /3-singles events (Fig. 4d) were exploitable. The decay of the daughter nucleus 59Cr, with Ti/2 = 460(50) ms [9], has been taken into account.

4. Discussion

Quadrupole deformation parameters (e2) have been predicted by recent macroscopicmicroscopic mass models, e.g. the Finite Range Droplet Model [20] (FRDM) or the Extended Thomas-Fermi with Strutinski-Integral [21] (ETFSI) approach. These two models calculate similar deformations for the mother and daughter nuclei. For the vanadium isotopes, prolate deformations in the range of e2 = 0.15-0.17 are obtained by the FRDM, whereas the ETFSI model predicts more spherical shapes of s~ = 0.08-0.14. For the scandium isotopes, the two models agree on slightly oblate shapes. In the FRDM predictions, only the deformation of the deepest minimum in the potential-energy surface is defined as g.s. In this mass region, these are quite shallow. Since the calculated energies cannot be more precise than about 500 keV, we either may sit in the wrong minimum, or will have to face shape coexistence already below 1 MeV in the beta-decay daughter. Up to A = 54, the Sc and Ti isotopes are near-spherical with e2 < 0.1, but the heavier masses are moderately deformed, presumably prolate with an oblate isomer. This non-sphericity might be "seen" already in the gross property half-life. This integral value is mainly sensitive to the lowest-lying beta-strength. However, the actual g.s. shape should more likely be reflected in the y-data, i.e. the 2 + and 4 + energies and the general Gamow-Teller (GT) pattern. We have used the QRPA model of M611er and Randrup [22] to calculate GT-strength functions and/3-decay half-lives TI/2. th In this approach, Folded Yukawa (FY) wave functions and single-particle energies serve as a starting point to determine the deformationdependent wave functions. Experimental data are compared with QRPA predictions in order to get the "best possible agreement" and thus learn something about the underlying nuclear structure. This can be done by varying this deformation parameter e2 within

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

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Table 4 Compo.,-i on between c culated half-lives and measured h f-lives for sr,heroidal defo,'m ,tion parameter ~2. The choice of ~2 is discussed in the text. The uncertainty of the Q~ value is reflected in the theoretical half-lives by giving upper and lower limits Isotope

QB (keV)

e2

TI~2 (ms)

T~l~2° (ms)

56V

9049(240)

0.10

57V

8010(265)

192+30 -25 400~ 153+40 - 13

230(25)

0.167 0.118

58V

11550(355)

205(20)

59V

9940(415)

0.15

545c

11299(520)

0.15

74 +17 -13 177+47 "----30 61~1~ IR~+68 .uv47

0.183 0.23

323(30)

70(40) 225(40)

and slightly beyond the model predictions in this mass region. We have used identical ground-state deformations for both parent and daughter nuclei as suggested by FRDM and ETFSI models. The Lipkin-Nogami approximation is applied to calculate pairing correlations. The Q~-values used to derive half-lives from the GT strength functions are known from recent mass-measurements [23 ]. Table 4 gives the calculated half-lives T~ e, where the error bars correspond to the uncertainty of the experimental masses. Table 5 lists the major GT-transitions and the corresponding B-feedings (la). In this mass-region, the half lives are dominated by strong GT-transitions; hence, first-forbidden transitions can be neglected. In some cases, the measured probability p of feeding excited states, or Pg.s. = 1 - p to populate the ground state (g.s.), can be used as a constraint on the deformation. For example, in the case of 56V33, one would expect 100% feeding of the g.s. for a spherical shape due to the strong Pfs/2 --* ~rfT/2 GT-transition. The measured p = 45(10) %, however, indicates a configuration mixing from deformation. For 56V33 , a half-life of 7"1/2 = 230 i 25 ms has been found experimentally. It is much shorter than in the neighbouring nucleus 55V32 (7"1/2 = 6.54 4-0.15 s [24]). At first glance, it resembles the corresponding Ca isotones where the half-life of 53Ca33 (TI/2 = 90(15) ms [7] ) is much shorter than that of 5eca32 (Tl/2 = 4.6(3) s [8] ) just at the N = 32 subshell. The strong GT g.s. ~ g.s. transition Pfs/2 --~ 7rf7/2 in 53Ca33 decay is responsible for this effect. In analogy, a 100% g.s. ---, g.s. decay for 56V33leads to a half-life of 60 ms in the QRPA calculation with a spherical shape. In contrast to this, the experiment shows that the half-life is somewhat longer, and that 45( 10)% of the decay proceeds to excited states. We therefore have calculated 56V half-lives for different shapes. Quadrupole deformations of e2 = 0.1 and e2 = 0.167 yield a g.s. branching of 78% and 40%, respectively, to be compared with our experimental value of 55( 10)%. The half-lives deduced for these two deformations are .lo,~+30 . . . 25 ms and 400+~ _ ms. Higher deformations will only slightly change the feeding probability of the ground state and the value of the calculated half-life. The configurations of the corresponding 2QP states are given in Table 5 for a deformation of e2 = 0.167. For this shape parameter, a variety of levels should be fed at about 3.5 MeV excitation energy. Their decay to the ground

