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Intruder orbitals in the shell structure play important roles in the existence and disappearance of the magic numbers and the nuclear shape. Magicity loss of $N=8$ in light beryllium nuclei is one of the attractive subject from this viewpoint.
The $^{12}$Be has low-lying $0^+$ isomeric state at 2.2~MeV due to the narrow gap at $N=8$ caused by the intruder orbital from $sd$-shell[1] and its ground state is largely deformed[2]. As the origin of the narrow gap at N=8, the effect of the monopole interaction[3], the deformation[2], and the weakly bound nature[4] were suggested but there relationship was not clear. The neighboring nucleus $^{13}$ has one more proton and its ground state is spherical shape. Adding one proton to $^{12}$Be causes drastic change of the ground state structure. But the excitation structure of $^{13}$B was not known well since the spin-parity of the excited states was not determined. Considering the proton orbitals in $^{13}$B, binding energy is large enough and the counter orbital of the neutrons for the monopole interaction is fully occupied. However, the deformation of the matter shape can still have effect on the structure if it exists. To reveal the effect of one proton addition to the deformed nucleus, proton single particle excitation in $^{13}$B was studied via the helium induced proton transfer reaction on $^{12}$Be[5].
The experiment was performed at RIPS course of the former RIBF, the RARF, in RIKEN. The high intensity (200~kcps) $^{12}$Be beam was produced as the fragmentation of the projectile of $^{18}$O primary beam and separated by using RIPS. The direction and arrival timing of the $^{12}$Be was measured by using two delay-line readout parallel plate avalanche counters and plastic scintillator located upstream of the secondary target. The $^{12}$Be beam bombarded the secondary target of liquid helium surrounded by the position sensitive gamma-ray detector array, the GRAPE. The beam-like outgoing particle of $^{13}$B was detected and identified by using plastic scintillator hodoscope, which is also the position sensitive. The $^{13}$B was identified event-by-event basis via TOF-dE-E method. The excited state of $^{13}$B was identified via the gamma-ray spectroscopy after the doppler correction and the scattering angle was deduced from the incident direction of the $^{12}$Be and the outgoing direction of $^{13}$B.
The de-excitation gamma ray from the 4.8-MeV excited state is clearly observed. The spin-parity of this state is assigned as $1/2^{+}$ from the DWBA analysis of the angular distribution of the differential cross section, which has forward peak corresponding to the transfer angular momentum of zero. Since the ground state of the $^{13}$B has the spin-parity of $3/2^-$ and the energy of $1/2^{+}$ state seems smaller than the normal shell gap at $Z=8$, the 4.8-MeV $1/2^+$ state is concluded to be the low-lying proton intruder state. The existence of the proton intruder state is explained by the Nilsson orbit in deformed $^{12}$Be nucleus assuming the one-body potential is equally deformed for protons and neutrons. This indicates that the one proton excitation in the spherical nucleus causes the phase transition to the deformed nucleus dynamically.
In this paper, we discuss dynamical shape transition in $^{13}$B relating to the magicity loss of $^{12}$Be.
References
1. S. Shimoura, S. Ota {\it et al.}, Phys. Lett. B 654 (2007) 87-91
2. I Hamamoto and S Shimoura 2007 J. Phys. G: Nucl. Part. Phys. 34 (2007) 2715
3. Toshio Suzuki and Takaharu Otsuka, Phys. Rev. C 78 (2008) 061301(R)
4. I. Hamamoto, Nucl. Phys. A (2004) 211-223
5. S. Ota {\it et al.} Phys. Lett. B 666 (2008) 311
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