application/xmlSpectroscopy of 39,41Si and the border of the [formula omitted] island of inversionD. SohlerS. GrévyZs. DombrádiO. SorlinL. GaudefroyB. BastinN.L. AchouriJ.C. AngéliqueF. AzaiezD. BaiborodinR. BorceaC. BourgeoisA. ButaA. BurgerL. CaceresR. ChapmanJ.C. DalouzyZ. DlouhyA. DrouardZ. ElekesS. FranchooS. IacobI. KutiB. LaurentM. LazarX. LiangE. LiénardS.M. LukyanovJ. MrazekL. NalpasF. NegoitaF. NowackiN.A. OrrYu.E. PenionzkhevitchZs. PodolyákF. PougheonA. PovesP. Roussel-ChomazM. StanoiuI. StefanM.G. St-LaurentNuclear structureKnockout reactionsShell closuresNeutron-rich Si nucleiPhysics Letters B 703 (2011) 417-421. doi:10.1016/j.physletb.2011.08.004journalPhysics Letters BCopyright © 2011 Elsevier B.V. All rights reserved.Elsevier B.V.0370-2693703420 September 20112011-09-20417-42141742110.1016/j.physletb.2011.08.004http://dx.doi.org/10.1016/j.physletb.2011.08.004doi:10.1016/j.physletb.2011.08.004http://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/JournalsS300.3PLB27850S0370-2693(11)00913-010.1016/j.physletb.2011.08.004Elsevier B.V.ExperimentsFig. 1γ-ray energy spectra obtained for 39Si and 41Si.Fig. 2γ-gated spectra for 39Si using the 163 (left) and 303+397 keV (right) transitions as gates.Fig. 3Comparison of the experimental level schemes of the N=25 isotones 39Si and 45Ca [18] with shell-model calculations for 39Si assuming a closed proton core (“neutrons only”), and using the full valence sd–pf space (“full”). In the proposed level scheme for 39Si the energies and relative intensities are listed with the uncertainties along the transitions. The width of the arrows is proportional to the intensity of the γ-rays.Fig. 4Comparison of the experimental level schemes of the N=27 isotones 41Si and 47Ca [15] with shell-model calculations of 41Si assuming a closed proton core (“neutrons only”), and using the full valence sd–pf space (“full”).Fig. 5Contributions of the neutron cross shell excitations to the 7/21− (top), 3/21− (middle) states and proton cross shell excitations (bottom) to the ground state wave functions of odd Si isotopes between N=20 and 28. On the x axis the number of excitations with respect to the νf7/2 and the πd5/2 orbits are indicated.Fig. 6Correlation energies calculated for the 7/21− state in the Si isotopes. Lines are to guide the eye.Spectroscopy of 39,41Si and the border of the N=28 island of inversionD.Sohlera⁎sohler@atomki.huS.GrévybcZs.DombrádiaO.SorlinbL.GaudefroydB.BastinbN.L.AchourieJ.C.AngéliqueeF.AzaiezfD.BaiborodingR.BorceahC.BourgeoisfA.ButahA.BurgerijL.CaceresbR.ChapmankJ.C.DalouzybZ.DlouhygA.DrouardiZ.ElekesaS.FranchoofS.IacobhI.KutiaB.LaurenteM.LazarhX.LiangkE.LiénardeS.M.LukyanovlJ.MrazekgL.NalpasiF.NegoitahF.NowackimN.A.OrreYu.E.PenionzkhevitchlZs.PodolyáknF.PougheonfA.PovesoP.Roussel-ChomazbM.StanoiuhI.StefanfM.G.St-LaurentbaInstitute of Nuclear Research, H-4001 Debrecen, Pf. 51, HungarybGANIL, CEA/DSM-CNRS/IN2P3, BP 55027, F-14076 Caen Cedex 5, FrancecCentres dʼEtudes Nucléaires de Bordeaux Gradignan, Université Bordeaux 1, UMR 5797 CNRS/IN2P3, F-33175 Gradignan Cedex, FrancedCEA/DAM, DIF, Bruyeres-le-Chatel, F-91297 Arpajon Cedex, FranceeLPC, ENSICAEN et Université de Caen, IN2P3/CNRS, F-14050 Caen cedex, FrancefInstitut de Physique Nucleaire, IN2P3-CNRS, F-91406 Orsay cedex, FrancegNuclear Physics Institute, AS CR, CZ-25068 Rez, Czech RepublichInstitute of Atomic Physics, IFIN-HH, Bucharest-Magurele, P.O. Box MG6, RomaniaiCEA Saclay, DAPNIA/SphN, F-91191 Gif-sur-Yvette Cedex, FrancejHelmholtz-Institut fur Strahlen- und Kernphysik, Universitat Bonn, Nussallee 14-16, D-53115 Bonn, GermanykSUPA, School of Engineering, University of the West of Scotland, Paisley PA1 2BE, United KingdomlFLNR, JINR, 141980 Dubna, Moscow region, RussiamIPHC, Université de Strasbourg, IN2P3/CNRS, BP28, F-67037 Strasbourg Cedex, FrancenUniversity of Surrey, GU2 7XH, United KingdomoDepartamento de Física Teórica e IFT-UAM/CSIC, Universidad Autónoma de Madrid, E-28049 Madrid, Spain⁎Corresponding author.Editor: D.F. GeesamanAbstractThe structure of the very neutron-rich nuclei 39Si and 41Si has been investigated via in-beam γ-ray spectroscopy and few-nucleon knockout from radioactive beams. The observation of low-lying states in 39Si is a clear evidence for a drastic lowering of the intruder neutron 3/2− state when going from Z=20 to Z=14. The energy of the only γ-ray transition (672(14) keV) observed in 41Si is significantly lower than that of the first excited state in 47Ca (2014 keV) suggesting a