application/xmlErosion of [formula omitted] shell in [formula omitted] investigated through the ground-state electric quadrupole momentK. ShimadaH. UenoG. NeyensK. AsahiD.L. BalabanskiJ.M. DaugasM. DepuydtM. De RydtL. GaudefroyS. GrévyY. HasamaY. IchikawaD. KamedaP. MorelT. NagatomoL. PerrotCh. StodelJ.-C. ThomasY. UtsunoW. VanderheijdenN. VermeulenP. VingerhoetsE. YagiK. YoshidaA. YoshimiElectric quadrupole moment of [formula omitted]β-NMRIsland of inversionShell modelQuasiparticle-vibration coupling modelPhysics Letters B 714 (2012) 246-250. doi:10.1016/j.physletb.2012.07.030journalPhysics Letters BCopyright © 2012 Elsevier B.V. All rights reserved.Elsevier B.V.0370-26937142-514 August 20122012-08-14246-25024625010.1016/j.physletb.2012.07.030http://dx.doi.org/10.1016/j.physletb.2012.07.030doi:10.1016/j.physletb.2012.07.030http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/

Journals

S300.3

PLB28748S0370-2693(12)00770-810.1016/j.physletb.2012.07.030Elsevier B.V.Experiments

Fig. 1

Schematic layout of the β-NMR apparatus. Details are given in Ref. [23].

Fig. 2

(a) The NMR spectrum obtained for the ground state of Al33 in a Si crystal. (b), (c) The NQR spectra obtained in an α-Al2O3 crystal with wide and narrow νQ-window scans. The ordinate of each spectrum shows a double ratio R/R0, where R denotes the up/down ratio of the β-ray counts measured with application of the B1 field for the quadrupole coupling frequency νQ, and R0 the up/down ratio without the B1 field. The vertical bar attached to the data point represents the statistical error due to β-counting statistics, while the horizontal bar indicates the width of the ν (νQ) frequency sweeps. The results of the least-χ2 fitting analysis are shown by solid curves.

Fig. 3

(a) Experimental (solid circles) and theoretical (lines) Q moments of odd-mass neutron-rich aluminum isotopes as a function of mass number. The data for A=31 is plotted by taking a weighted average of the results from Refs. [20] and [22]. Theoretical values are obtained from shell model calculations with USD interactions using isospin-dependent effective charges (solid line). Theoretical values of Monte Carlo Shell Model (SDPF-M), for which (i) constant effective charges and (ii) isospin-dependent effective charges are adopted, and a particle-vibration coupling model (PVC) are also shown by dotted and dashed lines, respectively. (b) The probabilities for normal and intruder configurations predicted by SDPF-M are shown.

Erosion of N=20 shell in Al33 investigated through the ground-state electric quadrupole moment

Shimada

Ueno

⁎

ueno@riken.jp

Neyens

Asahi

D.L.

Balabanski

J.M.

Daugas

Depuydt

De Rydt

Gaudefroy

Grévy

Hasama

Ichikawa

Kameda

Morel

Nagatomo

Perrot

Ch.

Stodel

J.-C.

Thomas

Utsuno

Vanderheijden

Vermeulen

Vingerhoets

Yagi

Yoshida

Yoshimi

aDepartment of Physics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, JapanbRIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, JapancInstituut voor Kern- en Stralingsfysica, KU Leuven, Celestijnenlaan 200D, B-3001 Leuven, BelgiumdInstitute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, BG-1784 Sofia, BulgariaeCEA, DAM, DIF, F-91297 Arpajon, FrancefGrand Accélérateur National dʼIons Lourds, CEA/DSM-CNRS/IN2P3, BP 55027, F-14076 Caen Cedex 5, FrancegInstitut de Physique Nucléaire dʼOrsay, 15 Rue G. Clemenceau, F-91406 Orsay, FrancehJapan Atomic Energy Agency, Tokai-mura, Ibaraki 319-1195, JapaniDepartment of Physics, Graduate School of Science and Technology, Niigata University, Niigata 950-2181, Japan⁎Corresponding author.1

Present address: Cyclotron and Radioisotope Center, Tohoku University, 6-3 Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-8578, Japan.

Present address: Institut de Physique Nucléaire, CNRS/IN2P3, Université Claude Bernard Lyon 1, F-69622 Villeurbanne Cedex, France.

