クラスターガス状態と モノポール励起 関東学院大 工 山田泰一
|
|
- Sandra Shana Sharp
- 5 years ago
- Views:
Transcription
1 クラスターガス状態と モノポール励起 関東学院大 工 山田泰一
2 Contents of my talk 1. -particle condensation in 4n nuclei 2. Hoyle-analog states in A 4n nuclei 3. IS monopole transitions to search for cluster states Dual nature of ground states IS monopole strength function of 16 O (typical case) : -cluster states at low energy mean-field-type states at higher energy 4. Summary
3 Introduction Cluster picture as well as mean-field picture is important viewpoint to understand structure of light nuclei. Structure of light nuclei Cluster states + Shell-model-like states Microscopic cluster models, AMD,... 8 Be=2, C=3, 16 O= C+ / 4, -condensate states in 4n nuclei: -gas-like state described by a product state of -particles, all with their c.o.m. in (0S) orbit. Typical states: C: Hoyle state (2 nd 0 + ) cluster Cluster gas Tohsaki, Horiuchi, Schuck, Roepke, Phy. Rev. Lett.87 (2001) Funaki et al., PRC (2003) Yamada et al., EPJA (2005), Matsumura et al.,npa(2004) ρ R 3.8 fm 3~ρ 5 0 0
4 cluster Cluster gas ρ R 3.8 fm 3~ρ Condensed into the lowest orbit 70% 3 (0 S) shell-model like structure
5 Overlap 3 GCM Brink wf exact 0 state + 2 -gas-like nature of Hoyle state Kamimura et al., (1977): 3 RGM Uegaki et al, PTP57(1977): 3 GCM The state has a distinct clustering and has no definite spatial configuration. Chernykh, Feldmeir et al., PRL98(2007) UCOM + FMD, 3 RGM About 55 components of the Brink-type wave functions are needed to reproduce the full RGM solution for the Hoyle state. Tohsaki,Horiuchi,Schuck,Roepke, PRL87(2001) Uegaki et al, PTP57(1977) THSR wave function: -condensate-type cluster wf 1 base THSR : THSR + Φ3 exact 0 state (3RGM) 99% 2 2 Funaki et al., PRC67, (2003)
6 THSR wave function Tohsaki, Horiuchi, Schuck, Roepke, PRL (2001) X 3 X 1 X G 2 Condensed into the lowest orbit (0 ) 3 S Φ 3 ( B) = exp X ( ) 2 i φi i= 1 B B B Φ3 ( B) exp X ( ) 2 i φi i= 1 B 4 8 b Φ 3 ( B ) (0 s ) (0 p ) B: parameter b: nucleon size parameter 3 (0 S) Funaki et al., PRC (2003) + Φ3 ( B) exact 0 state (3RGM) 0.9 THSR 2 3 RGM: Kamimura & Fukushima (1978) Deformation (B x,b y,b z ) R 3.8 fm: alpha-gas-like structure
7 Occupation probabilities of -orbits in C 70% C(g.s) Hoyle state (λµ)=(04)-nature 0S-orbit SU(3) nature: confirmed by no-core shell model, Dytrych et al., PRL98 (2007) Single cluster density matrix: d r ' ρ ( rr, ') ϕ a( r ') = λϕ ( r ), () Yamada & Schuck EPJA26 (2005) with 3 OCM wf Matsumura & Suzuki, NPA739 (2004) Funaki et al., PRC (2010) with 3 THSR wf ρ(r,r') ϕ r : single-cluster orbital w.f. λ : occupation probability
8 -density distribution and -momentum distribution in C Density r 2 Momentum distribution (g.s) (g.s) Compact (0 1+ ) vs. Dilute (0 2+ ) state: δ function-like Similar to dilute atomic cond. Yamada & Schuck EPJA26 (2005) with 3 OCM wf
9 Single -orbits in C(0 + ) (g.s.) S-orbit (N =35%) S-orbit (N =70%) G-orbit (N =27%) D-orbit (N =35%) 2 ref.: r N0( a)exp( ar ) Large oscillation : strong Pauli blocking effect Compact structure SU(3) model: [f](λµ)=[444](04)-like structure Small oscillation: weak Pauli blocking effect Long tail: dilute structure Radial behavior: Gaussian form with a= 0.04 fm -2
10 cluster Cluster gas ρ R 3.8 fm 3~ρ Condensed into the lowest orbit 70% 3 (0 S) shell-model like structure
11 Family of the Hoyle state No-core shell model calculation C P. Navr atil et al., PRC62 (2000)
12 Family of the Hoyle state Kurokawa, Kato, PRC71 (2005) Funaki et al., EPJA24 (2005) Yamada et al., EPJA26 (2005) Exp. for 2 nd 2+ state Itoh et al., NPA738, 268 (2004) C Freer et. al. PRC80, (2009) M. Gai et. al, (2011)
13 Precursor of a 3 condensate state: 3 -, 1 - Yamada et al., EJPA26, 185 (2005) 1 3 (0P) 3 : superfluid? vortex? 3a OCM: Occup. Prob. ~ 40% precursor of 3 condensate Condensed into the lowest orbit C 70% 3 (0 S)
14 Structure of 16 O 1. 4 condensate? 2. 4 linear chain state? 3. Monopole excitation (later) Funaki s talk
15 (0S ) 3 : 70%
16 Cluster-model analyses of 16 O + C OCM Y. Suzuki, PTP55 (1976), C GCM M. Libert-Heinemann, D. Bay et al., NPA339 (1980) 4 THSR wf Not include + C configuration. Tohsaki, Horiuchi, Schuck, Roepke, PRL87 (2001) Funaki, Yamada et al., PRC82(2010) 4 OCM 4-gas, + C, shell-model-like configurations Funaki, Yamada et al., PRL101 (2008) Reproduction of lowest six 0+ states up to 4 threshold (15MeV)
