Beyond-mean-field approach to low-lying spectra of Λ hypernuclei
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1 Beyond-mean-field approach to low-lying spectra of Λ hypernuclei Kouichi Hagino (Tohoku Univ.) Hua Mei (Tohoku Univ.) J.M. Yao (Tohoku U. / Southwest U.) T. Motoba (Osaka Electro-Commun. U. ) 1. Introduction 2. Mean-field approximation and beyond 3. Microscopic particle-rotor model for hypernuclei 4. Results for 13 ΛC, 21 ΛNe, and 155 ΛSm 5. Summary H. Mei, K.H., J.M. Yao, and T. Motoba, PRC90 ( 14) PRC91 ( 15)
2 Introduction Impurity effects: one of the main interests of hypernuclear physics how does Λ affect several properties of atomic nuclei? size, shape, density distribution, single-particle energy, shell structure, fission barrier Theoretical approaches: cluster model shell model AMD (Isaka s talk) self-consistent mean-field models (Zhou and Vesely s talks) A figure from a recent review: K.H. and J.M. Yao, arxiv:
3 Mean-field approximation and beyond Self-consistent mean-field (Hartree-Fock) method: independent particles in a mean-field potential global theory for the whole nuclear chart intuitive picture for nuclear deformation optimized shape can be automatically determined suitable for a discussion on shape of hypernuclei Myaing Thi Win and K.H., PRC78( 08)054311
4 Mean-field approximation and beyond Drawbacks of the mean-field approximation : nuclear spectrum body-fixed frame formalism intuitive picture of nuclear def. spectrum: lab-frame transformation from intrinsic to lab. frames angular momentum + particle number projections nuclear spectrum: requires to go beyond the mean-field approximation quantum fluctuation MF GCM generator coordinate method (GCM) beyond the mean-field approximation
5 beyond mean-field approximation 76 Kr J.M. Yao, K.H. et al., PRC89 ( 14)
6 beyond mean-field approximation Projection+GCM for the whole (A c +1) system H. Mei, K.H. and J.M. Yao, in preparation coll. wf Microscopic particle-rotor model for single-λ hypernuclei H. Mei, K.H., J.M. Yao, and T. Motoba, PRC90( 14)064302, PRC91( 15) i) beyond mean-field calculations for e-e core: ii) coupling of Λ to the core states Λ j,l I c (IM) Λ+core model with core excitations
7 Microscopic Particle-Rotor Model for Λ hypernuclei Example: 13 ΛC i) beyond mean-field calculations for e-e core ( 12 C) : GCM + projections axial symmetry relativistic PC-F1 7.6(4) 5.4(2)
8 Microscopic Particle-Rotor Model for Λ hypernuclei Example: 13 ΛC (i) beyond mean-field calculations for e-e core ( 12 C) (ii) coupling of Λ to the core states Λ core particle-core model with core excitations 5.4(2) 7.6(4) cf. conventional particle-rotor model: core states macroscopic rotor (Wigner s D-functions) with a fixed deformation our approach: a microscopic version of particle-rotor model
9 Results for 13 ΛC H. Mei, K.H., J.M. Yao, T. Motoba, PRC91( 15) coupling to 0 +, 2 +, and 4 + of 12 C parameters B Λ of 13 ΛC ls splitting: 199 kev cf. expt. 152+/-90 kev * qualitatively similar to the previous cluster model calc.
10 Results for 13 ΛC H. Mei, K.H., J.M. Yao, T. Motoba, PRC91( 15) B(E2) transition rates (e 2 fm 4 ) 13 Λ C (1/2 + ) Λ 12 C (0 + ) B(E2) : ~ 14% reduction 12 C 13 Λ C β r p (fm)
11 Results for 21 ΛNe H. Mei, K.H., J.M. Yao, T. Motoba, PRC91( 15) E* [MeV] B(E2) [e 2 fm 4 ] /2-3/ /2 +,9/ /2 +,5/ Ne 0 + 1/ Λ Ne (β min = 0.376, 0.67) (β min = 0.376, 0.63)
12 Results for 155 ΛSm E* [MeV] B(E2) [e 2 b 2 ] H. Mei, K.H., J.M. Yao, T. Motoba, PRC91( 15) /2-3/ /2 +,9/ /2 +,5/ / Sm 155 Λ Sm (β min = ) (β min = )
13 Summary Microscopic particle-rotor model for spectrun of Λ-hypernuclei Λ + GCM states for core microscopic version of particle-rotor model first calculation for low-lying spectrum based on mean-field type calculations application to 13 ΛC: good agreement with the experimental data reduction of B(E2) due to a change in def. param. application to heavier hypernuclei: 21 ΛNe and 155 ΛSm Future perspectives more consistent interaction (the derivative and tensor terms) : in progress extension to include triaxiality (cf. 25 ΛMg) Challenging problem application to formation reactions of hypernuclei description of ordinary odd-mass nuclei: Pauli principle?
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