deformed ground state for 41Si. These results are consistent with large-scale shell-model calculations implying that strong proton–neutron correlations are the main reason for the lowering of the intruder configurations over the normal ones.KeywordsNuclear structureKnockout reactionsShell closuresNeutron-rich Si nuclei1IntroductionThe nuclei in the vicinity of the N=28 shell closure offer a fertile ground for studying the various aspects of nuclear forces and correlations. The change in the single-particle energies as a function of the proton and neutron numbers leading to the reduction of the N=28 shell gap below 48Ca, as well as that in the splitting between the spin–orbit partners of the neutron f7/2 and p3/2 orbits, arises from the monopole terms of the nuclear interaction. In addition, correlations of a quadrupole character drive the development of a new “island of inversion” around 42Si, where according to mean field [1] and shell-model [2–4] calculations, deformed intruder configurations fall below the spherical ones.The development of the N=28 island of inversion can be followed through the evolution in structure of the N=27 isotones. In 45Ar, a low-lying 3/2− state has been observed at 537 keV above the 7/2− ground state [5]. It has been shown via the 44Ar(d,p) reaction that this state contains about half of the p3/2 strength [3]. In 43S, the ordering between the normal 7/2− and the intruder 3/2− states is changed. A low-energy 7/2− isomer has been discovered [6] connecting the 3/2− ground state with a very low reduced transition probability B(E2). Based on the B(E2) and the measured g-factor, the 7/2− isomeric state has been assigned to the νf7/2 spherical configuration [7].The observation of a deformed ground state [8] and a spherical isomeric 0+ state [9] in 44S confirms that it is within the island of inversion. From the low energy of the first excited state, 42Si is also expected to have a deformed ground state [10]. The slight decrease of the 2+ energy in 40Si relative to the systematics was also invoked as an argument in favor of an enhanced collectivity [11].To confirm that deformation is favored around 4214Si28 and to determine the location of the border of the island of inversion in the neutron-rich Si isotopes, we have studied the 3914Si25 and 4114Si27 isotopes, having 3 and 1 neutron–hole configurations with respect to an N=28 core, respectively.2ExperimentExcited states in 39Si and 41Si were populated and studied in the present work via in-beam fragmentation of fast secondary beams. A 48Ca beam of 60 MeV/u energy and 4 μAe intensity, delivered by the GANIL facility, was employed to bombard targets of 12C and 181Ta (∼200 mg/cm2). The secondary beams of interest were collected and selected using the SISSI device coupled to the α spectrometer in which a 50 μm Al achromatic degrader was placed between the two sets of dipole magnets. The magnetic rigidity (Bρ) was tuned to optimize the production of 40,41,42P and 42,43,44S for which average rates of 65, 130, 20, 120, 220 and 125 pps were obtained, respectively. A combination of energy-loss (ΔE) and time-of-flight information, measured using a 50 μm-thick Si and microchannel plate detectors, allowed unambiguous identification of the secondary beam particles on an event-by-event basis. Behind the Si detector a secondary Be target of 185 mg/cm2 was used to induce secondary fragmentation.The nuclei produced by the secondary fragmentation were selected using the SPEG spectrometer and identified by the ΔE, time-of-flight and Bρ. The ΔE was measured using an ionization chamber, while the time-of-flight was determined between the channel–plate detector located upstream of the target and a thick plastic-detector placed just behind the focal plane of the spectrometer. The Bρ was inferred from the trajectories of the nuclei, which were obtained using two pairs of drift chambers straddling the focal plane. By combining the Bρ and time-of-flight information, the mass-over-charge ratio can be derived to provide the identification matrix of the secondary fragments.The 39Si nuclei were produced by 1p, 1p1n, 2p1n and 2p2n knockout reactions from the 40,41P and 42,43S secondary beams, respectively. The production of 41Si was almost equally shared between the 1p, 2p and 2p1n reaction channels from 42P, 43S and 44S. The 2p knockout cross section 43S→41Si at 41.5A MeV was measured to be 71±14 μbarn. This is comparable to the value of 80±10 μbarn obtained for the 2p removal reaction 