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Precise reaction cross sections (oR) for 24_38M g on C targets at energies around 240 M eV /nucleon have been measured at the Radioactive Isotope Beam Factory at RIKEN. The oR for 36-38 Mg have been measured for the first time. An enhancement o f oR compared to the systematics for spherical stable nuclei has been observed, especially in the neutron-rich region, which reflects the deformation of those isotopes. In the vicinity of the drip line the aR for 37Mg is especially large. It is shown by analysis using a recently developed theoretical method that this prominent enhancement of oR for 37Mg should come from the p-orbital halo formation breaking the N = 28 shell gap.Since the early years of the study of atomic nuclei, the nuclear shell model has been the basic framework for understanding nuclear structure. The high stability of nuclei with certain numbers of neutrons (or protons) observed in stable nuclei indicates the existence of the shells filled at certain so-called "magic numbers." Studies in the last few decades have revealed that those magic numbers are sometimes broken or changed in unstable nuclei [1], The breakdown of the N = 20 shell gap between the sd and f p shells has been extensively studied since the irregularities in binding energies and 2+ excitation energies were observed in neutron-rich nuclei around N = 20 [2-6]. The term "island of inversion" was applied to this region [6] and deformed nuclear structures related to the changing of shell structures have been reported in this region [7]. The vanishing of the N = 28 shell closure has been also extensively studied, starting from neutronrich S-Ar isotopes [8][9][10][11][12][13][14]. The development of deformation observed in those nuclei could be interpreted as degeneracy of the f p shell, which induces strong quadrupole deformation [9][10][11][13][14][15][16][17][18]. Such deformation has been reported also for Si isotopes [19,20], and studies have recently indicated that this * takechi @ np.gs .niigata-u. ac .jp PACS number(s): 21.10.Gv, 25.60.Dz phenomenon could be seen even in a very neutron-rich Mg region [21].The purpose of our present study is to elucidate the changes of nuclear structures, such as a development of deformation, a breakdown of the magic numbers and possible halo formation in Mg isotopes, from the stability line to the vicinity of the neutron drip line. For this purpose, precise measurements of reaction cross sections for 24_38Mg have been performed at the Radioactive Isotope Beam Factory (RIBF) at RIKEN. The reaction cross section aR or interaction cross section ay reflects the nuclear size, and has been a powerful probe in searching for halo formation since the first study by Tanihata et al. [22], Recently, measurements of o, for Ne isotopes performed at RIBF [23] have successfully revealed the halo structure of 3lNe in which the sd-pf shell inversion associated with nuclear deformation causes the formation of a halo [23][24][25]. Moreover, theoretical studies on those data have shown that a precise data set on crR is v...

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