217

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

Folded-Yukawa potential

3[

STv ---> 5 7 C r + e" E2=0 Tl/2 =222.5 ms P g.s = 95%

2.52t_

[;3

1.5-

95%

5% 3%

1 0.50

7"r

0

2

4

TwaT-r77~q~-r-r~

6

10

12

Energy [MeV] 1.4-

fq

/g.s ~30 I- Y

1.2-

: 58% keV : 21%

E2=0.118 TI/2 = 153.2 ms Pg.s = 58%

0.8 L

0.6

14%

5%

;3 0.4 0.2

0

!~

i[i

~~

~ FI I I I I ~11

0

2

~ l

I I I I I ] I I [ ~ I I I I qlqrl'~F r III

4 Energy

1.2y

1 0.8

76%

I I [

rlll~lllllll~rl

8

10

6 [MeVI

g.s : 20% lOOkeV: 10% 120 keV : 46%

I~ 2 =0.167 Tl/2 = 155.7 ms P g.s = 20%

25%

0.6b" ;3 0.40.2 ~ 0

rl~]

0

i~lrllll ....

Energy

. . . . . . . . .

8'6 ....... ib

. . . . . . . . . .

[MeV]

Fig. 6. Calculated Gamow-Teller (GT) strength functions and corresponding /3-intensities 1# (indicated by arrows) for 57V decay. The calculations were performed for selected spheroidal deformation-parameters, i.e. e2 = 0. (top), 0.118 (centre), and 0.167 (bottom). The one-neutron separation energies S, and the QB-values were taken from Ref. [23 ], and are indicated by arrows on the x-axis.

218

O. Sorlin et aL/Nuclear Physics A 632 (1998) 205-228

Table 5 Calculated QP-configurationsfor mother and daughter nuclei assumingspheroidal deformationse2. The choice of deformationparameters correspond to the best agreementbetweentheory and experimenttaking into account both the half-life and the excited-states feeding probabilities (p). The calculated probabilities 1¢~of feeding a state at an energy E* are also given. In the case of g.s. to g.s. transition, I• can be compared to the probability pg.s. of feeding g.s., which is derived from the measured population of excited states above the 100 keV energy-threshold (pg.s. = 1 - p) Mother isotope 56V ~[32113/2- ®v131213/257V ~1321]3/258V ~[32113/2- @vi30113/2-

~132113/2- ®v[44011/2 +

e2

DaughterQP configur~ion

0.167 ~[32113/2- ®v[31213/2~[32113/2- ®vl301]l/2~[312]3/2- ®v131213/20.118 v[310]1/2v[30113/2u[321]1/20.183 ~132113/2- ®vi30113/2~131215/2- ®vi30113/2~[32113/2- ®vi31213/2~[32113/2- @v[310]1/20.23 ~[32113/2- ®v[31213/2~[31215/2- ®vl30111/2~[31215/2-®v[30113/2-

59V ~132113/2-

0.15

54Sc ~[33011/2- ®v[31213/2-

0.15

v[30113/2u[31213/2v[301]1/2v[32111/2~133011/2- ®v[31213/2~[330]1/2- ®v[310]1/2~[31215/2- ®v[321]1/2~[330]1/2- ®v[30113/2-