44S→42Si [10].The secondary target was surrounded by the 4π “Chateau de Crystal” array consisting of 74 BaF2 scintillators to measure the emitted γ-rays. The individual detector threshold was set to about 100 keV. As the scintillators of the array were closely packed, an addback procedure was used to increase the photopeak efficiency leading to efficiencies of 38% at 779 keV and 24% at 1.33 MeV for fragments with v/c≈0.3. The γ-ray spectra were obtained by selecting, event-by-event, the nuclei of interest in the secondary beam and in SPEG following the interaction with the secondary target. Doppler corrections were applied based on the velocity of the ions as determined from the time-of-flight and trajectory information. The energy of the γ-ray lines used for the calibrations could be reproduced with a 6 keV uncertainty, which corresponds to the systematic uncertainty of the energy determination.3ResultsThe γ-ray energy spectra for 39,41Si are displayed in Fig. 1. In 41Si, a clear peak is seen at 672±14 keV. In the spectra for 39Si, two strong γ transitions at 163 and 397 keV, as well as weaker ones at 303, 657, 906, 1143 and 1551 keV, were identified. The spectrum for 39Si obtained using 1p knockout from 40P is dominated by the 163 keV transition.A γγ-coincidence analysis was possible for 39Si after adding together all the data from the various reaction channels. As shown in Fig. 2, the 163 keV transition is in coincidence with the 657, 1143 and 1551 keV ones, but not with the 397 keV transition. The two lines of the 303+397 keV doublet are in mutual coincidence, and one or both of them are in coincidence with the 906 keV transition.The level scheme of 39Si displayed in Fig. 3 was constructed from the γγ coincidences, the relative intensities and the energy balance of the transitions. The energy of the excited states was determined using the fitting procedure of the Radware package [12] and the energies of the feeding and de-exciting γ lines, including uncertainties. As the most intense 163 and 397 keV γ-rays are not in coincidence, they are placed in parallel and directly connected to the ground state. The 397(14)+906(17) and 163(12)+1143(27) keV sum energies overlap with each other, within the experimental errors. Thus, they establish an excited state at 1304 keV. Although, the 303 keV transition is placed above the 401 keV state based on the γγ coincidences and the intensity argument, it cannot be excluded that this γ-ray feeds a higher-lying level. Based on the coincidence information, the 657 and 1551 keV transitions connect the levels at 817 and 1711 keV with the state at 160 keV, respectively.4DiscussionGiven that the strengths of the Z=14 (∼5 MeV at N=28[13]) and Z=20 (∼5.3 MeV between N=22 and 26 [14]) shell gaps are similar, it may be instructive to compare the spectra of the Si1439,41 and Ca2045,47 isotones.The 7/2− ground state of 47Ca corresponds to a 1 neutron–hole configuration f7/2−1. The first excited state lies at 2.01 MeV excitation energy. This 3/2− state has a rather pure 1 particle–2 hole configuration [15], being well populated in the 46Ca(d,p) neutron stripping reaction [16] and extremely weakly populated in the 48Ca(d,t) neutron pick-up reaction [17] owing to the closed shell structure of 48Ca. In 41Si, only a γ transition was identified, which we assign to the decay of a level at 672 keV (Fig. 4). This is significantly smaller than the energy of the first excited state in 47Ca, indicating that the two nuclei have very different structure. The low energy of the state at 672 keV in 41Si suggests a deformed configuration, as for the neighboring nucleus 42Si which has a low-lying 21+ state [10].The low-energy structure of 45Ca can be described by 3 neutron–hole configurations with respect to a 48Ca core. This leads to a multiplet of states based on the f7/2−3 configuration: the two first states – the 7/2− ground state and the 5/2− first excited state – are separated by only 174 keV, while the other members of the multiplet are found above 1.43 MeV [18]. In 39Si, the ground and the first excited states are separated by 160 keV and may also arise from the neutron f7/2−3 configuration. However, the existence of other low-lying states in 39Si reveals a structural change relative to 45Ca and indicates the presence of low-lying intruder configurations already at N=25.These results point to a significant change in nuclear structure between the Ca and the Si isotopic chains. This feature could be accounted for by the