17 16 O= C+ cluster model Even-parity Y. Suzuki, PTP55 (1976), 1751 Odd-parity 4 C+ EXP CAL EXP CAL C+ : molecular states
18 Funaki et al., PRL101 (2008) Suzuki, PTP55 (1976)
19 E x [MeV] Experimental data R [fm] M(E0) [fm 2 ] Γ [MeV] R [fm] 4 OCM M(E0) [fm 2 ] Γ [MeV] no data no data over 15% of total EWSR 20% of total EWSR
20 4 OCM calculation Funaki, Yamada et al., PRL101 (2008) 4 cond. state C(1 1- )+(P) strong candidate 4 (0 S) 60% C(0 1+ )+(S): higher nodal C(2 1+ )+(D) C(0 1+ )+(S) shell-model-like: (0s) 4 (0p)
21 -particle condensates in heavier 4n nuclei than 16 O 1. THSR approach 2. Gross-Pitaevskii approach
22 THSR approach Energy curve of HW equation n condensate Tohsaki, Horiuchi, Schuck, Roepke, NPA738, 259 (2004)
23 Single- potential given via Gross-Pitaevskii approach n 2 ( n ) φ ( r ), 1 + U( r) φ ( r) = εφ ( r) Φ = i= 1 i 2 2m ( ) ( 1) ( ) v ( ) 1 n ( n 1)( n 2) ( ) ( ) ( ) U r = n dr φ r 2 r, r + dr dr φ r φ r v 3 r, r, r 2 Pure bosons n states are assumed Coulomb barrier quasi-stable states Weakly interacting gas-like states condensates : up to about 10 ( 40 Ca) Yamada & Schuck, PRC 69, (2004)
24 Hoyle-analog states in A 4n nuclei ( 11 B and 13 C)
25 Search for Hoyle-analogue states in A 4n nuclei Definition of Hoyle-analogue state: A cluster-gas-like state described mainly by a product state of clusters, all with their c.o.m. in respective 0S orbits A=4n nuclei C=3 : (0S ) 3 70% 16 O=4 : (0S ) 4 60% A 4n nuclei, for example, 11 B=2+t : (0S ) 2 (0S t ) 13 C=3+n : (0S ) 3 (0S n ) Condensed into lowest orbit exit or not? 3 (0 S)
26 Purposes of present study Cluster structures in A 4N nuclei: 11 B ( 13 C) Hoyle-analogue states? Conditions of appearance? 11 B=2+t : (0S ) 2 (0S t ) 8 Be density 13 C=3+n : (0S ) 3 (0S n ) Which states of 11 B ( 13 C) correspond to the Hoyle-analogue? R.B. Wiringa et al., PRC(2000) What happens in 11 B ( 13 C) when an extra triton (neutron) is added into 8 Be=2 (Hoyle=3) state?
27 -t potentials: parity-dependent odd waves : attractive enough to make resonances/bound states even waves: weakly attractive 11 B 8 Be(2) + triton 2 part in 11 B J π ( 11 B) p-orbit reduced: 1/2-,3/2 - s-orbit not so changed: 1/2 + Thus, one can expect cluster-gas-like states in 1/ B 1/2 + : Hoyle-analogue exists or not? C 2 nd 0 + (Hoyle) S-orbit t S 1/2 -orbit t S-orbit
28 -n phase shifts -triton phase shifts -n potential (1) P-wave: attractive (2) S-wave: weakly attractive -triton potential (1) P-, F-waves: attractive (2) S-, D-waves: weakly attractive Parity-dependent potentials
29 3 2, + states in 11 B Results of OCM calculations Yamada and Funaki, PRC82 (2010)
30 Structure study of 11 B ++t OCM with H.O. basis Nishioka et al., PTP62 (1979) AMD calculation Enyo-Kanada, PRC75 (2007) No-core shell model Navratil et al., JPG36 (2009) Not well understood for even-odd states of 11 B
31 No-core shell model Navratil et al., JPG36(2009) Experimentally, three 3/2- states 7 Li+ 11 B energy levels (T=1/2)
32 No-core shell model Navratil et al., JPG36(2009) Not studied well for even-parity states Even-parity states ++t 7 Li+ 11 B energy levels (T=1/2)
33 Total wave function: 2 +t OCM Φ = Φ 11 (,3) L( B) Ac( ν, µ ) c ( ν, µ ) c, ν, µ + B Φ c, ν, µ (23,1) + (31,2) c( ν, µ ) c ( ν, µ ), Φ ( ν, µ ) =Φ ( ν, µ ) +Φ ( ν, µ ), (23,1) + (31,2) (23,1) (31,2) c c c 2 Φ ( νµ, ) = ϕ( r, νϕ ) ( r, µ ), ϕ ( r, ν) = N ( ν) r exp νr Y ( ), m r ( ij, k ) c ij λ k L m Hamiltonian ( ) H = T + V ( r ) + V ( r ) + V ( r ) + V ( r ) l s+ V ( r ) + V + V, Coul c LS Coul t ij + t ij ij + t ij 2t Pauli ( ij) = (23),(31) 2xe V r V r V r ar 2 Coul ( β ) ( ) (2) (2) 2 + x( ) = n exp n, + x ( ) = erf n r t t t OCM+GEM (Gaussian expansion method) V = lim λ u ( r ) u ( r ) + u ( r ) u ( r Pauli λ n n n ij n ij 2n+ < 4 2n+ < 3 ij= (23),(31) +, +t phase shifts 7 Li:3/2 -,, 1/2 -, 7/2 -, 1/2 - ), : Pauli blocking operator = : effective 2+t force π π V2 t η SU3( λµ ) : L Q SU3( λµ ) : L Q π L, Q( = 7,8) Equation of motion δ [ Φ E H Φ ] = 0
