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Three-body cluster state in 11 B

Three-body cluster state in 11 B. Center for Nuclear Study, University of Tokyo KAWABATA Takahiro. 12 C. 0 + 1. 0 + 2. T.Yamada and P. Schuck, Euro. Phys. J. A 26 , 185 (2005). Introduction. Alpha particle clustering is an important concept in nuclear physics for light nuclei.

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Three-body cluster state in 11 B

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  1. Three-body cluster state in 11B Center for Nuclear Study, University of Tokyo KAWABATA Takahiro

  2. 12C 0+1 0+2 T.Yamada and P. Schuck, Euro. Phys. J. A 26, 185 (2005). Introduction Alpha particle clustering is an important concept in nuclear physics for light nuclei. Alpha cluster structure is expected to appear near the a-decay threshold energy. • The 0+2 state at Ex = 7.65 MeV in 12C • Famous 3alpha cluster state. • Condensed state where three alpha particles occupy the lowest s-orbit. • Dilute-gas state of alpha clusters. • Similar dilute-gas-like states have been predicted in self-conjugate N = 4n nuclei. Does such a dilute cluster state exists in the other N≠4n nuclei ?

  3. GT strengths in 11B GT Strengths have been measured by the (3He,t) reaction. T. Kawabata et al., Phys. Rev. C 70, 034318 (2004). • The 3/2-3 state has exotic characters. • Suppressed GT strength • Not predicted by the shell-model calculation • Locate 100-keV below the a-decay threshold. It is interesting to study the 3/2-3 state from view of the cluster model.

  4. Transition Strengths Nuclear transition strengths provide structural information. Alpha cluster states are mainly excited by natural-parity isoscalar transitions. Monopole (E0) and Quadrupole (E2) operators (e,e’) and g-decay measurements were extensively performed, but those are sensitive to proton parts only. IS strengths are different from the EM transition strengths in N≠Z nuclei. The IS excitation strengths should be determined by the different measurement.

  5. Hadron Scattering Hadron scattering is a good probe for nuclear excitation strengths. Simple reaction mechanism - Good linearity between ds/dW and B(ô). Selectivity for the DT = 1 and DT = 0 components. Multiple decomposition analysis is useful to separate DJp. (3He,t) … DT = 1 only (DTz = -1) (d,d’) … DT=0 only (DTz =0) (p,p’) … DT = 1 and DT = 0 (DTz = 0) We measured the (d,d’) reactionsto investigate the cluster structure in 11B.

  6. Experiment 11B(d,d’) RCNP-E207E= 200 MeV, qlab= 0˚~25˚- ds/dW, Ay, Ayy Experiment was performed at RCNP, Osaka University. B(E0; IS) and B(E2; IS) have been determined as well as B(s).

  7. Isoscalar strengths from 11B(d,d’) Deformed potential model were used to analyze the (d,d’) data. DP model well-explains the 12C(d,d’) result. 12C(d,d’) is used as a reference for DJ decomposition. • B(s) for 4.44 MeV was not reliably determined. • 8.56 MeV is strongly excited by the monopole transition.

  8. Comparison with Shell model Measured strengths are compared with SM calculation by SFO. epeff = 1.24, eneff = 0.23. • Reasonably well-reproduced except .... • M1 and GT strengths are overestimated by 20-50%. • 3/2-3 state is not predicted. 3/2-3 state is inferred to be a cluster state.

  9. 1/2＋2 11B 3/2+ 2 3/2－３ 1/2+ 7/2+ 2 2 5/2- 1/2＋1 5/2+ 3 2 7/2+ 3/2- 1 3 2a+ t 5/2- 3/2+ 1 2 shell-like 1/2+ 5/2+ 1 7Li+a-like 1 3/2－２ 3/2- 2 7/2- 1 5/2- 1 1/2- 1 3/2－１ 3/2- 1 AMD(VAP) 5/2－2,3 shell-like AMD (VAP) Calculation Y. Kanada-En’yo • AMD (VAP) calculation successfully predict the 3/2-3 state with the 2a + t structure. • The 5/2-2 and 5/2-3 states were described as a mixture of the SM and cluster components. • Lower states have shell-like structures.

  10. Comparison with AMD (VAP) • AMD (VAP) successfully predicts the experimental data. • E2 strength for the 5/2-2 state implies coexistence of the SM and CM wave functions. E0 and M1 strengths for the 3/2-3 states are well described by a 2a + t cluster w.f.

