Reaction dynamics and nuclear structure of moderately neutron-rich Ne isotopes by heavy-ion reactions

Reaction dynamics and nuclear structure of moderately neutron-rich Ne isotopesby heavy-ion reactions

S. Bottoni1,2, G. Benzoni2, S. Leoni1,2∗, D. Montanari1,2†, A. Bracco1,2, F. Azaiez3, S. Franchoo3,

I. Stefan3, N. Blasi2, F. Camera1,2, F.C.L. Crespi1,2, A. Corsi1,2, B. Million2, R. Nicolini1,2, E. Vigezzi2, O. Wieland2,

F. Zocca1,2, L. Corradi4, G. De Angelis4, E. Fioretto4, B. Guiot4, N. Marginean4,5, D.R. Napoli4, R. Orlandi4, E.

Sahin4, A.M. Stefanini4, J.J. Valiente-Dobon4, S. Aydin6, D. Bazzacco6, E. Farnea6, S. Lenzi6,7, S.

Lunardi6,7, P. Mason6,7, D. Mengoni7, G. Montagnoli6,7, F. Recchia6,7, C. Ur6, F. Scarlassara6,7, A.

Gadea8, A. Maj9, J. Wrzesinski9, K. Zuber9, Zs. Dombradi10, S. Szilner11, A. Saltarelli12, G.Pollarolo131 Dipartimento di Fisica, University of Milano, Milano, Italy

2 INFN, Sezione di Milano, Milano, Italy3 IPN, Orsay, France

4 INFN Laboratori Nazionali di Legnaro, Padova, Italy5 National Institute of Physics and Nuclear Engineering, Bucharest-Magurele,Romania

6 INFN, Sezione di Padova, Padova, Italy7 Dipartimento di Fisica, University of Padova, Padova, Italy

8 CSIC-IFIC, Valencia, Spain9 The Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Krakow, Poland

10 Atomki, Debrecen, Hungary11 Ruder Boskovic Institute, Zagreb, Croatia

12 University of Camerino and INFN Sezione di Perugia and13 Dipartimento di Fisica Teorica, University of Torino and INFN, Sezione di Torino, Italy

(Dated: June 13, 2012)

The heavy-ion reaction 22Ne+208Pb at 128 MeV beam energy has been studied using the PRISMA-CLARA experimental setup at Legnaro National Laboratories. Elastic, inelastic and one nucleontransfer differential cross sections have been measured and global agreement is obtained with semi-classical and distorted wave Born approximation (DWBA) calculations. In particular, the angulardistribution of the 2+ state of 22Ne is analyzed by DWBA and a similar calculation is performedfor the unstable 24Ne nucleus, using existing data from the reaction 24Ne+208Pb at 182 MeV (mea-sured at SPIRAL with the VAMOS-EXOGAM setup). In both cases the DWBA model gives agood reproduction of the experiment, pointing to a strong reduction of the βC

2 charge deformationparameter in 24Ne. This follows the trend predicted for the evolution of the quadrupole deformationalong the Ne isotopic chain.

PACS numbers: 25.70.Bc,25.70.Hi,24.10.Eq,27.30.+t

I. INTRODUCTION

Low-energy transfer reactions with heavy ions have re-cently become a powerful tool for the production and in-vestigation of exotic neutron-rich systems, not accessibleby standard fusion evaporation reactions [1, 2]. In par-ticular, the combination of a large acceptance magneticspectrometer with a high efficiency and high resolutionmulti-detector array for γ spectroscopy (based on Ge de-tectors) has turned out to be a key instrument in link-ing reaction dynamics and nuclear structure studies, farfrom stability [3, 4]. Recent works, focusing on nuclei inthe mass region around doubly magic 48Ca, have clearlydemonstrated the possibility to employ heavy-ion trans-fer reactions both for detailed particle-spectroscopy (withenhanced sensitivity to specific excited states by γ-gatingtechniques), and to perform full in-beam γ-spectroscopy

∗Corresponding author: [email protected]†Present Address: University of Padova, Padova, Italy

(i.e. angular distributions, polarizations, and lifetimesanalysis) [5–7]. This has outlined a new method whichcan become very valuable for future investigations, also inthe case of radioactive heavy-ion beams, providing com-plementary information to transfer reactions with lighttargets.