E* (MeV) g.s. 3.52 3.57 g.s. 0.030 0.74 g.s. 3.5 3.58 3.73 3.49 3.66 5.19 g.s. 0.37 0.58 1.69 g.s. 3.5 3.75 4.0

1B (%) 41 17 22 58 21 14 23 23 13 23 24 38 31 19 19 40 12 9.5 44 20 23

pg.s. (%)

55(10)

55(5)

20(10)

20(10)

*

veryweak

* Not determined due to low statistics. state will then occur by y-cascades. From the 55% probability of feeding the 0 + g.s. of 56Cr, we adopt a spin of I ~ = 1+ for the 56V g.s. The 1.00(5) MeV y-line observed in the present experiment probably corresponds to the known 2 + ~ 0 + transition at 1.007(2) MeV [16,17]. The known 4 + level is at 2.682(1) MeV [16,17]. We do not observe a 1.675 MeV transition (4 + ~ 2 +) transition. This may have two possible explanations: either the too low efficiency of the BGO detector, or - more likely - the non-feeding of the 4 + level, due to the adopted 1+ spin of the mother nucleus. We do not yet have an interpretation of the other y-rays observed at lower energy (Fig. 5c). They do not correspond to escape peaks of the 4 + ~ 2 + transition. In the case of the decay of 57V, the probability of feeding excited states above the 100 keV energy threshold of the BGO detector is 4 5 ( 5 ) % . This number excludes a spherical shape for 57V, for which pg.s. = 95%. By varying the deformation parameter in our QRPA calculations, one finds that for e2 ~ 0.1 18 the g.s. feeding is reduced to 58%. The calculation further predicts the GT-feeding of two levels at E3 = 30 keV and E2 = 740 keV with respective intensities 18 of 21% and 14%. Up to three y-transitions may arise from such feedings. The lowest observed ),-ray is found at 267(4) keV.

--0.6

•1 8

-13

-8

"3

--0.2

Spheroidal

-0.4

0.0

0.2

Deformation

0.4 e~

0.6

0

I-

17

12

7

2

--0.6

_271I

.22

LI .

>

>

I

I

lX, I

~

" ~<%

--0.2

0.0

0.2 Deformation

0.4 e~

•

0.6

i~'~"l~

"C'-'..

\3 "~" . ~ "

an = 0 . 8 0 fm

IJ'~" I II I~ '~ II I 'i 'i 'i [[ II II I~'~ II I

Spheroidal

--0.4

I

\%.

@

~ = 29.45,

Zig. 7. Folded-Yukawa single-particle level schemes for 58V as a function of the deformation parameter e2. The full lines correspond to positive )arity orbitals, the dashed lines to those with negative parity. The Nilsson quantunl numbers are given. The magic numbers are also indicated as :ircles. The parameters ,40 and tip (or ,t,, and a,, ) describe the depth and the shape diffuseness of the Folded-Yukawa potential.

-

U

.4

~"