Present address: Centre dʼEtudes Nucléaires de Bordeaux-Gradignan, Université de Bordeaux 1 – UMR 5797 CNRS/IN2P3, Chemin du Solarium, BP 120, 33175 Gradignan Cedex, France.

Present address: Institute of Materials Structure Science, High Energy Accelerator Research Organization, Ibaraki 319-1106, Japan.

Present address: Research Core for Extreme Quantum World, Okayama University, Okayama 700-8530, Japan.

Editor: V. Metag

Abstract

Electric quadrupole moment Q of the Al33 ground state has been measured by means of β-NMR spectroscopy using a spin-polarized Al33 beam produced in a projectile fragmentation reaction. The obtained Q moment, |Qexp(33Al)|=132(16) emb, shows a significant excess from the prediction of shell model calculations within the sd shell. The result indicates sizable admixing of pf intruder configurations in the ground state, demonstrating that the N=20 shell closure certainly erodes in Al33, a nucleus located on the border of the island of inversion. Comparison was made with predictions of the Monte Carlo shell model, and also a particle-vibration coupling model treating the neutron pairing correlations in the ground state of Al33. Again, a significant admixture of pf intruder configurations to the Al33 ground state was needed in both theoretical approaches to explain the observed large Q.

Keywords

Electric quadrupole moment of Al33β-NMRIsland of inversionShell modelQuasiparticle-vibration coupling model

The region of the nuclear chart consisting of neutron-rich Ne, Na, and Mg isotopes around the neutron number N=20 is known as the island of inversion, where the nuclear ground states are dominated by intruder configurations from the upper pf orbits and are considerably deformed [1]. Among the N=20 isotones, numerous studies have been conducted for nuclei inside the island of inversion[2–6], but not much effort has been devoted to their neighbors, such as Al33. In the systematic mass measurements around A≃32[7], from which the anomalously tight binding of nuclei in this region was recognized, no remarkable feature was found for Al33[8].Nuclear magnetic dipole (μ) and electric quadrupole (Q) moments are sensitive respectively to the nucleon configuration and to the E2 collectivity. Recently, the μ-moment measurement of the Al33 ground state has been reported [9], where it is suggested that the mixture of pf intruder configurations could explain an observed difference, Δμ(33Al)=3.9%, between the experimental μ(33Al) moment and a shell-model calculation within the sd model space. This observation contradicts a β–γ spectroscopic work carried out on Al33[10], which reports that the observed β-decay properties of Al33 are well described by the sd shell model calculations, suggesting that the ground state of this nucleus lies primarily outside of the island of inversion. Contrary to this, a β-decay study [11] indicates a sizable admixture of intruder configurations in the Al33 ground state.It would be worth noting here that, although most of theoretical analyses of the nuclear structures arising in the island of inversion are based on the consideration of strong nuclear deformations [7], the possibility of other mechanisms may also be important. For instance, the importance of the neutron pairing correlation instead of nuclear deformation [12] and a picture of quadrupole-shape fluctuations which dominate both the ground and the excited Iπ=0+ states [13] were proposed to describe the Mg32 nucleus.In the present work, the ground-state Q moment of Al33 (Iπ=5/2+, T1/2=41.7(2) ms) has been measured by means of β ray-detected nuclear magnetic resonance (β-NMR) [14] with incorporation of the technique of fragmentation-induced spin-polarized radioactive isotope beams [15,16]. Comparing the obtained Q(33Al) with those reported for other neutron-rich aluminum isotopes, possible evolution of nuclear structure around Al33 will be signified due to its high sensitivity to the collectivity such as deformation and paring correlation. So far, the μ moments of 30–34Al [9,17–19] and the Q moments of 31, 32Al [20–22] have been measured.The experiment was carried out at the Grand Accélérateur National dʼIons Lourds (GANIL). A beam of Al33 was obtained from the fragmentation of S36 projectiles at E=77.5A MeV on a 0.22 g/cm2 thick Be9 target. In order to produce spin-polarized Al33, fragments emitted at finite angles, θLab=1–3°, from the primary beam direction were introduced to the fragment separator LISE. The primary beam was deflected by 2° with respect to the target located at the spectrometer entrance. A range of momenta p/pb=1.026–1.041 was selected with slits placed at the momentum-dispersive intermediate focal plane. Here, pb=11.7 GeV/c is the fragment momentum corresponding to the projectile velocity. With a 2 μA intensity of the primary S16+36 beam, LISE provided the beam of Al33 with a purity of 75% and intensity of 1300 particles/s. The spin-polarized Al33 fragments were transported to a β-NMR apparatus [23] located at the final focus of LISE, and were implanted in a stopper of hexagonal α-Al2O3 single crystal (corundum). A static magnetic field B0=497.62 mT was applied to the stopper in order to preserve the Al33 spin polarization. The layout of the β-NMR apparatus is shown in Fig. 1