34 Single-cluster motions in 11 B(++t) Single-cluster density matrix: ρ ( rr, ') = Φ ( B) δ( r') δ( r) Φ ( B), alpha: triton: ( G ) ( G) 11 J rn rn J 2 n= 1 ρ ( rr, ') = Φ ( B) δ( r r') δ( r r) Φ ( B), 11 ( G) ( G ) 11 t J 3 3 J d r ' ρ ( rr, ') ϕ a( r ') = λϕ ( r ), λ = 1 dr ' ρ ( rr t, ') ϕ t( r ') = λϕ t t( r ), λ = 1 t ϕ() r λ 11 Φ J ( B) : single-cluster orbital w.f. : occupation probability : ++t OCM w.f. Suzuki et al., PRC65 (2002); Matsumura et al., NPA739 (2004) Yamada et al., EPJA 26 (2005); Funaki, Yamada et al., PRL101 (2008) Yamada et al., PRA (2008), PRC(2009) triton r ( G) 3 r r G ( G) 1 ( G) 2 11 B=++t
35 Energy levels of 11 B 3/2- and 1/2+ states Even-parity states 7 Li+ + + t OCM + + t OCM
36 11 B = + + t OCM - 32 R=3.0 fm cluster state + 7 Li(3/2-) with S-wave But 7 Li part has a distorted +t structure E0 R=2.43 fm E0 shell-model-like state R=2.22 fm shell-model-like state B(E0,IS)=96±16 fm 4 B(E0,IS)=92 fm 4 T. Kawabata et al., PRC70 (2004) vs. Hoyle state: B(E0,IS)=0±9 fm 4
37 11 B = + + t OCM - 32 Overlap amplitude with + 7 Li(g.s) channel R=3.0 fm 1 st 1/2+ 3rd 3/2- E0 E0 R=2.43 fm R=2.22 fm 1st 3/2- B(E0,IS)=96±16 fm 4 B(E0,IS)=92 fm 4 T. Kawabata et al., PRC70 (2004) vs. Hoyle state: B(E0,IS)=0±9 fm 4 main configuration 3/2-3: + 7 Li(3/2-) with S-wave But 7 Li part has a distorted +t structure Yamada & Funaki, PRC82(2010)
38 11 B = + + t OCM Occupation probabilities 11 B: 3rd 3/2 - No concentration on a single orbit! R=3.0 fm NOT cluster condensate triton E0 E0 R=2.43 fm R=2.22 fm C: Hoyle state B(E0,IS)=96±16 fm 4 B(E0,IS)=92 fm 4 T. Kawabata et al., PRC70 (2004) vs. Hoyle state: B(E0,IS)=0±9 fm 4 70% S-orbit 3 (0 S)
39 11 B = + + t OCM Occupation probabilities 11 B: 3rd 3/2 - No concentration on a single orbit! 3 MeV R=3.0 fm NOT cluster condensate triton E0 E0 R=2.43 fm R=2.22 fm C: Hoyle state B(E0,IS)=96±16 fm 4 B(E0,IS)=92 fm 4 T. Kawabata et al., PRC70 (2004) vs. Hoyle state: B(E0,IS)=0±9 fm 4 70% S-orbit 3 (0 S)
40 + states in 11 B
41 Structure of 1/2 + states 11 B 1/2 + : Hoyle-analogue exists or not? Overlap amplitudes with + 7 Li(g.s) channel 1 st 1/2+ S-orbit t S 1/2 -orbit 3rd 3/2- E 2+t [MeV] (1 2 ) t 2+t OCM EXP Candidate? CAL ( T = ) 2+t 7 Li st 3/2- R rms = 3.14[fm] vs fm for 3 rd 3/2-7 Li(3/2 - ) + : P-wave Parity doublet partner of 3 rd 3/2-
42 t Structure of 1/2 + states 11 B 1/2 + : Hoyle-analogue exists or not? S-orbit E 2+t [MeV] (1 2 ) t ( T = ) 2+t 7 Li+ S 1/2 -orbit 2+t OCM EXP Candidate? CAL /2 + : E x =.6 MeV (E 2a+t =1.5 MeV) 7 Li( 9 Be, 7 Li) 5 He T=1/2 Soic et al. NPA Li( 7 Li, 11 B*)t T=1/2 11 B* + 7 Li Curis et al. PRC Be(p,γ), 9 Be( 3 He,p) T=3/2 Goosman et al. PRC Zwiegliski NPA Ajenberg-Selove R rms = 5.98[fm] : dilute! R rms = 3.14[fm] vs fm for 3 rd 3/2-7 Li(3/2 - ) + : P-wave Parity doublet partner of 3 rd 3/2-
43 Complex-scaling method for 1/2 + with ++t OCM Bound state 1 st 1/2+ 2 nd 1/2+ exists as a resonant state. Resonant state 2 nd 1/2+ 7 Li(1/2-)+ ++t 7 Li(3/2-)+ E x (cal)= 11.9 MeV, Γ=190 kev E x (exp)=.56 MeV, Γ=210±20 kev
44 Occupation probabilities of cluster orbits 1 st 1/2 + 7 Li + structure 2 nd 1/2 + triton triton 52% 96% P-orbit S-orbit S-orbit Concentration on S-wave orbits! 2 nd 1/2 + : Hoyle-analogue state C(g.s) 70% Hoyle state S-orbit T. Yamada et al., EPJA 2005
45 Occupation probabilities of cluster orbits 1 st 1/2 + 7 Li + structure 2 nd 1/2 + triton triton 52% 96% P-orbit S-orbit S-orbit Concentration on S-wave orbits! 2 nd 1/2 + : Hoyle-analogue state C(g.s) 2 nd 1/2+: 65% (0S ) 2 (0S t ) 65% = (2 52%+96%)/3
46 Hoyle-analogue states (0S ) 3 : 70% (0S ) 4 : 60% (0S ) 2 (0S t ): 65%
47 , + states in 13 C What happens in C when an extra neutron (n) is added into the Hoyle state (3)? Hoyle-analogue states? 3+n OCM with GEM n S-orbit S 1/2 -orbit(0s ) 3 (S n ) n π + J =1/2
48 -n and -t potentials: parity-dependent odd waves : attractive enough to make resonances/bound states even waves: weakly attractive 13 C C(Hoyle) + neutron p-orbit s-orbit 3 part in 13 C reduced: not so changed: J π ( 13 C) 1/2 -,3/2-1/ B 8 Be(2) + triton p-orbit s-orbit 2 part in 11 B J π ( 11 B) reduced: 1/2-,3/2 - not so changed: 1/2 + Thus, one can expect cluster-gas-like states in 1/2+.