decrease in size of the N=28 shell gap by about 1 MeV in the Si nuclei compared to the corresponding Ca isotones, as it has been shown both for N=20[19] and 28 [20]. For instance, the N=28 gap of ∼4.5 MeV in 48Ca [14] is estimated to decrease to ∼3.5 MeV in 42Si [20]. Thus, it may be assumed that the decreasing N=28 shell gap is responsible for the lowering of the intruder configurations observed.To verify this hypothesis, shell-model calculations were carried out using the SDPF-U interaction [2] with a closed proton Z=14 core and the neutron fp-valence space. These calculations are labeled “neutrons only” in Figs. 3 and 4. As it may be seen in the level schemes reported in Fig. 3, the low-energy structure of 39Si is not fully reproduced by these calculations which rather predict a spectrum similar to that of 45Ca, but more compressed in energy. Only two low-lying states are calculated, together with a high-density region of levels starting at 866 keV. The latter occurs lower in energy compared to 45Ca in line with the decrease in energy of the 2+ states in the Si isotopes relative to Ca. These calculations suggest that the decrease in the N=28 shell gap alone cannot explain the lowering of the intruder states. By inhibiting proton excitations, there is not enough degree of freedom to account for the observed experimental spectrum.To investigate the role of the proton excitations across the Z=14 gap, the level schemes for 39,41Si were recalculated using the full sd proton and fp neutron valence space reported as “full” in Figs. 3 and 4. Comparing the results of these calculations to the experiment, the low-energy level scheme of 39Si is better reproduced by the full space calculations which predict a νf7/2−35/2− ground state and low-lying 7/2− and 3/2− states with strong νf7/2 and νp3/2 components. The decay of the first two excited states in 39Si is consistent with this picture. In addition, the calculated level density is also consistent with the experimental one. In 41Si, two groups of low-lying states, centered around 750 keV and 150 keV, are predicted by the “full” shell-model calculations. These groups are separated by about 600 keV, which is close to the energy of the observed peak in the γ-ray spectrum at 672 keV. Note that, given its energy width, this line may correspond to a multiplet. The observation of γ lines from the lowest energy group of states is hampered for two reasons. First, they lie below the 150 keV threshold of the gamma-array. Second the 7/21 state in 41Si, built principally on the νf7/2 orbit, is predicted to be an isomeric state with a half-life of about 400 ns similar to 43S [6,7]. Such a decay could not be observed here where only prompt γ-rays were detected. The “full” shell-model calculations, which predict a low-lying intruder 3/2− state in 39Si and a 3/2− ground state for 41Si, suggest that the order of the normal 7/2− and the intruder 3/2− states inverts between A=39 and 41.To better identify the respective contributions of the proton and neutron excitations to the onset of collectivity while approaching N=28, the shell-model wave functions of the “normal” 7/21 and the “intruder” 3/21 states were analyzed in the heavy odd Si nuclei. As it may be seen in Fig. 5, near N=20both the 7/21− and the 3/21− states exhibit clear neutron single-particle characters. Indeed, the wave functions correspond mainly (more than 85%) to 0-particle–0-hole and 1-particle–1-hole configurations, respectively. Conversely, when approaching N=28, the amount of cross-shell excitations, i.e. the collectivity of the states, gradually increases in both the “normal” and “intruder” states. Despite the fact that the N=28 shell gap increases by about 0.8 MeV per pair of neutrons added between N=20 and 28 [14], deformation develops as if N=28 was at mid-shell. As it is shown in Fig. 5, the role of proton and neutron cross shell excitations in the shell-model calculations increases with increasing mass, being a maximum for the ground state of 41Si. Experimentally, the lowering of the intruder states is indicated by the increasing complexity of the level schemes of the odd Si nuclei with increasing mass number. The gradual increase of the ground state deformation has been revealed by (p,p′) studies of the even–even Si nuclei [21].To obtain a better understanding of which type of correlations induce the deformation at N=28 in the Si chain, Fig. 6 presents the correlation energy of the 7/21− state calculated using three different valence