In this work we discuss the results of a similar anal-ysis on light neutron-rich nuclei around 22Ne, which areinstrumental for the understanding of the evolution ofthe shell structure moving towards the neutron-drip line.This is the region close to the so called ”island of in-version”, where a weakening of the N=20 magic num-ber has been observed. In particular, we present thestudy of the dynamics of the heavy-ion binary reaction22Ne+208Pb (at 128 MeV), performed at Legnaro Na-tional Laboratories with the PRISMA-CLARA setup, al-lowing for particle-γ coincidence experiments. The anal-ysis focuses on the measurement of differential cross sec-tions for the elastic, inelastic and one particle trans-fer channels. The experimental data are interpreted bythe semiclassical model GRAZING [8] and by the dis-torted wave Born approximation approach (DWBA), im-plemented in the code PTOLEMY [9]. The latter can be

2

used to obtain information on the parameters of the op-tical model potential, which are directly connected tothe structure/deformation of the colliding nuclei. Inthe case of the inelastic scattering to the 2+ state of22Ne, the present results are also compared with exist-ing data from the reaction 24Ne+208Pb (at 182 MeV),obtained in a similar experiment at GANIL using theVAMOS-EXOGAM setup, starting from the radioactive24Ne beam from SPIRAL [10]. In both cases, a DWBAanalysis is performed and βC2 deformation parameters forthe nuclear charge distributions are extracted and com-pared to existing experimental values and to predictionsof the evolution of the quadrupole deformation along theNe isotopic chain. The results follow the trend predictedby various calculations, supporting the existence of a de-formation minimum at 24Ne (N=14).

The paper is organized as follows: in Sec. II we de-scribe the 22Ne+208Pb reaction and the experimentalsetup, briefly recalling the procedure adopted for theidentification of the reaction products in the magneticspectrometer. In Sec. III we discuss the main points ofthe analysis, which focuses on the study of the elastic,inelastic and one-nucleon transfer channels. Emphasis isgiven to the inelastic scattering data and their interpre-tation by the DWBA model. Conclusions are given inSec. IV.

II. THE EXPERIMENT

The experiment has been performed at Legnaro Na-tional Laboratories of INFN, using the PRISMA-CLARAexperimental setup [11]. The 22Ne beam, provided by thePIAVE-ALPI accelerator complex at 128 MeV of bom-barding energy, impinged on a 208Pb target 300 µg/cm2

thick, sandwiched between two layers of 12C (10 and 15µg/cm2 thick respectively). The magnetic spectrome-ter PRISMA, described in Refs. [12–15], was placedaround the grazing angle for this reaction, which hasbeen estimated to be θlab = 70. PRISMA consists ofone quadrupole and one dipole magnet, with a solid an-gle of 80 msr (corresponding to ±6 in θ and ±13 inφ), a momentum acceptance ∆p/p = 10% and a disper-sion of 4 cm per percent in momentum. Being basedon a system of entrance and focal plane detectors (con-sisting in a micro-channel plate detector and a ioniza-tion chamber plus an array of parallel plates of multi-wire type, respectively), the trajectory of the ions in thePRISMA spectrometer can be reconstructed, event byevent. As described in detail in Ref. [5], the identificationof the reaction products is achieved: i) by determiningthe atomic number Z through the energy released in theionization chamber, and ii) by determining the A/q ratiovia time-of-flight and ion trajectory measurements, foreach charge state q. The coupling of the PRISMA spec-trometer with the γ-array CLARA, placed opposite toPRISMA, made possible particle-γ coincidence measure-ments for each ion detected in the magnetic spectrometer.

In the present experiment, the CLARA array consisted of21 high-purity (HpGe) Clover detectors covering a solidangle of 2π, with a total efficiency of the order of 2.5%at 1.3 MeV.

