直交条件模型を用いた 16 O における α クラスターガス状態の研究

1. 直交条件模型を用いた16Oにおけるαクラスターガス状態の研究直交条件模型を用いた16Oにおけるαクラスターガス状態の研究 ・ Introduction ・ ｎα cond. w. f. ・4α ｓｙｓtem ・４αＯＣＭ ・ Summary Yasuro Funaki (RIKEN) Taiichi Yamada (Kanto Gakuin) Akihiro Tohsaki (RCNP) Hisashi Horiuchi (RCNP) Peter Schuck (IPN, Orsay) Gerd Röpke (Rostock Univ.) Contents

2. Energy region of cluster gas states appearing Energy 12C Nucleon 100 MeV Nucleon gas αcluster Appearing near the 3αthreshold Cluster gas ～10 MeV Condensed into the lowest orbit luquid 0 MeV Lowest energy state

3. mean field a a a 0s a-condensation in finite nuclei ・12C, 02+(E3a=0.38 MeV): Tohsaki et al., PRL 87, 192501 (2001) a-condensate-type w.f. （Schuck-type, microscopic) Rrms=4.29 fm ⇔ Volume(02+)/V(01+)～3　（dilute) Conjecture of dilute a condensation ・ 12C, 22+(E3a=2.6 MeV)observed at RCNP (Itoh et al.) described well by single deformed a-cond.-type w.f. Funaki et al., EPJA, (2005). similar structure to 02+ : dilute a condensation Funaki et al., PRC67, (2004)

4. RGM ３αcluster condensate model Extremely reliable solution was obtained for the Hoyle state As for the Hoyle state, both are almost equivalent (～90 %). 3 α clusters occupy the same Ｓ orbit

5. nαcondensate wave function b ： width parameter of the internal wave function of αparticle φ(α) （size of αcluster） Ｘ： center-of-mass coordinate of αparticle Ａ： anti-symmetrizing operator acting on all of constituent nucleons β → Large ： “Bose condensed state‘’ C. M. motion of ｎαclusters occupy the same S-orbit exp(-2X2/B2), forming a gas-like structure. β → ０ ： （if normalized） approaching shell model w. f. Hill-Wheeler eq.

6. Low lying 0+ levels of 16O (MeV) ０５＋state： Acandidate of ４αcondensate Ｅ＝１３．５ＭｅＶ Γ＝０．８ＭｅＶ １６Ｏ（α、α’） Ｗａｋａｓａ ｅｔａｌ. (０3＋)theor: ４αcondensed state Ｅ=14.9 MeV Γ=1.5 MeV (based on R-matrix theory) ４αcond. w.f. Exp. 0２+：α＋１２Ｃ(０+) 04+：α＋１２Ｃ(2+) α＋ １２Ｃ　ＯＣＭ 4αＯＣＭ

7. Cross sections of (α,α’) inelastic scattering to the 4αcondensed state（13.5 MeV）（preliminary） Not bad agreement between theory and experiment The observed 0+ state (13.5 MeV) can be assigned to the 4 αcondensed state By M. Takashina(YITP）

8. Density（1２Ｃ） Density（1６Ｏ） Defined by En’yo-san How much ingredients are in low density region.

9. 4αＯＣＭ（orthogonality condition model） 4αＯＣＭ（H. O. basis） K-type 2 2 4 4 1 3 + + + ・・・ 1 1 3 4 2 3 H-type 4 4 4 1 3 1 + + + ・・・ 2 3 2 3 1 2 Adopted angular momentum channels Total wave function Gaussian basis

10. 4αＯＣＭ（orthogonality condition model） 0p 0s Equation of motion Hamiltonian Remove Pauli forbidden states between 2a parts with the relative h.o. quanta Qrel <4 Pauli blocking operator for 2a parts Pauli forbidden state: h.o.w.f

11. Convergence of 0+states of 16O + H-type + K-type チャンネル 数

12. (MeV) Exp. 4αOCM 0+states of 16O obtained by ４αOCM （preliminary） Bound state approximation Possible mixture of spurious continuum states

13. 0+state as a function of δ Measured from 12C+α threshold Identification of resonances　（preliminary）

14. 0+state as a function of δ Measured from 4α threshold Identification of resonances　（preliminary）

15. (MeV) Exp. 4αOCM 0+states of 16O obtained by ４αOCM （preliminary） Bound state approximation Possible mixture of spurious continuum states

16. Summary and future study ・ The recently observed 05+state can be assigned to the 03+state which 4αcondensate w. f. (microscopic model) gives. （Energy, width and (α、α’)cross section（preliminary）） 4αcond. w. f. may have a difficulty to represent the 12C+α structure. Analysis by using ４αOCM（orthogonality condition model） in order to describe both 12C+αand 4αgas states. ・The number of resonances can be determined by introducing a pseudo potential. ・3 states with 12C+α resonance are obtained. Two of them may be considered to have 12C(0+)+α, 12C(2+)+α structures, respectively. ・Resonance state obtained near the ４αthreshold may correspond to the 4αgas state.

17. Rr.m.s. dependence of transition density and inel. form factor （12C） Inel. form factor (linear scale) Transition density Absolute value of form factor largely depends on the r.m.s. radius of the excited state. Possibility of measuring r.m.s radii of excited states. Corresponding r.m.s radius Rr.m.s. are shown in the parenthesis. Units are all in fm.

18. Transition density Rr.m.s. dependence of transition density and inel. form factor （1６Ｏ） Inel. form factor (linear scale) Similarly to the case of 12C, large Rr.m.s. dependence can be seen. monopole matrix elements 12C : M(０1＋→ ０2＋ ) =6.5 fm2 1６Ｏ : M(０1＋→ ０3＋ ) =2.5 fm2 Corresponding r.m.s radius Rr.m.s. are shown in the parenthesis. Units are all in fm.