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Study of the Tensor Correlation in Oxygen Isotopes using Mean-Field-Type and Shell Model Methods

Study of the Tensor Correlation in Oxygen Isotopes using Mean-Field-Type and Shell Model Methods. Satoru Sugimoto Kyoto University 1. Introduction 2. Charge- and parity-projected Hartree-Fock method (a mean field type model) and its application to sub-closed shell oxygen isotopes

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Study of the Tensor Correlation in Oxygen Isotopes using Mean-Field-Type and Shell Model Methods

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  1. Study of the TensorCorrelation in OxygenIsotopesusing Mean-Field-Type and Shell Model Methods Satoru Sugimoto Kyoto University 1. Introduction 2. Charge- and parity-projected Hartree-Fock method (a mean field type model) and its application to sub-closed shell oxygen isotopes 3.Shell model calculation to 15,16,17O 4. Summary

  2. Introduction • The tensor force is important in nuclear structure. • There remain many open problems to be solved. • How does the tensor correlation change in neutron-rich nuclei? • Shell evolution (Ostuka, PRL 95 232502 (2005)). • The breakdown of the magic number in 11Li (Myo et al.) • The relation to the ls splitting in 5He (Myo et al. PTP 113 (2005) 763)

  3. The correlation to be included 2p-2h correlation • In the simple HF calculation, 2p-2h correlations are hard to be treated. • We need to include at least 2p-2h correlations to exploit the tensor correlation.beyond mean field model cf. Single-particle (H-F) correlation

  4. Charge- and parity-symmetry breaking mean field method • Tensor force is mediated by the pion. • Pseudo scalar (s) • To exploit the pseudo scalar character of the pion, we introduce parity-mixed single particle state. (over-shell correlation) • Isovector (t) • To exploit the isovector character of the pion, we introduce charge-mixed single particle state. • Projection • Because the total wave function made from such parity- and charge-mixed single particle states does not have good parity and a definite charge number. We need to perform the parity and charge projections. Refs. Toki et al., Prog. Theor. Phys. 108 (2002) 903. Sugimoto et al., Nucl. Phys. A 740 (2004) 77; ; nucl-th/0607045. Ogawa et al., Prog. Thoer. Phys. 111 (2004) 75; Phys. Rev. C 73 (2006) 034301.

  5. Results for 16O • MV1(VC)+G3RS(VT,VLS) • By performing the parity and charge projection the potential energy from the tensor force becomes sizable value.

  6. d3/2 p1/2 d5/2 s1/2 p3/2 VT and VLS per particle • The potential energy from the tensor force has the same order in magnitude as that from the LS force. • The tensor potential energy decreases as neutron numbers.

  7. Wave function（１６O, ｘT=1.5) s1/2 proton dominant Opposite parity components mixed by the tensor force have narrow widths. It suggests that the tensor correlation needs high-momentum components.

  8. Mixing of the opposite parity components in single-particle states • If a next j=1/2 orbit is occupied newly, the mixing probabilities of the j=1/2 orbit reduce by ablocking effect. • Mixing of the opposite-parity component may affect excitation spectra of nuclei. 0p1/2 1s1/2

  9. Shell model calculation • We perform the shell model calculation including 1p-1h and 2p-2h configurations to study the tensor correlation. • inclusion of narrow-width single-particle wave functions • The shell model calculation can treat the correlation which cannot be treated in a mean-field-type calculation. cf. Myo et al. PTP 113 (2005) 763

  10. Model space • 16O: (0p-0h)+(1p-1h)+(2p+2h)17O: (1p-0h)+(2p-1h)+(3p+2h)15O: (0p-1h)+(1p-2h)+(2p+3h) • Core (hole state) • (0s1/2)4(0p3/2)6(0p1/2)4 • Harmonic oscillator single-particle wave functions • Particle state • Harmonic oscillator single-particle wave functions+Gaussian single-particle wave functions with narrow (half) width parameters • These are ortho-normalized by the G-S method

  11. Effective interaction • Central force: Volkov No. 1 • A.B. Volkov, Nucl. Phys. 74 ( 1965 ) 33 • Tensor: Furutani force • H. Furutani et al., Prog. Theor. Phys. Suppl. 68 ( 1980 ) 193 • LS: G3RS • . Tamagaki, Prog. Theor. Phys. 39 ( 1968 ) 91 • No Coulomb force

  12. 16O • HO: (1s 0d)+(1p 0f)+(2s 1d 0g) • NWG: bNW = bHO/2 = 1.8 fm • d-orbit: (1s 0d)+sNW+pNW+dNW • f-orbit: (1s 0d)+sNW+pNW+dNW+fNW • By including single-particle orbits with narrow width parameters the correlation energy from the tensor force becomes large.

  13. 17,15O (NWG (up to f-orbit)) • DKE+DVC+DVT≈0 • ls-splitting nearly equals to DVLS 17O 15O

  14. Magnetic Moment • Magnetic moments change a little in spite of the large correlation energy form the tensor force. A=17 A=15

  15. Summary • We apply a mean-field model which treats the tensor correlation by mixing parities and charges in single-particle states (the CPPHF method) to oxygen isotopes. • The opposite parity components induced by the tensor force is compact in size. (high-momentum component) • We perform the shell model calculation up to 2p-2h states to 15,16,17O. • The tensor correlation energy becomes large by including Gaussian single-particle wave functions with narrow widths. • The tensor correlation changes ls splitting and magnetic moments in 15,17O a little in spite of its large correlation energy.

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