Fig. 1 shows the mass spectra for the most in-tense products populated in the 22Ne+208Pb experiment.They correspond to pure neutron transfer (0p), one-proton stripping (-1p) and one-proton pick-up (+1p) re-action channels. As already observed in a similar workon heavier systems around 48Ca [5], a slight asymmetryis visible in the one proton transfer products, pointing toa favorable population of lighter (heavier) masses in thestripping (pick-up) channels.

III. THE ANALYSIS

The aim of the present work is the evaluation of ab-solute differential cross sections for elastic, inelastic andone-particle transfer channels. For this purpose, the re-sponse function of PRISMA for the specific 22Ne+208Pbreaction had to be determined by the Monte Carlo proce-dure described in Ref. [15]. This is needed for a correcttreatment of the measured yields that can be stronglyaffected by the transmission into the spectrometer, es-pecially at the edges of the angular acceptance. As asecond point, the elastic channel has been studied in de-tail, in order to provide both a reference scale for crosssection measurements and the starting point for reactiondynamics investigation.

Following the method described in Ref. [16] and suc-cessfully applied in previous works [5, 10, 16], total ki-netic energy loss spectra (TKEL), defined as TKEL=-Qvalue, have been constructed, as a function of the scat-tering angle, for 22Ne ions detected in PRISMA. Theywere used to obtain the elastic cross section by subtract-ing TKEL spectra of 22Ne measured in coincidence withγ transitions detected in the CLARA array. The latterrepresent the inelastic contribution to the TKEL distri-butions. Due to the different efficiencies of the PRISMAand CLARA setup, this subtraction can be performedonly after a proper normalization of the two spectra.This is done in the high excitation energy region (above 4MeV) where the total and inelastic TKEL spectra mustcoincide, as shown in Fig. 2. The difference spectrum(shaded area) is a peak centered at TKEL ≈ 0, with aFWHM of ≈ 2.5 MeV, which agrees with the energy res-olution of the experimental setup. It consists of elasticevents, whose ratio with the Rutherford cross section,over the angular acceptance of the magnetic spectrome-ter (64 ≤ θlab ≤ 76), is shown in the inset of Fig. 2.The experimental data have been normalized, in the pureRutherford region (θlab = 66.5), to the theoretical ratioσel/σruth, calculated by the semiclassical code GRAZ-ING [8]. This allows to both extract a conversion factorbetween counts and mb/sr (i.e. 1 mb/sr = 215 counts)and to confirm the validity of the experimental proce-dure. To further check this experimental result, a more

3

2 1 2 2 2 3 2 4 2 5 2 6 2 70

5

1 0

10- 2 Co

unts

M a s s [ u ]

c ) N a ( + 1 p )

1 8 1 9 2 0 2 1 2 2 2 3 2 40

1

2

3F ( - 1 p )b )

M a s s [ u ]10- 3

Count

s

2 0 2 1 2 2 2 3 2 4 2 5 2 60

5

1 0

1 5

10- 4 Co

unts

M a s s [ u ]

N e ( 0 p )a )

FIG. 1: Mass spectra of the most intense isotopic chains produced in the 22Ne+208Pb reaction. The three panels correspondto the pure neutron transfer a), the one proton stripping b) and the one proton pick-up c) reaction channels.

detailed study of the elastic cross section has been donewith the DWBA model implemented in the PTOLEMYcode [9]. The parameters used for the nuclear potential,reported in Table I, have been obtained by fitting theσel/σruth experimental data and are consistent with thevalues used by the GRAZING model (see the discussionof inelastic scattering for a detailed description of theparameters). The result of the PTOLEMY calculation isshown in the inset of Fig. 2 by thick solid line.