  11. Comparison with AMD (VAP) Large B(E2) value reported from the (e,e’) experiment contradicts the AMD result. E0, M1, and E2 are allowed, nevertheless, previous analysis takes only M1 and E2 into account. Re-analyze the (e,e’) data by taking E0 and M1 into account, and neglecting E2. B(E0) = 18.7 +/- 0.7 e2fm4 If Mn= (N/Z)Mp, B(E0;IS) = 90 +/- 3 fm4. Large E0 and negligibly small M1 and E2 stregths !! The previous (e,e’) data do not contradict the present experimental and theoretical results. AMD (VAP) nicely predicts the excitation strengths for the 3/2-3 state.  Evidence for the 2a + t cluster structure.

  12. <r2>1/2 = 2.5 fm <r2>1/2 = 3.0 fm AMD (VAP) Calculation by Y. Kanada-En’yo Analogies to the 0+2 state in 12C • Analogies between the 3/2-3 state and the 0+2 state in 12C (dilute-gas-like 3a cluster state) has been observed. • Located near the a-decay threshold. • Similar monopole strengths. • Not predicted in SM calculations. • Analogies suggests a dilute structure of the 3/2-3. • Large RMS radius is predicted. The 3/2-3 state is inferred to be a 2a+t cluster state with the dilute density.

  13. 11B, 13C(a,a’) Experiment Recently, the 11B and 13C(a,a’) reactions have been measured for further clarification. Y. Sasamoto et al. • Radius of the 3/2-3 state should be experimentally determined. • Analogue state for the 0+3 state in 12C as well as the 0+2 state might exist. • Similar analog states are also expected in 13C.

  14. Summary • Isoscalar excitation strengths in 11B are measured via the 11B(d,d’) reaction. • Experimental results are compared with the SM and AMD (VAP) calculations. • AMD (VAP) successfully predicts the 3/2-3 state with a 2a + t configuration. • Strong E0 transition for the 3/2-3 state should be an evidence of the 2a + t cluster structure. • Analogous relation between 11B and 12C is speculated. • 3/2-3 state in 11B is inferred to be a dilute cluster state in similar to the 0+2 state in 12C.

  15. Dilute Character of 3/2-3 To evaluate the dilution of the 3/2-3 state, new quantity D is introduced. D: Fraction of nucleon numbers in low density region with r/r0< 1/5. RGM: M. Kamimura, Nucl. Phys. A351, 456 (1981). • Rrms and D for 3/2-3 are ... • Extraordinary larger than those for the ground state, • As large as those for the 0+2 state in 12C . • -> Dilute structure of the 3/2-3 state.

  16. Excitation Modes in 11B G.S. of 11B is Jp=3/2- and T=1/2. Excitation modes in 11B are complex. • To extract the IS transition strengths.... • Each DJp transition must be isolated. • Isoscalar and isovector transitions must be separated.

  17. 0+ and 2+ transitions are parameterized in terms of DP model. • Fit the 1+ transition by the spherical Bessel function. Macroscopic analysis for the 12C(d,d’) reaction 12C(d,d’) can be a reference for the DJp decomposition. Transition form factors in 12C and 11B are expected to be similar.

  18. Measured Spectra (3He,t) Vst is strong. Spin-flip transitions are dominant. (d,d’) V0 is strong. Non-spin-flip transitions are dominant. M1 transitions are dominant. E2 transitions are dominant. Unpredicted by SM calculation. Non-spin-flip transition is dominant. Expected to be a cluster state.

  19. Proton and Neutron Quadrupole Strengths Quadruple proton and neutron transition strengths are defined by

  20. B(GT) from (3He,t) reactions B(GT) for excited states were obtained from DWBA analysis. Eff. Int. for DWIA were adjusted for ground-state transitions.B(GT)=0.345±0.008, B(F)=N-Z=1 Present results are consistent with previous (p,n) result.

  21. Proton Inelastic Scattering DWIA calculation- Franey-Love NN interaction-H.O. single-particle w.f. - Strengths from (d,d’) and (3He,t) No parameters adjusted. 8.92-MeV state- DWIA underestimates 50%.- Problem on linearity between B(GT) and ds/dW.- Interference between IS and IV parts??- The reason is still unclear. Describe experimental results except 8.92-MeV state.

  22. Inelastic Alpha Scattering • Alpha scattering is suitable to investigate molecular states. • Simple reaction mechanism. • Only central interaction V0 contributes. • Extract transition densities in the surface region for discrete states. • Search for analog states of 0+3 in continuum region by means of MDA. • Precise measurement of B(E2;IS) for the 5/2-2 state. M. Itoh et al. M. Itoh et al. Beam time is scheduled in October.

  23. Transition Strengths Alpha cluster states are mainly excited by isoscalar transitions. IS transition strengths are important to study the cluster structures. g-decay measurements were extensively performed, but world is not enough... M1: IV parts are dominant [(gIVs/gISs)2=28.6]. E0, E2: Sensitive to proton parts only. For light N=Z nuclei, mirror symmetry gives missing parts, but for the other nuclei .....

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