49 -n phase shifts -triton phase shifts -n potential (1) P-wave: attractive (2) S-wave: weakly attractive -triton potential (1) P-, F-waves: attractive (2) S-, D-waves: weakly attractive Parity-dependent potentials
50 3 + n OCM for 13 C J=1/2-, 1/2+ : Yamada et al., Int.J.Mod.Phys. E17 (2008) reproduction of M(E0), Hoyle-analogue state energy spectra of 13 C R=5.4fm 1/2+ states Probability S -orbit C (Hoyle) + n 9 Be(1/2+) + 55% R=4.0fm 9 Be(3/2-,1/2-) + [larger than C (Hoyle) + n] 28% R=2.68fm C (g.s) + n neutron-halo-like 20%
51 Hoyle-analogue states (0S ) 3 (S n ): 55% (0S ) 3 : 70% (0S ) 4 : 60% (0S ) 2 (0S t ): 65%
52 IS monopole transition in light nuclei 1. Useful to search for cluster states 2. Dual nature of ground states 3. typical case: 16O IS monopole strength function: -cluster states at low energy mean-field-type states at higher energy
53 16 E (MeV) O x MeV ( Γ= 1.5 kev) C 7.16 MV e [11.26 M( E 0) ( Γ= = MeV)] fm (6%) + Monopole strengths M(E0) in 16 O and C Exp Strong candidate (4 condensate) C(1 - )+ (P) higher nodal C(2 1+ )+ (D) EWSR values 2 M( E 0) = 4.03 ± 0.09 fm (8%) C(0 1+ )+ (S) 2 M( E 0) = 3.55 ± 0.21 fm (3%) EWSR values E x (MeV) MeV Single particle M(E0)~5.4 fm C EWSR value M( E 0) = 5.4 ± 0.2 fm (16%) 0 + 1
54 Isoscalar Monopole Excitations in 16 O cluster states at low energy and mean-field states at higher energy
55 Isoscalar Monopole Excitation density fluctuation Typical example IS-GMR (heavy, medium-heavy nuclei) exhaust EWSR ~ 100% 208 Pb(, ) IS-GQR IS-GQR IS-GMR breathing mode E x =13.7 MeV Γ=3.0 MeV Harakeh et al., PRL(1977)
56 N=10 h.o.quanta 208 Pb: RPA E x =18.0 MeV N= collective motion with coherent 1p-1h states IS-GMR is well reproduced by RPA cal. Blaizot, Gogny, Grammticos, NPA(1976) N=14
57 Light Nuclei (p-, sd-shell,,,) Isoscalar monopole strengths are fragmented. For example, 16 O, ( C, 11 B, 13 C, 24 Mg, ) IS-monopole response fun. of 16 O(, ) (i) discrete peaks in E x 15 MeV ~20% of EWSR large M(E0) states cluster states (ii) three-bump structure : E=18, 23, 30 MeV
58 IS Monopole Strength Function of 16 O 16 O(, ) Exp. vs Cal. Relativistic RPA cal. Exp: histogram Lui et al., PRC 64 (2001) discrete peaks in Ex 15 MeV three bumps in 18, 23, 30 MeV Cal: real line Relativistic RPA Ma et al., PRC 55 (1997) Multiplied by 0.25 Shifted by 4.2 MeV Exp. condition: E x > 10 MeV Not well reproduced by RRPA cal.
59 Non-rela. Mean-field calculations of IS-monopole strengths for 16 O (1) RPA calculation: 1p-1h excitations Blaizot et al., NPA265 (1976) (2) Second-order RPA (SRPA) calculations: : 1p1h + 2p2h i) Drozdz et al., PR197(1980): D1-force ii) Papakonstantino et al., PLB671(2009): UCOM iii) Gambacurta et al., PRC81(2010) : full SRPA calculation with Skyrme force
60 Experiment 16 O(, ) RPA calculation Isoscalar Relativistic RPA cal. Blaizot et al., NPA(1976) Exp. condition: E x > 10 MeV
61 SRPA(1p1h+2p2h) SRPA RPA RPA(1p1h) E x [MeV] E x [MeV] Gambacurta et al., PRC(2010) Papakonstantino et al., PLB(2009) Exp: histogram Lui et al., PRC 64 (2001) Exp. condition: E x > 10 MeV Exp. condition: E x > 10 MeV 61
62 Ex [MeV] R [fm] Experiment M(E0) [fm 2 ] Γ [MeV] R [fm] 4 OCM M(E0) [fm 2 ] Γ [MeV] no data no data
63 0 + 2 SRPA(1p1h+2p2h) RPA(1p1h) No sharp peak! SRPA RPA No sharp peak! E x [MeV] E x [MeV] Gambacurta et al., PRC(2010) Papakonstantino et al., PLB(2009) Exp: histogram Lui et al., PRC 64 (2001) Exp. condition: E x > 10 MeV Exp. condition: E x > 10 MeV
64 RPA calculations: (1) Reproduction of 3-bump structure, but the energy positions are by about 3-5 MeV higher than the data. (2) No reproduction of discrete peaks at E x 15 MeV SRPA calculations: (1) Reproduction of 3-bump structure (2) Discrete peaks at E x 15 MeV are not reproduced well. In particular, M(E0: g.s 2 nd 0+) is not seen in SRPA cal. E x (2 nd 0+) = 6.1 MeV This peak should exit sharply at E x =6.1 MeV because Γ 1 ev.