V rV aV W rW aW rC β2

[MeV] [fm] [fm] [MeV] [fm] [fm] [fm]22Ne 67.37 1.167 0.668 19.26 1.167 0.668 1.25 0.37024Ne 66.98 1.167 0.671 35.00 1.167 0.671 1.25 0.075

TABLE I: Parameters of the Wood-Saxon optical poten-tials describing the collisions 22Ne+208Pb at 128 MeV and24Ne+208Pb at 182 MeV. V and W indicate the depth of thereal and imaginary parts, aV and aW the corresponding dif-fusenesses. rV and rW are the radii of the real and imaginarypotential, while rC is the radius of the Coulomb potential,for which standard values are used. The β2 deformation pa-rameters (obtained by fitting the inelastic cross section) arereported in the last column. It is assumed β2 = βC

2 = βN2 .

(See text for details).

The extracted conversion factor between counts andmb/sr has been kept as a reference for the following anal-ysis of differential cross sections. Fig. 3 shows the in-clusive (energy integrated) angular distribution for theelastic channel (22Ne in panel a)), the one neutron pick-up channel (23Ne in panel b)) and the one proton strip-ping channel (21F in panel c)), which are the most in-tense reaction products. The experimental data are com-pared with theoretical calculation performed by the semi-classical GRAZING model, which is able, in general, to

- 5 0 5 1 0 1 50

2

4

6

8

6 0 6 5 7 0 7 5 8 00 . 1

1

θl a b [ d e g ]σ el/σ

ruth

2 2 N e

10- 3Co

unts

T K E L [ M e V ]FIG. 2: (Color online) TKEL spectra for 22Ne ions detectedby PRISMA (thin red line) and in coincidence with γ transi-tions detected in CLARA (thick blue line). The shaded area isthe difference spectrum corresponding to elastic events. Inset:Elastic cross section over Rutherford cross section as a func-tion of the scattering angle. The experimental data (circles)have been normalized in the Rutherford region to the the-oretical calculation performed by the code GRAZING (thinblack line). The calculation performed by the PTOLEMYcode (with the optical model parameters listed in Tab. I), isshown by the thick red line.

well describe one particle transfer processes in low-energyheavy-ion binary reactions [1, 8]. We see that the ex-perimental angular distributions are rather well repro-duced by the calculations, with a global agreement be-tween data and theory. Similar quality of agreement wasalso obtained for the one-nucleon transfer channels in the

4

work of Ref. [10], where the more exotic 25Ne and 23Fchannels were studied, following the heavy ion reaction24Ne+208Pb. This indicates that the basic ingredientsentering the prescription of the reaction dynamics by theGRAZING model are still valid in the case of heavy-ionreactions induced by rather light systems such as Ne iso-topes, and moving away from the stability valley.

1 0 0

1 0 1

1 0 2

1 0 3

dσ/dΩ

[mb/s

r] b )

2 3 N e ( 0 p , + 1 n )

6 0 6 5 7 0 7 5 8 01 0 - 1

1 0 0

1 0 1

1 0 2

1 0 3

θ l a b [ d e g ]

c )

2 1 F ( - 1 p , 0 n )

1 0 0

1 0 1

1 0 2

1 0 3

1 0 4

a )

2 2 N e ( 0 p , 0 n )

FIG. 3: (Color online) Inclusive angular distributions for themost intense reaction channels 22Ne, 23Ne and 21F (panels a),b) and c)). Symbols correspond to experimental data, solidlines to theoretical calculations by the semi-classical modelGRAZING [8].

The γ spectra measured by the CLARA array in coinci-dence with the most intense 22Ne, 23Ne and 21F channelsare shown in Fig. 4. They have been Doppler corrected,on event by event basis, using the velocity and angles pro-vided by the trajectory reconstruction in the PRISMAspectrometer. In all three cases, the decay from the firstexcited state is clearly observed. Moreover, in the caseof 22Ne, the 2+ → 0+ transition at 1275 keV has enoughstatistics to determine the differential cross section forthe inelastic scattering to the 2+ state. This has beendone by integrating the area of the 1275 keV peak, foreach θlab angle covered by the acceptance of PRISMA. As