>

58V

xi )o

I

,I

220

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

Because of the 100 keV detection threshold, it is difficult to settle that the 276 keV-line corresponds to the first calculated excited level at the energy E~ and that the observed 900(50) keV line corresponds to the second excited state E2. The calculated short halflife of 153 ms is strongly influenced by the 30 keV level which attracts 21% of the GT-strength. A first excited state at higher energy would increase the half-life closer to the experimental value. The GT-strength functions for the decay of 57V are shown in Fig. 6 for three different deformation parameters e2 = 0, 0.118, and 0.167. For any larger deformation, our calculations always give shorter half-lives than measured and predict a too small feeding of excited states above 100 keV. For 58V, the measured half-life is 205 ms and the ground-state feeding is about 20%. Small e2-values result in large g.s. feedings (pg.~. = 100% for e2 = 0), and in too short half-lives in the range 5 0 - 8 0 ms. A rather long 7"1/2 can be reproduced by the QRPA-calculations with a deformation of e2 = 0.23; but then the predicted g.s. feeding is negligible. In fact, it occurs at e2 ~ 0.20, that the neutron Nilsson levels [ 3 0 1 1 3 / 2 - and [440] 1/2 + cross. Fig. 7 shows the single-particle levels of protons and neutrons, and Fig. 8 represents the calculated strength functions before and after the cross point. It is interesting to note that at e2 = 0.23 the g.s. configuration of 58V is ~ [ 3 2 1 1 3 / 2 - ® v [ 4 4 0 ] 1 / 2 + where the neutron orbital is a strongly downsloping intruder of vgg/2 shell-model origin. This excludes any g.s. feeding due to its negative parity. With our experimental findings, one can deduce that the g.s. configuration is moderately prolate with a complex mixture of configurations. The decay of this nucleus may be "hindered" by about a factor 2.5 due to the different deformation of mother and daughter. According to Table 5 the decay of 58V at e2 = 0.183 mostly proceeds to configurations at excitation energies higher than 3.5 MeV. Thus, the population of a 4 + state is energetically possible, and the 4 + --~ 2 + --, 0 + cascade may be observed. Fig. 5e shows two unresolved peaks in the y-spectrum at about 800-1000 keV. If one assumes E (2 + ) = 800 keV and E (4 + ) = 1800 keV, their ratio becomes E (4 + ) / E (2 +) = (800 + 1000)/800 = 2.25. Known E(2 +) energies are shown in Fig. 9 for even-even 28Ni, 26Fe, 24Cr and 22Ti isotopes. Our, admittedly quite speculative, assumptions about the levels in 58Cr would indicate the presence of an N = 32 subshell closure, in contrast to the behaviour of Ni and Fe. It would be very interesting to check in future experiments if such a trend is indeed developing and holding true for Ti before becoming definitively established for Ca. The E ( 4 + ) / E ( 2 +) values call for some caution: 56Cr this ratio is 2.68 [ 16,17], which is quite high for a subsheil closure. For the isotope 59V, the calculated half-lives depend only weakly on the deformation parameter: Ti/2 = 57 ms fore2 = 0.1,60.5 ms fore2 = 0.118, 64 ms fore2 = 0.158, 67 ms for e2 = 0.2, and 74 ms for e2 = 0.25. The experimental half-life of Ti/2 = 70(40) ms does not significantly favour a particular deformation. The expected decay pattern of 59V is similar to the one of 57V, with three levels below 800 keV fed in GT-decay. It would be interesting to study this isotope with higher statistics in order to derive, from the observed y-lines, an indication for the deformation. We have observed a quite long half-life for S4Sc (T1/2 = 230(70) ms) and no g.s. feeding. This is to be compared with the predicted value of T1/2 = 14 ms for a

221

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

Folded-Yukawa potential SSV -~ SSCr + e 2 E2=O. 1 1.6

Tl/2 = 51.8 ms

27%

\

1.2 0.8

|

[=.

Pn = 0.71%

18%

43%

/

%

0.4 0

E

o

2

Energy [MeV] 2z ~ - 65%

£ 2 = 0.183 T1/2 = 82.9 ms

1.5-

Pn = 1.23% 10%

1 !

22% 0.5

S

0 [ll]lll[llll

0

2

4

6

8

10

Energy [MeVl 2£ 2 = 0.23 32%

T1/2 = 177 ms

1.6-

Pn = 1.90% 37%

1.2r~

[.,|

0.80.4-

.........!!!H ....

0 0

2

4

6

8

10

12

Energy [MeV] Fig. 8. Calculated Gamow-Teller strength functions and corresponding fl intensities 18 (mchcated by arrows) for the decay of 58V. The calculations were performed for different spheroidal deformation parameters, i.e. e2 = 0.1 (top), 0.183 (centre), and 0.23 (bottom). The one-neutron separation energies S, and Q~-values were taken from 123], and are indicated by arrows on the x-axis.

O. Sorlin et aL/Nuclear Physics A 632 (1998) 205-228

222

3 E(2 ÷) [MeV]

X

.--x--Ni

2.5

A

Fe

-~u -Cr

N=28

-e-Ti

2 1.5

N=32

/,~\ N "'X..