65 Purposes of my talk What kind of states contribute to the discrete peaks? Recently, 4 OCM succeeded in describing the structure of the lowest six 0+ states up to 4 threshold (E x 15 MeV). The discrete peaks correspond to cluster states? We study the strength function of IS M(E0) with the 4 OCM framework. Funaki s talk
66 4 OCM calculation Funaki, Yamada et al., PRL101 (2008) 4 cond. state C(1 1- )+(P) strong candidate 4 (0 S) 60% C(0 1+ )+(S): higher nodal C(2 1+ )+(D) C(0 1+ )+(S) shell-model-like: (0s) 4 (0p)
67 O(, ) Relativistic RPA cal Exp. condition: E x > 10 MeV Exp: histogram Lui et al., PRC 64 (2001) Cal: real line Ma et al., PRC 55 (1997) Multiplied by 0.25 Shifted by 4.2 MeV
68 IS monopole strength function of 16 O within 4 OCM
69 Monopole Strength Function + 0 n : resonance state with E n - iγ n /2 1 SE ( ) = Im[ RE ( )] π 1 Γ /2 + + = M (0n 01 ) π n 2 2 n ( E En) + ( Γn / 2) 2 IS-monopole m.e.: Energy weighted sum rule (EWSR): n ( En E1) M(0n 01) = 16 R, m rms radius of 16 O R = 0 ( r R ) i cm 1 i= 1
70 Energy weighted sum rule within 4 OCM (OCM-EWSR)
71 4 OCM and OCM-EWSR Total w.f. : internal w.f.s of clusters relative motion S [ ] π Ψ( J ) = f ( ν) ϕ ( ξ, ν ) ϕ ( ξ, ν ) ϕ ( ξ, ν ) ν π u F Ψ ( J ) = 0 c L J : Orthogonality condition to Paul forbidden states Hamiltonian for Ψ ( J π ) 4 4 ( N ) (Coul) OCM = i cm i= 1 i< j H T T V (, i j) V (, i j) 4 + V ( i, jk, ) + V (1,2,3,4) i< j< k 3 4 : 4-body problem with orthogonality condition
72 4 OCM and OCM-EWSR Total w.f. : internal w.f.s of clusters relative motion IS monopole matrix element rms radius of 16 nucleons where we used
73 Interesting characters of IS monopole operator 16 nucleons ( ri+ 4( k 1) R ) 4( R cm ) k k R k = 1 i= 1 k = 1 = + internal part of each -cluster ri R + ri R C i= 1 i= 5 relative parts acting on relative motions of 4 s with respect to c.o.m. of 16 O R R = ( ) ( ) + 3( ) C internal part of internal part of C relative part acting on relative motion of and C Decomposition into Internal part and relative part plays an important role in understanding monopole excitations of 16 O. 2 C
74 4 OCM and OCM-EWSR Total w.f. : internal w.f.s of clusters relative motion EWSR of IS monopole transition in 4 OCM: OCM-EWSR OCM-EWSR where O OCM 4 2 4( R Rcm ), k k = 1 = R ( cm ) 0 + ri R 1 i= 1 = 16 : r.m.s radius of 16O : r.m.s radius of -particle
75 4 OCM and OCM-EWSR Ratio of OCM-EWSR to total EWSR: 4 OCM shares over 60% of the total EWSR value. ( c.f. + C OCM : 31%) This is one of important reasons that 4 OCM works rather well in reproducing IS monopole transitions in low-energy region of 16 O. n ( En E1) M(0n 01) = 16 R m 2 Yamada et al.
76 IS monopole strength function S(E) within 4 OCM framework
77 Monopole Strength Function + 0 n : resonance state with E n - iγ n /2 1 SE ( ) = Im[ RE ( )] π 1 Γ /2 + + = M (0n 01 ) π n 2 2 n ( E En) + ( Γn / 2) 2 : calculated by 4 OCM Γ n E n 2 2 = Γ n(ocm) + (exp. resolution) : experimental energy of n-th 0+ state 50 kev
78 Ex [MeV] R [fm] Experiment M(E0) [fm 2 ] Γ [MeV] R [fm] 4 OCM M(E0) [fm 2 ] Γ [MeV] no data no data
79 Exp. vs. Cal. IS monopole S(E) with 4 OCM O(, ) Relativistic RPA cal Exp. condition: E x > 10 MeV It is likely to exist discrete peaks on a small bump in E x < 15MeV This small bump may come from the contribution from continuum states of + C
80 Exp. vs. Cal. IS monopole S(E) with 4 OCM O(, ) Relativistic RPA cal Exp. condition: E x > 10 MeV Excitation to cluster states (-cluster type) Monopole excitation of mean-field type (RPA)
81 IS monopole S(E) with 4 OCM Exp. vs. Cal Two features of monopole excitations They come from a dual nature of the ground state of 16 O Excitation to cluster states (-cluster type) Monopole excitation of mean-field type (RPA)
82 IS monopole S(E) with 4 OCM Exp. vs. Cal Two features of monopole excitations They come from a dual nature of the ground state of 16 O next discuss! Excitation to cluster states (-cluster type) Monopole excitation of mean-field type (RPA)
83 Dual nature of ground state of 16 O mean-field character and -clustering character
84 Ground state of 16 O Dominance of doubly-closed-shell structure: (0s) 4 (0p) = SU(3)(0,0) Cluster-model calculations: 4 OCM, 4 THSR, + C OCM,... Mean-field calculations : RPA, QRPA, RRPA,... Supported by no-core shell model calculations: Dytrych et al., PRL98 (2007) Bayman-Bohr theorem : SU(3)[f](λµ) = cluster-model wf Doubly-closed-shell w.f, (0s) 4 (0p), is mathematically equivalent to a single -cluster w.f. This means that the ground state w.f. of 16 O originally has an -clustering degree of freedom together with single-particle degree of free dom. We call it duality of -clustering and mean-filed characters in g.s.