reported in Ref. [5], this procedure provides the directpopulation of the first excited state, after subtracting thefeeding contribution from higher lying levels and takinginto account the γ efficiency of the CLARA array. In thiscase, the feeding from the 4+ →2+ decay is negligible, asindicated by the absence of the corresponding γ peak inFig. 4 a), while at most a 25% feeding contribution canbe expected from higher-lying states around 5 MeV. Thisis suggested by the presence of a high-energy tail in theTKEL spectrum gated by the 2+ → 0+ γ-transition, asshown in the inset of Fig. 5 a). In the same panel, the re-sults (open symbols) are presented together with the datacorrected for this feeding contribution (filled circles). Inpanel b) we present inelastic scattering data taken fromRef. [10], relative to the 2+ state of the unstable 24Ne,populated by the 24Ne+208Pb reaction at 182 MeV.

0 5 0 0 1 0 0 0 1 5 0 0 2 0 0 0 2 5 0 00

7

1 4

2 1 Fc ) 1 / 2 + → 5 / 2 + 2 8 0 k e V

Eγ [ k e V ]

0

2 0

4 0 1 / 2 + → 5 / 2 + 1 0 1 7 k e V

2 3 N e

Count

s b )0

5 01 0 01 5 0

4 + → 2 + 2 0 8 3 k e V

2 2 N e

2 + → 0 + 1 2 7 5 k e V

a )

FIG. 4: Gamma spectra of 22Ne, 23Ne and 21F (panel a), b)and c), respectively). In each spectrum the γ transition fromthe first excited state to the ground state is clearly visible. Inthe case of 22Ne, the arrow indicate the position of the 4+ →2+ decay, at 2083 keV, not observed in this experiment.

Calculations of the inelastic scattering to the 2+ statehave been performed for both experiments, using the Dis-torted Wave Born Approximation model, implementedin the code PTOLEMY [9]. For the Wood-Saxon opti-cal model potentials we used the parameters reported inTab. I. In particular, the depth V and the diffusenessaV of the real part have been taken from the proxim-ity potential model [17], while the real radius rV andthe imaginary depth W have been determined by the fitof the σel/σRuth experimental data (see Fig. 2 and theinset of panel b) for 24Ne). The assumption rW = rV

5

and aW = aV has been adopted for the radius and dif-fuseness of the imaginary part of the nuclear potential.Furthermore, we have put βC2 = βN2 , because the fit tothe inelastic cross sections favored very similar values forthe nuclear and Coulomb deformation parameters. Thisis shown in Fig. 6, where the sensitivity to the deforma-tion parameters βC2 and βN2 is investigated for both 22Ne(panels a) and b)) and 24Ne (panels c) and d)) by chang-ing the optimal βC2 and βN2 values by 25%. In particular,we note that the fit of the inelastic distribution is notvery sensitive to the value of βN2 , while the variation ofβC2 influences the strength of the inelastic cross sectionsin a similar way for both nuclei. As a consequence, inthe following we discuss our results in terms of chargedeformation parameters βC2 only.

The values for βC2 obtained by the experimental analy-sis of 22Ne and 24Ne are reported in the last column of Ta-ble I and in Fig. 7 a) by filled diamonds. It is found that22Ne has a rather large quadrupole deformation (βC2 ≈0.4), with a value consistent with the one obtained by anearlier analysis of 22Ne+208Pb inelastic-scattering data,performed with a rotational coupled-channel model [18].In that work the reaction 22Ne+208Pb was also studied,and a very similar value was obtained for 20Ne (followingthe 20Ne+208Pb reaction), as shown by open diamondsin Fig. 7 a). On the contrary, in the present analysissmall values for the deformation parameters of 24Ne arefound (βC2 ≈ 0.1).