. The α-Al2O3 crystal was cut into a 25.5×28×1 mm slab, and was mounted in a stopper chamber so that the c axis was oriented parallel to the B0 field. The stopper was kept in vacuum and cooled to a temperature T≃80 K to suppress the spin-lattice relaxation of Al33 during the β-decay [20].

The Q moment interacts with an electric field gradient eq acting at the site of the implanted nucleus in a single crystal stopper. The eqQ interaction causes energy shifts in the individual Zeeman magnetic sublevels. Under the present situation of the experiment, where the angle between the c axis and the B0 field was set at θ=0°, the resonance frequency νm,m+1 between magnetic sublevels m and m+1 (m=−I,−I+1,…,I−1) of the nuclear spin I=5/2 is given by(1)νm,m+1=νL−νQ(3cos2θ−1)3(2m+1)8I(2I−1)=νL−340(2m+1)νQ, where νL denotes the Larmor frequency, νQ=eqQ/h the quadrupole coupling constant, and eq the electric field gradient along the c axis. Q and h denote the Q moment and the Planckʼs constant, respectively. If the true value for νQ is inserted in Eq. (1), the application of an oscillating magnetic field B1 whose frequency is swept across νm,m+1(νQ) should lead to a reversal of the population between sublevels m and m+1 (the adiabatic fast passage technique (AFP) [24]). Application of a B1 field having all these five (=2I) different νm,m+1 frequency components ensures that through scanning the single parameter νQ, the fulfillment of νQ=eqQ(33Al)/h could be detected through the simultaneous occurrence of all the 2I=5 resonances, which consequently leads to collective alteration of the spin polarization [20]. Note that the full reversal of spin requires a sequence of stepwise reversals between two contiguous sublevels. The B1 field was applied in I(2I+1)=15 steps in the same sequence as described in Ref. [25]. In each step the frequency ν was swept from νm,m+1(νQlower) to νm,m+1(νQupper) with νQlower and νQupper denoting the lower and upper bounds of the searched νQ region.Thus, the νQ resonance was detected as a change in the β-ray asymmetry (we hereafter denote this technique of β-ray detected NMR spectroscopy in a non-cubic crystal by the β-NQR method). The β-rays emitted from the implanted Al33 nuclei were detected with scintillator telescopes located above and below the stopper. They were housed inside the vacuum chamber, each consisting of three 1 mm-thick plastic scintillators. The up/down ratio R of the β-ray counts is written as(2)R=a1+v/c⋅AβP1−v/c⋅AβP≃a(1+2AβP), where a is a constant factor representing asymmetries in the counter solid angles (Ωβ≈4π×0.22 sr each) and efficiencies, v/c the velocity of the β particle, Aβ the asymmetry parameter, and P the Al33 nuclear spin polarization. The primary branch of the Al33β-decay is to the ground state of Si33 with a branching ratio of ∼89%[10] and decay Q value Qβ=11.990 MeV[26]. Since a β particle looses part of its energy in penetrating the materials around the stopper before entering the β-ray telescope, only those β particles with Eβ≳1600 keV[27] (or v/c≳0.97) were counted. Thus, the ratio R in Eq. (2) is well approximated by the second expression setting v/c≈1. By taking a double ratio R/R0, where R0 is the value for R measured without the B1 field, the change in the R/R0 ratio of the β-ray yields upon the NQR is given as(3)RR0≃a(1−2AβP)a(1+2AβP)≃1−4AβP, if the fragment spin polarization is fully reversed from P to −P. Since the constant a is canceled out in Eq. (3), the alternation of the spin polarization can be detected as the deviation of R/R0 from the unity. The resonance frequency is derived from the position of a peak or dip in the R/R0 spectrum. The experiment was done with a pulsed beam with typical beam-on and beam-off periods of 20 and 109 ms, respectively. In the beam-off period, the sequence of the B1-field for the nuclear magnetic resonance was applied in the first 9 ms duration, and then the β-rays were counted in the remaining 100 ms duration.