85 Bayman-Bohr theorem Nucl. Phys. 9, 596 (1958/1959) 1 det (0 4 s ) (0 p ) cm ( cm ) 16!!4! 16! [ φ R ] 1 { ( ξ,3 νφ ) } L 0( C) = φ ( ) = N0 A u40 3 J = 0!4! 16! { ( ξ } 3,3 νφ ) L ( C) = φ ( ) = N2 A u42 2 J = 0 φ 3/4 32ν 2 cm Rcm = νrcm ( ) exp( 16 ) π c.o.m. w.f. of 16 O G.S. has mean-field-type and -cluster degrees of freedom. Excitation of mean-field-type degree of freedom in g.s 1p1h states (3-bump structure) Excitation of -cluster degree of freedom in g.s + C cluster states: 2 nd 0+, 3 rd ri R + ri R C i= 1 i= 5 R R = ( ) ( ) + 3( ) C internal parts relative part 2
86 4 OCM calculation Funaki, Yamada et al., PRL101 (2008) 4 cond. state C(1 1- )+(P) strong candidate 4 (0 S) 60% C(0 1+ )+(S): higher nodal C(2 1+ )+(D) C(0 1+ )+(S) shell-model-like: (0s) 4 (0p)
87 Monopole excitation to 0 + 2,3 and state 0 + 2,3 states: C(0 1+,2 1+ )+(S) main configuration Bayman-Bohr theorem: (0s) 4 (0p) has an + C(0 1+,2 1+ ) degree of freedom relative motion (- C) is excited by IS monopole operator state: 4-gas like structure Bayman-Bohr theorem: (0s) 4 (0p) has a 4 degree of freedom main configuration relative motion among 4 is excited by IS monopole operator
88 Bayman-Bohr theorem G.S. has a 4-cluster degree of freedom O(g.s.) (0s) 4 (0p) SU(3)(00) wf (N 2-,L 2- )=(4,0) = (N 3-,L 3- )=(4,0) (N 2,L 2 )=(4,0) Bayman-Bohr theorem
89 4 gas-like or + C(Hoyle) state 4 -gas-like M(E0)=1.0 fm 2 by 4 OCM Monopole transition O(g.s.) (0s) 4 (0p) SU(3)(00) wf (N 2-,L 2- )=(4,0) = (N 3-,L 3- )=(4,0) (N 2,L 2 )=(4,0) ( ri+ 4( k 1) R ) + ( k k= 1 i= 1 k = 1 = R R internal part 4 ) relative part k coherent excitation Bayman-Bohr theorem cm 2
90 C 3 gas-like = (Hoyle) state 3 4 = ( r R ) k = 1 i= 1 i+ 4( k 1) k 2 internal part portion of EWSR 2 M( E 0) = 5.4 ± 0.2 fm (16%) + 3 k = 1 4( R k R cm ) 2 relative part Monopole transition coherent excitation C(g.s.) (0s) 4 (0p) 8 SU(3)(04) wf = (N 84,L 84 )=(4,0) (N 44,L 44 )=(4,0) Yamada et al., PTP0 (2008) Bayman-Bohr theorem Dominance of SU(3)(04) : no-core shell model by Dytrych et al., PRL98 (2007)
91 C Bayman-Bohr theorem 4 π + J = 0( C) = (0 s) (0 p) ;(, ) = (0,4), J = 0 φ λµ internal 4!4!4! 8 = N0 A u40( 2, ν) u40( 1,2 ν) φφφ ( ) ( ) ( )! ξ ξ 3 J = 0 Dominance of SU(3)(04) : confirmed by no-core shell model Dytrych et al., PRL98 (2007) This means that the ground state w.f. of C originally has an -clustering degree of freedom together with single-particle degree of free dom.
92 Monopole excitation to and state state: C(1 1- )+(P) main configuration Bayman-Bohr theorem: (0s) 4 (0p) has no configuration of C(1-)+ Why this state is excited? Coupling with C(0+,2+)+ and C(Hoyle)+ configuration Coherent contribution from these configurations state: C(0 1+ )+(S): higher nodal Coherent contributions from C(0+,2+)+ and C(Hoyle)+ configurations
93 Components of + C(L π ) channels in 0 + states of 16 O R=2.7fm SU(3)-nature (0s) 4 (0p) C(0 1+ )+(S) C(2 1+ )+(D) C(0 1+ )+(S) higher nodal C(1 1- )+(P) C(0 2+ )+(S): 4 gas-like
94 Components of + C(L π ) channels in 0 + states of 16 O R=2.7fm SU(3)-nature (0s) 4 (0p) C(0 1+ )+(S) C(2 1+ )+(D) C(0 1+ )+(S) higher nodal C(1 1- )+(P) C(0 2+ )+(S): 4 gas-like
95 Two features of IS monopole excitations in 16 O IS monopole S(E): 4 OCM Two features in IS monpole exci Excitation to cluster states (-cluster type) Monopole excitation of mean-field type (RPA) 4 OCM Meanfield Fine structure E x < 16 MeV OK difficult 3-bump structure 16 < E x < 40 MeV difficult OK Origin: dual nature of G.S. of 16 O (1) -clustering degree of freedom (2) mean-field-type one (0s) 4 (0p) : SU(3)(00)= C+ : Bayman-Bohr theorem Huge model space is needed to reproduce S(E) in the whole energy region. cluster basis + collective basis
96 Dual nature of the ground states in C and 16 O : common to all N=Z=even light nuclei 20 Ne 20 Ne, 24 Mg, 32 S,.., 44 Ti,. Excitation of mean-field degree of freedom Excitation of -cluster degree of freedom + 16 O cluster states of K π = 0 + 4, 0 - bands + 16 O comp. = 80% for low spins: Q=10 quanta Almost pure + 16 O structures for low spins: Q=9 quanta
97 20 Ne AMD+GCM M. Kimura, PRC69, (2004)
98 Two features of IS monopole excitation Cluster states at low energy, Mean-field-type states at higher energy These features will persist in other light nuclei. Increasing mass number, effect of spin-orbit forces becomes stronger: some SU(3) symmetries are mixed. Goodness of nuclear SU(3) symmetry: gradually disappearing. Two features of IS monopole excitation will be vanishing. Eventually only 1p1h-type collective motions are strongly excited. Hope: Systematic experiments!!