It is interesting to compare our βC2 values with thecharge deformation parameters derived from experimen-tal B(E2;0+ → 2+) measurements (Coulomb excitationor lifetime analysis techniques). Such values can be ob-tained, for example, by the droplet model of Ref. [24], orby applying the first-order formula

βC2 = (4π/3ZR20)[B(E2; 0+ → 2+)/e2)]1/2 (1)

with R0 = 1.2A1/3 the spherical radius of the nuclearcharge distribution. In Fig. 7 a) we show by open cir-cles the ”adopted” βC2 values [25], while filled circles referto the most recent measurements, derived from interme-diate energy Coulomb excitation experiments (at MSUand RIKEN) and from low-energy Coulomb excitationmeasurements (at ISOLDE) [26–29]. These recent valuesare systematically lower than the adopted ones, clearlyindicating the difficulty in determining experimentally afirm value for the βC2 parameter. Our results are alsosignificantly smaller than the adopted value. They cor-respond to a 30% reduction in the case of 22Ne (whichcould be accounted for by the uncertainty of the differentexperimental techniques), and to a much larger suppres-sion (of the order of a factor of 5) for 24Ne. In thiscase, the adopted value corresponds to the only existingB(E2) measurement via lifetime technique, reported inRef. [30]. Such a large discrepancy is rather puzzling anddefinitely calls for additional experimental investigationon the collectivity in 24Ne, a nucleus of key importancefor understanding the evolution of shell gaps in light sys-tems, moving towards the neutron drip line.

25 30 35 40 45 5010-2

10-1

100

101

102

25 30 35 40 45 500.1

1

el

ruth

2+

lab

[deg]

b) 24Ne

60 65 70 75 8010-1

100

101

102

103

-5 0 5 10 150.0

0.2

0.4

0.6

0.8

2+ 0+

10- 3 C

ount

s

TKEL [MeV]

Inelastic

2+

22Nea)

dd[

mb/

sr]

FIG. 5: (Color online) Panel a): Angular distribution of 22Neions measured in coincidence with the 2+ → 0+ γ transitionof 1275 keV. Filled (open) symbols refer to the analysis per-formed on the γ spectrum of 22Ne taking (not taking) into ac-count the feeding from high-lying states around 5 MeV. Insetof Panel a): inelastic TKEL spectrum of 22Ne and the con-tribution coming from the 2+ → 0+ γ-decay (shaded area).Panel b): Angular distribution of 24Ne, measured in coinci-dence with the 2+ → 0+ γ transition of 1982 keV. The insetof panel b) shows the elastic over the Rutherford cross sectionof 24Ne, as a function of the scattering angle. Experimentaldata are indicated by symbols, while theoretical calculationsperformed by the code PTOLEMY (GRAZING) are given bythick (thin) red (black) lines. Data for 24Ne are taken fromRef. [10]. (See text for details).

In Fig. 7 b) we show the deformation parameters ofthe ground state, βgs2 , obtained in three recent theoreti-cal calculations of the ground state of even Ne isotopes,such as the deformed Hartree-Fock plus BCS calculationswith Skyrme interaction [19], the deformed mean-fieldapproach with BCS theory for pairing correlations [20]and the very recent relativistic Hartee-Fock-Bogoliubovmodel [21]. We note that these studies are found to re-produce quite accurately the experimental charge radiiof Ne isotopes (determined by optical isotope shifts mea-surements [22]), across the sd neutron shell. As shownin the figure, the models predict that the deformationdecreases close to the middle of the sd shell, as a con-

6

sequence of the closure of the d5/2 subshell [22], whichfavors a spherical state or a small oblate deformation forIπ = 0+ and 2+, while a prolate deformation is expectedalready at Iπ = 4+ [23]. Our data may suggest a similartrend, but a direct comparison is not possible, becausethe transition strengths are not calculated in these stud-ies.