\ \ \

0.5 15

20

25 Neutrons

30

35

Fig. 9. Energies of 2 + ---* 0 + transitions for 22Ti, 24Cr, 26Fe, and 28Ni isotopes. The values of the 2 + energies of 54Ti and 58Cr have been deduced from the present experiment. The N = 28 gap is observed for all isotopes; its effect appears to be particularly large for Ni (Z = 28) isotopes.

spherical shape with a g.s. feeding of 100%. In the case of e2 = 0.15, the expected g.s. configuration of 54Sc is 7r[330] 1 / 2 - ® v [ 3 1 2 1 3 / 2 - . Since no direct decay to the 0 + g.s. of 54Ti is observed, the g.s. spin assignment is I ~ = 2 +. According to the QRPAcalculations, the GT-decay will proceed to spin 1+ and 3 + at about 3.5-3.7 MeV. The corresponding half-life is 7"1/2 = 180_47 +68 ms, in agreement with experiment. From the observed y-lines (Fig. 5 b ) , one might assign the 2 + --~ 0 + transition at 1 MeV, and the very tentatively 4 + --~ 2 + transition at 1.7 MeV. These values should definitely be confirmed with higher statistics in a future experiment which also should allow to obtain more information on the development of the N = 32 subshell closure. QRPA-calculations of 55Sc GT-decay always give a half-life shorter than our measurement of T1/2 = 120(40) ms. For instance a spherical shape leads to a TI/2 = 26 ms and a 70% g.s. feeding. Larger deformations, be it prolate or oblate, only decrease the halt-life. The low statistics in our decay curve may lead to an overestimation of the halflife. In the present QRPA calculations, different g.s. shapes for the mother and daughter nucleus are not taken into account. However, such a situation may well occur according to the F R D M and E T F S I predictions [20,21]. One can estimate that this would lead to a hindrance of the GT-decay by roughly a factor of two.

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

223

5. Astrophysical considerations The discovery of isotopic anomalies in meteorites has led to a change in the view of the origin of the isotopic composition of the early solar system. Large positive isotopic anomalies of iron group neutron-rich, i.e. 58Fe, 64Ni and 66Zn found in refractory CaAIrich inclusions of the Allende meteorite [ 25,26] indicate the existence of nucleosynthesis processes that encounter either a Nuclear Statistical Equilibrium or r-process with large neutron fluxes. These deviations from the bulk solar-system composition seem to be correlated with the earlier observed excesses of 48Ca, 5°Ti and 54Cr [ 11,25,27]. For a decade, particular emphasis has been devoted to the search of an ultimate stellar combustion that would produce these isotopes in a realistic and self-consistent way [ 10,28,291. The most likely astrophysical site suggested for a neutron-capture process is just adjacent to the core of an exploding supernova, where the inner zones experience photodisintegrations leading to protons and neutrons, which then combine to a particles in a more or less neutron-rich environment. This process has been named the a-process 130-32]. At freeze-out of charged-particles captures, the element composition varies from a particles to Fe-group nuclei, and subsequent neutron captures can proceed on these seed nuclei, tn order get an idea on how many neutron captures are necessary at these temperatures and neutron densities to form neutron-rich progenitors of the above isotopes, one can compare the neutron-capture time ~'l/2(n) and the beta-decay time 7h/2(fl) in each isotopic chain. Branching to the next heavier element occurs when rl/2 ( f l ) becomes comparable to or shorter than rl/2(n). Assuming that the isotropic ratio 48Ca/46Ca = 270 observed in the EK-I-4-1 meteoritic inclusion can indeed be reproduced by such a process, the turning points r-process progenitors of 5°Ti, 54Cr, 5SFe, 64Ni and 66Zn have to occur around A = 50, 54 . . . . 66. From the 44S region, we have seen that different model predictions may lead to quite different astrophysical conclusions about the nucleosynthesis of the Ca-Ti-Cr anomalies [ 1]. Finally, experimental values which disagreed with any previous theory, resulted in an even further - and now realistic - astrophysical scenario. Far from stability, facing the well-known problems with very low production yields, one commonly starts with easy-to-measure quantities, such as Tl/2, Pn, and main beta-feeding to low-energy region. If one can get from these data some information on the underlying nuclear structure, one can use this knowledge to improve unmeasurable further properties necessary for astrophysical calculations, e.g. theoretical neutron-capture cross sections. Fig. 10 compares the neutron-capture times with the measured fl-decay half lives for Sc, Ti, and V. Furthermore, theoretical halt-lives from M611er et al. [33] and Staudt et al. [34] have been used. An arrow indicates the position where the branching might occur. A weaker arrow is shown when the branching is not established for both models. The following comments apply to the ingredients of this figure: - Assuming a neutron density n,, ~ 3 x 1019 cm -3, a process duration of 1 s and a stellar temperature of T ~ 1 x 109 K, the neutron-capture rates have been calculated within a Hauser Feschbach formalism [35,36]. These results should be reliable within a factor of 5 due to the fact that the level density is in principle high enough to justify a statistical approach.