99 Summary -condensation in C, 16 O, heavier 4n nuclei. Hoyle-analog states in 11 B, 13 C IS monopole tran. : useful to search for cluster states IS monopole excitations have two features: 16 O (typical) (i) -cluster type: discrete peaks in E x 15 MeV (ii) mean-field type: 3-bump structure (18,23,30 MeV) The origin: dual nature of the ground state of 16 O. (0s) 4 (0p) : SU(3)(00) = C+ : proved by Bayman-Bohr theorem Dual nature is common to all N=Z=even light nuclei クラスターガス状態 : 新しい物質形態拡がりと深さの探求 : 通常核 (4n 核 ), 中性子過剰核
Cluster-gas-like states and monopole excitations. T. Yamada
Cluster-gas-like states and monopole excitations T. Yamada Cluster-gas-like states and monopole excitations Isoscalar monopole excitations in light nuclei Cluster-gas-likes states: C, 16 O, 11 B, 13 C
More informationAlpha particle condensation in nuclear systems
Alpha particle condensation in nuclear systems Contents Introduction ncondensate wave function 3system (0 and states ) 4system (05 state) Yasuro Funaki (Kyoto Univ.) Peter Schuck (IPN, Orsay) Akihiro Tohsaki
More informationStudy of cluster structure by GCM. Ryosuke Imai and Masaaki Kimura (Hokkaido Univ.)
Study of cluster structure by GCM Ryosuke Imai and Masaaki Kimura (Hokkaido Univ.) Energy [ MeV] Introduction Cluster structure and α gas-like states 12 C(3α) 16 O(4α) Recent studies for gas-like states.
More informationα Particle Condensation in Nuclear systems
Particle Condensation in Nuclear systems A. Tohsaki, H. Horiuchi, G. Röpke, P. Sch. T. Yamada and Y. Funaki -condensation in matter 8 Be and Hoyle state in 12 C -condensate wave function Effective GPE
More informationFunctional Orsay
Functional «Theories» @ Orsay Researchers: M. Grasso, E. Khan, J. Libert, J. Margueron, P. Schuck. Emeritus: N. Van Giai. Post-doc: D. Pena-Arteaga. PhD: J.-P. Ebran, A. Fantina, H. Liang. Advantages of
More informationAlpha inelastic scattering and cluster structures in 24 Mg. Takahiro KAWABATA Department of Physics, Kyoto University
Alpha inelastic scattering and cluster structures in 24 Mg Takahiro KAWABATA Department of Physics, Kyoto University Introduction Contents Alpha cluster structure in light nuclei. Alpha condensed states.
More informationTensor-optimized antisymmetrized molecular dynamics (TOAMD) with bare forces for light nuclei
Tensor-optimized antisymmetrized molecular dynamics (TOAMD) with bare forces for light nuclei Takayuki MYO Mengjiao LYU (RCNP) Masahiro ISAKA (RCNP) Hiroshi TOKI (RCNP) Hisashi HORIUCHI (RCNP) Kiyomi IKEDA
More informationNew Trends in the Nuclear Shell Structure O. Sorlin GANIL Caen
New Trends in the Nuclear Shell Structure O. Sorlin GANIL Caen I. General introduction to the atomic nucleus Charge density, shell gaps, shell occupancies, Nuclear forces, empirical monopoles, additivity,
More informationCluster-orbital shell model approach for unstable nuclei and the developments
CANHP2015 (week 6), 25-30 Oct. 2015, Kyoto, Japan Cluster-orbital shell model approach for unstable nuclei and the developments Hiroshi MASUI Kitami Institute of Technology Outline of my talk 1. Cluster-orbital
More informationCentral density. Consider nuclear charge density. Frois & Papanicolas, Ann. Rev. Nucl. Part. Sci. 37, 133 (1987) QMPT 540
Central density Consider nuclear charge density Frois & Papanicolas, Ann. Rev. Nucl. Part. Sci. 37, 133 (1987) Central density (A/Z* charge density) about the same for nuclei heavier than 16 O, corresponding
More informationNuclear electric dipole moment in the Gaussian expansion method
Nuclear electric dipole moment in the Gaussian expansion method Nodoka Yamanaka (ithes Group, RIKEN) In collaboration with E. Hiyama (RIKEN), T. Yamada (Kanto-Gakuin Univ.), Y. Funaki (RIKEN) 2015/10/12
More informationCitation PHYSICAL REVIEW C (2006), 74(5) RightCopyright 2006 American Physical So
Title alphac-12 in angular distri 12(O-2()) Author(s) Takashina, M; Sakuragi, Y Citation PHYSICAL REVIEW C (2006), 74(5) Issue Date 2006-11 URL http://hdl.handle.net/2433/50458 RightCopyright 2006 American
More informationBeyond mean-field study on collective vibrations and beta-decay
Advanced many-body and statistical methods in mesoscopic systems III September 4 th 8 th, 2017, Busteni, Romania Beyond mean-field study on collective vibrations and beta-decay Yifei Niu Collaborators:
More informationEvolution Of Shell Structure, Shapes & Collective Modes. Dario Vretenar
Evolution Of Shell Structure, Shapes & Collective Modes Dario Vretenar vretenar@phy.hr 1. Evolution of shell structure with N and Z A. Modification of the effective single-nucleon potential Relativistic
More informationNuclear Alpha-Particle Condensation
Nuclear Alpha-Particle Condensation 40 Ca+ 12 C, 25 AMeV with CHIMERA First experimental evidence of alpha-particle condensation for the Hoyle state Ad. R. Raduta, B.Borderie, N. Le Neindre, E. Geraci,
More informationTitle. Author(s)Itagaki, N.; Oertzen, W. von; Okabe, S. CitationPhysical Review C, 74: Issue Date Doc URL. Rights.