Fig. 2

(a) shows a β-NMR spectrum obtained for Al33 in a cubic Si crystal in runs prior to the NQR measurements, using the same apparatus and B0 setting for the νL determination. The spectrum was analyzed based on a least-χ2 fitting procedure with a Gaussian function(4)Gσ(ν)=aexp(−(ν−ν(0))22σ2)+1. Here a and ν(0) are the parameters that were varied during the fitting procedure, while σ was kept constant at values obtained from a numerical simulation, in which a time-dependent Schrödinger equation of the spin motion in the AFP spin reversal process was solved under the actual B0 and B1 magnetic field settings. The resulting fitting curve is also shown in Fig. 2(a). From the peak frequency νL=6217(3) kHz, a result μ=4.097(2)μN was deduced. The error quoted here included an error in the B0 field calibration, performed for the present β-NMR setup with a proton NMR probe, of ΔB0⩽0.01 mT, which was in fact negligibly small. The presently obtained μ value agrees with the reported value μ=4.088(5)μN[9] within the experimental error. From the resonance amplitude the spin polarization of Al33 was determined to be P∼−2.0(5)%, assuming Aβ∼0.89, as deduced from the experimentally known β-decay branching ratios [10].

In Figs. 2(b) and (c) the measured R/R0 ratios for the Al33 in α-Al2O3 single crystal are shown as a function of the quadrupole frequency νQ (the β-NQR spectrum). In principle, the resonance width of AFP-NMR spectra becomes approximately a bin width of the swept frequency. The observed widths of the obtained NQR spectra are, however, much broader than ΔνQ=485(176) kHz of a wide (narrow) νQ-window scan. By fitting the spectrum of the wide νQ-window scan shown in Fig. 2(b) to a Gaussian function Gσ(νQ) of Eq. (4), a substantially broader width 1.3(2) MHz (FWHM), calculated from the resulting σ=564(97) kHz, was obtained, where σ, as well as a and νQ(0), were treated as free parameters to be determined through the fitting. The obtained parameter νQ(0)=2116(73) kHz represents the position of the peak, from which the quadrupole coupling constant eqQ/h will be deduced. According to a numerical simulation, σAFP=209 kHz is expected as a width caused by the AFP spin reversal process, in which further line-shape broadening effects, e.g., due to the fluctuation of an electric field gradient q are not included. As a result, an extra broadening σextra=524 kHz is needed in order to reproduce the observed σ=564 kHz. The origin of σextra has not yet been well understood. Although an externally implanted Al ion would most likely stop at the site of the same element in the host crystal, there may be a possibility that some fraction of the implanted ions stop at other, metastable, sites. Also, some of the implanted ions might stop at a site of Al27 atom that is accompanied by a near-by lattice defect produced by implantation, thus leading to a shifted NQR resonance. In these cases the NQR spectrum would show a broadened peak. In the present analysis such effects are expressed as a non-zero value of σextra. We therefore took into account the extra width determined in the fitting, σextra=524 kHz, as an independent systematic error. Thus, an experimental error δνQ(0)=±77(stat)±524(sys) kHz was assigned to the peak frequency νQ(0)=2116 kHz, where an uncertainty from the eq value, δνQ=14 kHz, and that from a θ setting error, 1.1 kHz, were also included. The same fitting procedure was then applied to a narrow νQ-window scan spectrum shown in Fig. 2(c), with a resulting peak frequency νQ(0)=2159(46) kHz. For the obtained peak an extra broadening effect was observed again with σ=263 kHz at this time, and was regarded to represent a systematic error in the obtained νQ(0). Thus, the peak frequency was determined to be νQ(0)=2159±46(stat)±263(sys) kHz. The νQ(0)ʼs determined from the wide and narrow νQ scans agree very well. We have obtained a quadrupole coupling constant |νQ|=|eqQ/h|=2.16(27) MHz from the narrow νQ scan, in which the observed extrabroadening effect is smaller. The Q moment of Al33 is deduced from the relation |Q(33Al)|=|Q(27Al)⋅νQ(33Al)/νQ(27Al)|, where Q(27Al) and νQ(27Al) denote the Q moment of Al27 and the quadrupole coupling constant of Al27 in α-Al2O3, respectively. By inserting the reported values Q(27Al)=146.6(10) emb[29] and νQ(27Al)=2389(2) kHz[30], the ground-state Q moment for Al33 has been determined as |Qexp(33Al)|=132(16) emb.Before turning to a closer examination of |Qexp(33Al)|, a few remarks should be made concerning its μ moment. In the study of the μ-moment measurement of Al33[9], μexp(33Al), it was reported that |μexp(33Al)| differs from the theoretical μ of the shell-model calculation with the USD interaction [31] by 3.9%, and that this difference can be explained by the admixture of pf-intruder configurations of at least 25%. This statement is also supported by a large scale shell model calculation in the Monte Carlo Shell Model (MCSM), with the SDPF-M interaction [32]. This calculation reproduces |μexp(33Al)| within a 0.4% difference, in which the admixture of 63% intruder configurations is predicted. The above observation also indicates that μexp(33Al) is rather insensitive to the pf admixture. This insensitivity seems reasonable if configurations, in which two neutrons are excited to the pf orbit, are considered. The contribution from these configurations to the μ moment is a second-order correction, while the contribution to the Q moment is a first-order effect. Reflecting this, the theoretical value of Q(33Al) in the SDPF-M model largely differs from that in the USD model, by ΔQ(33Al)=41%, in contrast to the small difference Δμ(33Al)=4.3%

