In-beam γ-ray spectroscopy of 38,40,42Si

Excited states in the nuclei 38,40,42Si have been studied using in-beam γ-ray spectroscopy following multi-nucleon removal reactions to investigate the systematics of excitation energies along the Z=14 isotopic chain. The most probable candidates for the transition from the yrast 4 + state were tentatively assigned among several γ lines newly observed in the present study. The energy ratios between the 2 +1 and 4 + 1 states were obtained to be 2.09(5), 2.56(5) and 2.93(5) for 38,40,42Si, respectively, indicating a rapid development of deformation in Si isotopes from N=24 to, at least, N=28. aPresent address: Center for Nuclear Study, University of Tokyo, RIKEN campus, Wako, Saitama 351-0198, Japan be-mail: matsushi@cns.s.u-tokyo.ac.jp DOI: 10.1051/ C © Owned by the authors, published by EDP Sciences, 2014 , / 02070 (2014) 201 66 epjconf EPJ Web of Conferences 46 602070 This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20146602070


Introduction
One of the most predominant properties of nuclei is nuclear shell structure, and the resultant "magic number" (2, 8, 20, 28, ...) have been provided experimentally by systematic behaviors of physical properties, such as quadrupole transition strengths B(E2) and excitation energies of the first 2 + state E x (2 + 1 ) [1].However, it is now well established that magic numbers are not universal and develop in the region far from stability line.One of well-known examples is the case of the neutron-rich isotope 32 Mg, where the low energy E x (2 + 1 ) and large B(E2) indicate shell quenching despite of a conventional magic number N=20 [2,3].It is a fundamental and open question whether and how the changes of the major shell closures and magic numbers occur along the nuclear chart.
The N=28 isotope, 42 Si, can be regarded as a magic nucleus in the traditional shell model, because a large energy gap exists at N=28 and Z=14 due to the f 7/2 − f 5/2 and d 5/2 − d 3/2 spin-orbit splitting, respectively.The disappearance of the spherical shell closure together with a large deformation, however, has been suggested for 42 Si from the observation of a low energy 2 + 1 state [4].Several experiments have been performed so far [5][6][7][8][9][10], but no experimental data have been reported on higher-lying state, such as 4 + 1 state, which may contribute valuable information on the nature of the collectivity and/or shell evolution.

Experiment
In order to investigate the 2 + 1 and 4 + 1 states, we performed in-beam γ-ray spectroscopy of 38,40,42 Si with multi-nucleon removal reactions [11].Experiment was carried out at the RI Beam Factory accelerator complex operated by the RIKEN Nishina Center and CNS, University of Tokyo.The 40 S and 44 S beams were produced by a projectile fragmentation reaction of a 48 Ca primary beam with a typical intensity of around 70 pnA.The primary beam with the energy of 345 MeV/nucleon bombarded a 15 mm-thick rotating Be target located at the F0 focal plane of the in-flight RI beam separator BigRIPS [12].The energy and intensity of the secondary 40 S ( 44 S) beam were approximately 210 MeV/nucleon (210 MeV/nucleon) and around 4×10 4 particles per second (pps) (6×10 4 pps), respectively.The secondary beams bombarded a reaction target of 2.54 g/cm 2 -thick carbon located at the F8 focal plane in the ZeroDegree Spectrometer [13], which was employed to analyze the reaction products 38 Si and 40,42 Si produced by the multi-nucleon removal reaction of 40 S and 44 S, respectively.De-excitation γ-rays were detected by the DALI2 γ-ray spectrometer [14] in coincidence with each beam and scattered particles.

Experimental Results
The Doppler-shift corrected γ-ray energy spectra obtained for 38 Si, 40 Si and 42 Si are shown in Fig. 1.As shown in Fig. 1 (c), the 2 + 1 → 0 + g.s.transition in 42 Si, previously observed at 770 (19) keV [4], is measured here at 742 (8) keV with high statistics, while three weaker γ-ray transitions with energies of 1431 (11), 2032 (9) and 2357 (15) keV are reported for the first time.Using γ-γ coincidences and γ-ray relative intensities, the 1431-keV line was deduced to fully feed the 2 + 1 state from a higher-lying excited state at 2173 keV.On the other hand, yield of the 2357-keV transition in γ-γ coincidence spectrum indicated that it does not, or at least does not fully, populate the 2 + 1 state at 742 keV.The present study indicates no direct evidence for firm spin assignments.However, the 1431-keV γ line was tentatively assigned as the 4 + 1 → 2 + 1 transition in 42 Si based on the fact that yrast states are preferentially populated for isotopes in this mass region via multi-nucleon removal reactions [15][16][17] and it directly feeds the 2 + 1 state, as mentioned above.Similar analytical techniques were applied 38 Si and 40 Si.The 1168(22)-and 1539( 16)-keV γ lines, as shown in Fig. 1

Discussion and Summary
The isotopic dependence of the excitation energy of 2 + 1 and 4 + 1 states are shown for 34−42 Si together with their ratio R 4/2 in Fig. 2, where the systematic properties of Ca isotopes are also given for the comparison.In the Ca isotopic chain, the relatively high energy 2 + 1 state clearly demonstrates the persistence of the conventional neutron magic number at N=28 as well as N=20.The depressed R 4/2 ratios at the both neutron magic numbers are much smaller than 2, showing the spherical nature of 40 Ca and 48 Ca, and supporting the above perception from the 2 + 1 state.In contrast, Si isotopes, with a lack of six protons from Ca isotopes, show different behaviors.The continuous decrease of E x (2 + 1 ) indicates the enhancement of nuclear collectivity from N=20 to N=28.The lowest energy 2 + 1 state, 742 keV observed in 42 Si, suggests the disappearance of its magic nature and the deviation from the conventional shell model scheme.As for the 4 + 1 state, the R 4/2 ratios for 36 Si and 38 Si are close to the vibrational limit (2.00), whereas it increases to 2.56(5) at 40 Si, indicating a deviation from the spherical shape at N=26.In the case of the N=28 isotope 42 Si, the R 4/2 ratio further increases to 2.93(5) despite the neutron magic number N=28, indicating a well-deformed ground state property of 42 Si.These results on Si isotopes are in good agreement with the prediction of the shell model calculations using SDPF-MU [18,19] and SDPF-U-MIX [20,21] effective interaction, which are denoted by solid and dashed line in Fig. 2, respectively.
In summary, the excited 4 + 1 states in 38,40,42 Si were tentatively assigned in the present study of inbeam γ-ray spectroscopy following multi-nucleon removal reactions [11].The results on 42 Si demonstrate the magicity loss together with a well-deformed ground state structure, which have been suggested in previous work [4], while the R

Figure 2 .
Figure 2. The energy of 2 +1 -and 4 + 1 state (left panel), and its ratio (right panel) of Si isotopes are compared with Ca isotopes.Filled symbols are results obtained from the present study.Solid and dashed lines show the prediction of the shell model calculations using SDPF-MU and SDPF-U-MIX interaction for Si isotopes, respectively.The horizontal lines at R 4/2 =2.00 (3.33) in right panel indicates the vibrational (rotational) limit.The vertical lines at the neutron magic number in both panels are intended to guide the eye.