spaces: “neutrons only” in which the proton core is frozen; “N=28 closed” in which the neutrons are frozen in the f7/2 orbit, and “full” in which both protons and neutrons can be excited. From the “neutrons only” calculations, the contribution of the neutron–neutron correlations slowly increases with increasing mass number but saturates at N=28. Calculations for the “N=28 closed” case exhibit a single closed shell behavior with an increased correlation at the mid-shell. These two calculations are consistent with N=20 and 28 shell closures. The role of the cross-shell proton–neutron excitations can be deduced from the “full” calculations. These exhibit a steady increase of the correlations up to 15.8 MeV, rather than a saturation at N=27. By comparing this to the estimated size of the N=28 spherical gap of 3.5 MeV, up to 5-particle–5-hole configurations are possible, again suggesting that the nuclei around N=28 rather behave as if they were at mid-shell. This observation may be connected with the fact that both the N=28 and Z=14 shell gaps occur within a major shell, i.e. the sd shell for protons and the fp shell for neutrons. As a consequence, 1-particle–1-hole quadrupole cross-shell excitations can also take place, which limit the energy required for cross-shell excitations in spite of there being relatively large shell gaps. In addition, the “normal” and “intruder” configurations have the same parity, which allows for mixing of the normal and cross-shell excitations resulting in deformation of the normal states, as well. Similar mechanism might dictate the energy of the intruder states in 78Ni, where both the Z=28 and the N=50 shell gaps separate states from the same major fp and gds oscillator shells, respectively. This mechanism differs significantly from the development of island of inversion at N=8 or N=20, where the cross-shell excitations take place between different oscillator shells having different parity.5SummaryExcited states in 39Si and 41Si have been identified for the first time. A comparison of the level structure of 39,41Si with that of the 45,47Ca isotones, as well as with the results of large-scale shell-model calculations, was used to infer the lowering of the intruder states in 39,41Si. A low-lying intruder state in 39Si and a deformed 41Si ground state are proposed. Based on the shell-model calculations, it is suggested that the border of the N=28 island of inversion falls between N=25 and 27 in the Si isotopes, confirming that 42Si lies in a region of deformation. It is shown that to account for the low-lying level structure of 39,41Si, both neutron and proton excitations across the N=28 and Z=14 shell closures are required.AcknowledgementsThe authors wish to thank the staff from GANIL and LPC for their assistance in preparing and executing the experiment. This work has partially been supported by the EC through the Eurons contract RII3-CT-3/2004-506065, OTKAK68801, TéTFR-9/2009, BMBF06BN109, Czech Republic GA202/040791, the “Dubna-IN2P3” Agreement, grant RFFI-09-02-91056 and by the Bolyai János Foundation. APʼs work is partly supported by a grant of the Spanish Ministry of Education and Science (FPA2009-13377) and by the Comunidad de Madrid (Spain), project HEPHACOSS2009/ESP-1473. FN and APʼs work is partly supported by the IN2P3(France)-CICyT(Spain) collaboration agreement.References[1]T.R.WernerNucl. Phys. A 5971996327P.-G.ReinhardtPhys. Rev. C601999014316G.A.LalazissisPhys. Rev. C601999014310S.PéruEur. Phys. J. A9200035R.Rodriguez-GuzmanPhys. Rev. C652002024304[2]F.NowackiA.PovesPhys. Rev. C792009014310[3]L.GaudefroyPhys. Rev. C782008034307[4]L.GaudefroyPhys. Rev. C812010064329[5]Zs.DombrádiNucl. Phys. A7272003195[6]F.SarazinPhys. Rev. Lett.8420005062[7]L.GaudefroyPhys. Rev. Lett.1022009092501[8]T.GlasmacherPhys. Lett. B3951997163[9]C.ForcePhys. Rev. Lett.1052010102501[10]B.BastinPhys. Rev. Lett.992007022503B. Bastin, PhD thesis, Université de Caen, LPCCT 07-03, http://tel.archives-ouvertes.fr/docs/00/26/98/86/PDF/these_bastin.pdf.[11]P.M.CampbellPhys. Rev. Lett.972006112501[12]D.C.RadfordNucl. Instrum. Methods A3611995297[13]P.D.CottleK.W.KemperPhys. Rev. C5819983761[14]O.SorlinM.G.PorquetProg. Part. Nucl. Phys.612008602[15]T.W.BurrowsNuclear Data Sheets1082007923[16]T.A.BelotePhys. Rev.1421966624[17]M.E.Williams-NortonNucl. Phys. A2911977429[18]T.W.BurrowsNuclear Data Sheets1092008171[19]S.NummelaPhys. Rev. C632001044316[20]L.GaudefroyPhys. Rev. Lett.972006092501[21]P.M.CampbellPhys. Lett. B6522007169