Ⅱ-1. Nuclear Physics

RIKEN Accel. Prog. Rep. 49 (2016)

23,25
Spectroscopic factors
factors ofFF
Spectroscopicof thethe proton
protonboundboundstatesstatesinin23,25

T. L. Tang,*1 S. Kawase,*1 T. Uesaka,*2 D. Beaumel,*2,*3 M. Dozono,*2 T. Fujii,*1,*2 N. Fukuda,*2 T. Fukunaga,*2,*4A. Galindo-Uribarri,*5 S. H. Hwang,*6 N. Inabe,*2 D Kameda,*2 T. Kawahara,*2,*7 W. Y. Kim,*6 K. Kisamori,*1,*2M. Kobayashi,*1 T. Kubo,*2 Y. Kubota,*1,*2 K. Kusaka,*2 C. S. Lee,*1 Y. Maeda,*8 H. Matsubara,*2 S. Michimasa,*1H. Miya,*1,*2 T. Noro,*2,*4 A. Obertelli,*9 S. Ota,*1 E. Padilla-Rodal,*10 S. Sakaguchi,*2,*4 H. Sakai,*2 M. Sasano,*2S. Shimoura,*1 S. S. Stepanyan,*6 H. Suzuki,*2 M. Takaki,*1,*2 H. Takeda,*2 H. Tokieda,*1 T. Wakasa,*2,*4 T. Wakui,*2,*11K. Yako,*1 Y. Yanagisawa,*2 J. Yasuda,*2,*4 R. Yokoyama,*1,*2, K. Yoshida,*2 and J. Zenihiro,*2 for SHARAQ04 collaboration
higher excitation energies. The wave function of 23F ȁ ଶଷ‫ ܨ‬ൿcan be expressed as a linear combination of proton single
particle wave functions ȁ‫ ۧ݌‬coupled to 22O wave functionsȁ ଶଶܱ ൿ, such that

The proton quasi-free knockout reaction on 23F (25F) was
studied in SHARAQ04 experiment at RIBF, RIKEN1). The
spectrum of excitation energy of the residue 22O (24O) wasdeduced and partitioned by the neutron thresholds2). The
orbital angular momentum of each partition was identified
by comparison with the DWIA calculation, and then thesum of the spectroscopic factors (SFs) was extracted 3).
Figure 1 shows the spectra of excitation energy.

ȁ ଶଷ‫ ܨ‬ൿ ൌ ෍ ߚ௜௝ ቂȁ‫ۧ݌‬௜ ȁ ଶଶܱൿ௝ ቃǡ௜ǡ௝

where ߚ௜௝ is the square root of the SF, and the squarebracket ሾ ሿ represents the angular and isospin coupling andanti-symmetry operator. The known parities of the excitedstates of 22O are all negative above 6.9 MeV (1-neutronthreshold is 6.8 MeV). Because the residual interaction
cannot mix different parity states, the sum of the SFs of the1d5/2 shell is almost limited up to 1-neutron threshold.
However, the knowledge of the excited states is notcomplete that there could be undiscovered positive parity
states above the neutron threshold.
A mean field calculation suggests that 23F is slightly
deformed (ߚଶ ൌ െͲǤʹ) 5,6). The deformed oxygen core has
to be expanded into many excited states of free oxygen;therefore, the deformation could reduce the knockout crosssection. In the reaction aspect, the (p,2p) cross section of aslightly deformed nucleus will be different from that of aspherical nucleus due to the focusing effect 7).
In conclusion, the SFs of the proton bound states of 23F
and 25F were deduced. The 1d5/2 proton of 25F is a strong
candidate of a single particle orbit. The nature of the 1d5/2
proton of 23F requires further study. The results will becompared with the shell model calculation in the nearfuture.

Fig. 1. Spectra of excitation energy of 23F(p,2p) (left) andF(p,2p) (right).

25

In 23F(p,2p), the partition (23F,22O) originates from the1d5/2 shell and the SF is 0.4 ± 0.1. The partitions (23F,21,20O)
originate from the p-shell with the sum of the SFs of 4.8 ±0.7. In 25F(p,2p), the partitions (25F,24,23O) originate from the1d5/2 shell and the sum of the SFs is 0.9 ± 0.7. The partitions(25F,22,21O) originate from the p-shell with the sum of theSFs of 4.4 ± 0.9.
The sum of the SFs of the 1d5/2 proton of 25F can beunderstood as a result of the double magic of 24O 4). The
sum of the SFs of the p-shell for both 23F and 25F areapproximately 75% of the shell limit. This result is similar
to most stable isotopes. The extraordinary small SF of the1d5/2 of 23F needs explanations.
The independent particle model should be valid in 23F
because the experimental proton shell gap between the 1d5/2
and 1p1/2 is 10 MeV, and the proton-neutron interactionenergy is only 0.7 MeV. There could be missing strength atReferences

1) S. Kawase et al.: CNS annual report 2012, (2013) 13.
2) T. L. Tang et al.: RIKEN Accel. Prog. Rep. 48 (2015) 57.
3) T. L. Tang et al.: CNS annual report 2014 (to be published).
4) R. V. F. Janssens: Nature 459 (2009) 1069.
5) G. A. Lalazissis et al.: The. Euro. Phys. Jour. A 22 (2004) 37.
6) M. K. Sharma et al.: Chin. Phys. C 39 (2015) 064102
7) P. A. Deutchman et al.: Nucl. Phys. A 283 (1977) 289.

Center of Nuclear Study (CNS), University of Tokyo
RIKEN Nishina Center
䠆3
Institut de Physique Nucléaire d’Orsay
䠆4
Department of Physics, Kyushu University
䠆5
Oak Ridge National Laboratory
䠆6
Department of Physics, Kyungpook National University
䠆7
Department of Physics, Toho University
䠆8
Department of Applied Physics, University of Miyazaki
䠆9
CEA Saclay
䠆10
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma deMéxico
䠆11
CYRIC, Tohoku University䠆1䠆2- 52 -