2 5 3 0 3 5 4 0 4 5

β N = 0 . 0 7 5 β N = 0 . 0 5 5 β N = 0 . 0 9 5 d )

2 4 N eβ C = 0 . 0 7 5

2 5 3 0 3 5 4 01 0 - 1

1 0 0

1 0 1

1 0 2

β C = 0 . 0 7 5 β C = 0 . 0 5 5 β C = 0 . 0 9 5 c )

θl a b [ d e g ]

2 4 N eβ N = 0 . 0 7 55 5 6 0 6 5 7 0 7 51 0 0

1 0 1

1 0 2

1 0 3

β C = 0 . 3 7 0 β C = 0 . 2 7 0 β C = 0 . 4 7 0

dσ

/dΩ [m

b/sr]

2 2 N eβ N = 0 . 3 7 0

a )5 5 6 0 6 5 7 0 7 5 8 0

β N = 0 . 3 7 0 β N = 0 . 2 7 0 β N = 0 . 4 7 0 b )

2 2 N eβ C = 0 . 3 7 0

FIG. 6: (Color online) Angular distributions of 22Ne (panelsa) and b)) and 24Ne (panels c) and d)) measured in coinci-dence with the corresponding 2+ → 0+ transitions. Symbolsrefer to data, lines to DWBA calculations performed by thePTOLEMY code, assuming different values for the parame-ters βC

2 (panels a) and c)) and βN2 (panels b) and d)), as given

in the legends. (See text for details).

IV. CONCLUSION

In this paper we have studied the dynamics of theheavy ion reaction 22Ne+208Pb at 128 MeV beam en-ergy. The experiment was performed at Legnaro Na-tional Laboratories, using the PRISMA-CLARA experi-mental setup, which allowed particle-γ coincidence mea-surements. Elastic, inelastic and one nucleon transferdifferential cross sections have been measured and com-pared with semiclassical and distorted wave Born ap-proximation (DWBA) calculations, resulting in a globalagreement between data and theory. A key point of theanalysis was the study of the angular distribution of the2+ state of 22Ne by the DWBA model, together withsimilar calculations performed for the 2+ state of theunstable 24Ne nucleus, based on existing data from the24Ne+208Pb reaction at 182 MeV beam energy [10]. Inboth cases the DWBA model gives a good reproductionof the data and allows to determine the βC2 deformationparameter of the nuclear charge distribution. In particu-lar, the analysis provides a very small βC2 value for 24Ne.This is consistent with the trend predicted for the evo-

1 8 2 0 2 2 2 4 2 6 2 8- 0 . 3

0 . 0

0 . 3

0 . 6

0 . 9

E b r a n e t a l . S i i s k o n e n e t a l . L a l a z i s s i s e t a l .

βgs 2

A [ u ]

b )- 0 . 3

0 . 0

0 . 3

0 . 6

0 . 9

E X P A d o p t e d E X P R e c e n t G r o s s e t a l . T h i s W o r k

a )

βC 2

FIG. 7: (Color online) Panel a): Quadrupole deformationparameter βC

2 of the nuclear charge distribution, along theisotopic Ne chain, as derived from experiments. Filled dia-monds refer to this work, open diamonds to a similar analysisperformed by Gross et al. [18], open circles to the experi-mental adopted values [25], filled circles to the most recentresults from Coulomb excitation experiments [26–29]. Panelb): Theoretical predictions for the ground state deformationparameter βgs

2 , as indicated by the legend [19–21]. (See textfor details).

lution of ground state quadrupole deformation βgs2 alongthe Ne isotopic chain, which suggests a subshell closureat N=14. Such a result calls, indeed, for additional ex-perimental investigation on this nucleus, which is of keyimportance for the understanding of the shell structurealong the Ne isotopic chain.

In conclusion, the present work demonstrates the va-lidity of heavy-ion reaction studies for both dynamicsand nuclear structure investigations, providing a fruitfulmethod which could be further exploited in the futurefor the investigation of very exotic species. This will re-quire the use of high-efficiency γ-detector spectrometer,such as the AGATA array currently under development[31–33], coupled to large acceptance spectrometer, suchas PRISMA at Legnaro and VAMOS at GANIL.

Acknowledgments

This work was supported by the Italian IstitutoNazionale di Fisica Nucleare and partially by theSpanish MICINN (AIC10-D-000568 bilateral action andFPA2008-06419) and Generalitat Valenciana (GrantPROMETEO/2010/101). The work has also been par-tially supported by the Polish Ministry of Science andHigher Education (Grant No. N N202 309135).

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