224

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

Z n (Th)

•

104 -

'[112 [ms]

~.

103

t." - . .

102 -

• ,,

~

t.

~

-

..... •

....

x^

(St)

xp

(MO)

/ . . . . . . . . . "I;PI~(exp) Ir

t \\

101 -

10 ° 53

52

54

55

56

57

Mass Number

104

58

59

60

(A)

'

'[1/2 [ms] lO 3

102

101

104

'

I

'

56

54

lO 4 "[1/2 [ms]

'

'

I

I

'

58 60 M a s s N u m b e r (A)

I

'

62

64

\ \

10 s

102

101

10 °

'

54

I

56

'

'

I

58

'

'

'

I

'

'

60

Mass Number

'

I

62

'

'

'

I

64

'

'

'

66

(A)

Fig. 10. Comparison between neutron capture times and fl-decay times in the Sc, Ti and V isotopic chains. Turning points (indicated by arrows) are located where the fl-decay time is shorter than the neutron-capture time. Neutron-capture times were calculated using a simple Hauser Feschbach formalism [35,36] and a neutron flux of nn x ~'r "~ 3.6 X l019 cm - 3 s. They are indicated by a thick line. These times are compared to calculated half-lives by M611er et al. 133] (dotted lines) and by Staudt et al. [34] (long dashed line). The experimental values are also indicated with their error bars.

O. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

225

For the theoretical half-lives predictions, a QRPA-formalism has been used for both models. However, M611er et al. have used Folded-Yukawa wave function and Lipkin-Nogami pairing whereas Staudt et al. have used Nilsson model and BCS-pairing. Different deformation-parameter have been adopted in the two calculations, strongly influencing the half-lives. Therefore the predictions diverge by up to one order of magnitude. Experiments are thus needed, and will be continued in order to reach the "real" turning-points. Let us note that the deformation of the compound nucleus may strongly influence the level density. One may therefore improve the neutron-capture calculations on shortlived radioactive target nuclei by including the deformations derived from an analysis similar to that presented in Section 4. Such refined calculations have been made "south" of 48Ca [ 37,38], and it is planned to pursue them in the region of interest for the present paper. Fig. I0 shows that the r-process turning points are expected at 57Sc, 586°Ti, 61-63V. For the Ca, Cr, Mn and Fe chains (not shown here), one obtains branching points around 54Ca, 64-66Cr, 69-71Mn and 74Fe from the comparison with the QRPA calculations. It is interesting to note that manganese and iron nuclei will probably not act as progenitors of the Fe-Ni-Zn anomalies because the branching will only occur at a rather high mass numbers. The identified progenitors can be compared with qualitative predictions assuming a steady-flow r-process in an ( n , y ) - ( y , n ) equilibrium [36,39]. Within this so-called waiting-point concept test (although somewhat at its limits for our neutrondensity and temperature conditions), a first order test can be made to determine the potential r-process progenitor in a given isotopic chain. Under these assumptions, one finds that for freeze-out temperatures (here 1.2 109 K), a 1-s r-process at a neutron density of n,, = 5 x 1019 to 1 x 10 20 cm -3 is able to produce simultaneously the abundances of 54Cr (from 54Ca), 58Fe (from 58Ti) and 66Zn (from 66Cr) [40]. A remaining concern may be the production of 64Ni, since only 64Cr may act as a precursor. This isotope is however not the most abundant in the Cr chain and no important precursor is identified neither from the competition of the neutron-capture with B-decay nor from the neutron-capture photodisintegration equilibrium. A determination of the mass and the half-life of 64Cr40, predicted to be spherical, would be of high interest for testing the strength of the N = 40 subshell far from stability and locating the A = 64 progenitor. Nevertheless, one may conclude that a simultaneous explanation of the meteoritic anomalies - from 46Ca up to 66Zn - seems possible under r-process-like conditions. A likely scenario may be the high-entropy bubble in a SNII, where the a-process forms a Si-Cr seed pattern with the even-Z's enhanced (similar to the solar pattern...), on which - after an a-rich freeze-out - the neutron-capture process can act [41]. This scenario may be regarded as an alternative to the recent Quasi-Nuclear Statistical Equilibrium of Meyer and Clayton [42] that is able to reproduce the solar 48Ca/46Ca = 53 ratio via direct production through a-particle captures in SNI. In this scenario, the bulk solarmaterial of 46Ca, 48Ca, 5°Ti, 54Cr, 58Fe, 64Ni and 66Zn would be produced from a SNI. However, small amounts of more exotic composition, such as EK-I-4-1, can be well produced in a SNII scenario [43]. -