The quoted value of difference Δμ(33Al)=4.3% is for a case when the free-nucleon M1 operators are adopted, as in Ref. [9]. If instead the effective operators of Ref. [33] are adopted, Δμ(33Al) becomes 6.7% which is still small compared to ΔQ(33Al).

in the theoretical values of μ(33Al) between the two models. A similar example is the case of Na29, in which both the USD and SDPF-M calculations well reproduce the experimental μ moment, while their theoretical Q moments differ by 30% from each other. The experimental Q agrees well with the SDPF-M prediction [34].The obtained |Qexp(33Al)|, together with those reported for other odd-aluminum isotopes [20,22,29], is plotted as a function of mass number in Fig. 3

(a). The values of the 27, 31Al and Al33I=5/2 ground states are all very similar, around 130–140 emb. However, if N=20 is a well-developed shell gap, then one would expect a much smaller quadrupole moment for Al33, as its quadrupole moment would be only determined by the odd-proton configuration (thus including only proton–proton correlations). No mixing of neutron configurations in the ground state wave function can occur if the N=20 shell is completely filled and excitations across N=20 are excluded. When opening the N=20 shell, as in Al27 and Al31, an increase in the quadrupole moment occurs due to proton–neutron and neutron–neutron correlations in the sd shell. This is nicely shown by the USD shell model calculations [31,35], which are performed in the sd shell model space for both protons and neutrons. As in our earlier studies [20,22,28], isospin-dependent effective charges were used for protons and neutrons [36].77

Specifically, we took effective charges of proton (neutron) ep(en)=1.10(0.56), 1.09 (0.53), 1.07 (0.44), and 1.05 (0.38) for 27, 29, 31, 33Al isotopes, respectively.

Independent on the used effective interaction (USD, USDA or USDB [37]), a similar trend is predicted for the odd-Al quadrupole moments, in agreement with the observed values for Al27 and Al31. However, the predicted value for Al33 (95 emb) is much smaller than the observed one (132(16) emb), suggesting that neutron–neutron and/or neutron–proton correlations are required to reproduce the increased Al33 quadrupole moment. Thus opening up the sd shell is needed, and excitations of neutrons into the fp shell, across the N=20 gap, need to be taken into account.

In Fig. 3(a) theoretical Q moments predicted by the MCSM, with the SDPF-M interaction [32] and the constant effective charges adopted in the study of Na isotopes [34], are shown by a dotted line (i). Also, the probability for the pf intruder configuration predicted by the MCSM is shown in Fig. 3(b). In fact, the predicted pf intruder probability increases from 5–10% for the cases of 29–32Al to 63% for the Al33 case, suggesting a weakening of the N=20 shell closure. Accordingly, the theoretical Q moment for Al33 is large, QMCSM(33Al)=166 emb. The observed Q, |Qexp(33Al)|=132(16) emb, falls in between the USD and MCSM values. We note, however, that MCSM well reproduces |Qexp(33Al)| if we adopt the above noted isospin-dependent effective charges, as shown by a dotted line (ii). The situation is definitely different from the neighboring nucleus Al31, for which the μ[17] and Q[20,22] moments as well as the level structure [17] are well reproduced by the sd shell model.The above observation indicates that the Al33 ground state is mixed with pf-intruder configurations whereas the Al31 ground state is not. In a next step, we can investigate whether the admixture of pf-intruder configurations is caused by a static nuclear deformation. Assuming an axially symmetric static deformation with the nuclear spin along the symmetry axis, the spectroscopic quadrupole moment Q is related to its intrinsic quadrupole moment Q0 through a relation:(5)Q=3K2−I(I+1)(I+1)(2I+3)Q0 with K the projection of the nuclear spin I on the deformation symmetry axis (thus K=I). The intrinsic quadrupole moment of an ellipsoidal charge distribution can then be related to the quadrupole deformation parameter β as follows:(6)Q0=(3/5π)ZR2β(1+0.36β+⋯)(R=1.2A1/3) Using these expressions, we find similar deformation parameters for Al31 and Al33, respectively β=0.25 and 0.24. This similarity between these β values suggests that the admixture of pf-intruder configurations in Al33 does not receive significant influence of the nuclear deformation, since such an admixture is considered to be small in Al31.Fig. 3(a) includes the prediction from the mean field approach [38] as indicated by a dashed line: The structure of Al33 was treated in a microscopic particle-vibration coupling (PVC) model in which the coordinate-space Skyrme–Hartree–Fock–Bogoliubov and quasiparticle-random-phase approximations were employed. In this model, the Al33 ground state was described as a proton single-hole state (πd5/2)−1 coupled to a Si34 core to form Iπ=5/2+.The PVC Hamiltonian is diagonalized in a model space consisting of the (πd5/2)−1 hole state coupled to the quadrupole vibrational states in Si34. The resulting Al33 ground-state wavefunction involves a substantial neutron mean occupation number in the pf orbit of ∼0.8. This feature is inherited from the Iπ=0+ core state of Si34. It is interesting to note that a spherical shape is predicted for the Si34 core state in spite of the substantial amplitude of intruder configurations, where the neutron pairing, instead of the static deformation, associated with the weakening of the N=20 magic number plays an important role. Also, a predicted theoretical Q moment QPVC(33Al)=130 emb[38] with this wavefunction reproduces excellently the presently obtained |Qexp(33Al)|.In summary, the ground-state Q moment of Al33 has been determined by the β-NQR method using the fragmentation-induced spin polarization. The obtained Q moment, |Qexp(33Al)|=132(16) emb, shows a significant excess from the prediction of the USD shell model calculation. The large Q is a clear signature that the N=20 shell closure erodes in Al33. The structure of the Al33 ground state was then investigated through the obtained |Qexp(33Al)| by comparing with theoretical values predicted from the large scale shell model MCSM and a particle-vibration coupling model treating the neutron pairing correlations in the ground state of Al33 instead of the static nuclear deformation. A significant admixture of pf intruder configurations to the Al33 ground state was needed in both theoretical approaches to explain the observed large Q.

Acknowledgements

The authors thank the staff of GANIL for their support during the experiment. This work was partly supported by the JSPS KAKENHI (22340071), by the JSPS and MAEE under the Japan–France Integrated Action Program (SAKURA), by the French–Japanese International Associated Laboratory for Nuclear Structure Problems (LIA), and also financed by the European Community FP6 – Structuring the ERA – Integrated Infrastructure Initiative contract EURONS No. RII3-CT-2004-506065, by the FWO-Vlaanderen, by the IAP-programme of the Belgium Science Policy under grand number P6/23, and by Bulgarian National Science Fund, grant No. DID-02/16. The experiment was carried out under Experimental ProgramE437b.

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