-

226

o. Sorlin et al./Nuclear Physics A 632 (1998) 205-228

6. Summary and conclusions The half-lives of 53-55Sc and 56-59V presented in this paper have been measured for the first time. They have been determined making use of/3-singles and/3-y time spectra which are correlated with the implantation of a precursor nucleus. Together with the work of D6rfler et al. [9] on 54-57Ti, part of the isotopic region north east of 53Ca has been covered. The nuclear deformations deduced from the decay properties are somewhat larger than expected from the ETFSI and FRDM models. The strong N = 32 subshell effect observed at 52Ca32 [7,8] is weaker at 56Cr. The possible influence of the 0g9/2-shell intruder has been shown in the 58V35 case, which features an unexpected long half-life and a small g.s. to g.s. transition probability. This intruder state presumably plays an important role to explain the existence of short-lived E2 and M2 isomers in 548c33 and 59Cr35 found at GANIL by R. Grzywacz et al. [44]. This finding may be an indication of shape co-existence between a prolate g.s., found with our QRPA-study, and an oblate excited-state, required for the observation of an M2 transition at N = 35 (see Fig. 7). In an astrophysical context, our half-lives are not clearly in favour of one model, be it FRDM or ETFSI. It reinforces the necessity of measuring nuclei further from stability in order to determine the turning points in the neutron-capture path in the Sc-V region. The most exotic measured nuclei 55Sc, 57Ti and 59V are already close to the actual branching points 57Sc, 58-6°Ti, 61-63V, 64Cr that will probably be studied in a near future. Our present experimental limitation for reaching more neutron-rich nuclei is due to the projectile fragmentation method with a 65Cu36 beam, where the production of nuclei exhibiting neutron numbers equal or larger than N = 36 is unfavored. Isotopes further from stability (up to 575c36, 58Ti36, 61V38, 64Cr40) have already been produced with reasonable rates at GANIL [44] and GSI [45,46] using either the fragmentation of a 86Kr beam, or the fission of relativistic 238U projectiles [47].

Acknowledgements We wish to thank the technical staff of LISE3/GANIL (R. Hue, R. Alves-Cond6, Y. Georget) for their permanent help during the experiment. This work was partly supported by the Deutsche Forschungsgemeinschaft (DFG) under contract Kr806/3 and by the German Ministry for Research and Technology (BMFT) under contract 06GO667/TP.3. We also acknowledge support from the European Community under contract number ERBCHGE-CT94-0056 (Human Capital and Mobility, Access to the GANIL large scale facility). One of us (TR) would like to thank the A. v. Humboldt Stiftung for a fellowship. We thank R. Grzywacz for providing us preliminary results on isomers before publication.

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