Title Linear-chain structure of three α clusters in 13C Author(s)Itagaki, N.; Oertzen, W. von; Okabe, S. CitationPhysical Review C, 74: 067304 Issue Date 2006-12 Doc URL http://hdl.handle.net/2115/17192
More informationQuantum Theory of Many-Particle Systems, Phys. 540
Quantum Theory of Many-Particle Systems, Phys. 540 Questions about organization Second quantization Questions about last class? Comments? Similar strategy N-particles Consider Two-body operators in Fock
More informationCa+ 12 C, 25 AMeV ( 40 Ca+ 40 Ca, 25 AMeV)
Search for alpha-particle condensation with CHIMERA 40 Ca+ 12 C, 25 AMeV ( 40 Ca+ 40 Ca, 25 AMeV) De-excitation of quasi-projectiles (primary and secondary products) C.R. Badita, B.Borderie, N. Le Neindre,
More informationNucleon Pair Approximation to the nuclear Shell Model
Nucleon Pair Approximation to the nuclear Shell Model Yiyuan Cheng Department of Physics and Astronomy, Shanghai Jiao Tong University, China RCNP, Osaka university, Japan Collaborators: Yu-Min Zhao, Akito
More informationMany-Body Resonances of Nuclear Cluster Systems and Unstable Nuclei
Many-Body Resonances of Nuclear Cluster Systems and Unstable Nuclei Contents of the lecture 1. Resonances and complex scaling method 2. Many-body resonances of He-isotopes and their mirror nuclei 3. Coulomb
More informationRPA and QRPA calculations with Gaussian expansion method
RPA and QRPA calculations with Gaussian expansion method H. Nakada (Chiba U., Japan) @ DCEN11 Symposium (YITP, Sep. 6, 11) Contents : I. Introduction II. Test of GEM for MF calculations III. Test of GEM
More informationPhysics of neutron-rich nuclei
Physics of neutron-rich nuclei Nuclear Physics: developed for stable nuclei (until the mid 1980 s) saturation, radii, binding energy, magic numbers and independent particle. Physics of neutron-rich nuclei
More informationCluster and shape in stable and unstable nuclei
luster and shape in stable and unstable nuclei Y. Kanada-En yo (Kyoto Univ.) ollaborators: Y. Hidaka (GOE-PD->Riken) F. Kobayashi (D2, Kyoto Univ.) T. Suhara (Kyoto Univ.->Tsukuba Univ.) Y. Taniguchi (Tsukuba
More informationMean field studies of odd mass nuclei and quasiparticle excitations. Luis M. Robledo Universidad Autónoma de Madrid Spain
Mean field studies of odd mass nuclei and quasiparticle excitations Luis M. Robledo Universidad Autónoma de Madrid Spain Odd nuclei and multiquasiparticle excitations(motivation) Nuclei with odd number
More informationSubbarrier fusion of carbon isotopes ~ from resonance structure to fusion oscillations ~
Subbarrier fusion of carbon isotopes ~ from resonance structure to fusion oscillations ~ Kouichi Hagino, Tohoku University Neil Rowley, IPN Orsay 1. Introduction: 12 C + 12 C fusion 2. Molecular resonances
More informationAlpha cluster condensation in 12 C and 16 O
Alpha cluster condensation in 12 C and 16 O A. Tohsaki, Department of Fine Materials Engineering, Shinshu University, Ueda 386-8567, Japan H. Horiuchi, Department of Physics, Kyoto University, Kyoto 606-8502,
More informationDynamics of nuclear four- and five-body systems with correlated Gaussian method
Journal of Physics: Conference Series OPEN ACCESS Dynamics of nuclear four- and five-body systems with correlated Gaussian method To cite this article: W Horiuchi and Y Suzuki 214 J. Phys.: Conf. Ser.
More informationCollective excitations of Lambda hypernuclei
Collective excitations of Lambda hypernuclei Kouichi Hagino (Tohoku Univ.) Myaing Thi Win (Lashio Univ.) J.M. Yao (Southwest Univ.) Z.P. Li (Southwest Univ.) 1. Introduction 2. Deformation of Lambda hypernuclei
More informationHybridization of tensor-optimized and high-momentum antisymmetrized molecular dynamics for light nuclei with bare interaction
Prog. Theor. Exp. Phys. 2015, 00000 (10 pages) DOI: 10.1093/ptep/0000000000 Hybridization of tensor-optimized and high-momentum antisymmetrized molecular dynamics for light nuclei with bare interaction
More informationStructures and Transitions in Light Unstable Nuclei
1 Structures and Transitions in Light Unstable Nuclei Y. Kanada-En yo a,h.horiuchi b and A, Doté b a Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization, Oho 1-1, Tsukuba-shi
More informationMedium polarization effects and pairing interaction in finite nuclei
Medium polarization effects and pairing interaction in finite nuclei S. Baroni, P.F. Bortignon, R.A. Broglia, G. Colo, E. Vigezzi Milano University and INFN F. Barranco Sevilla University Commonly used
More informationCluster Models for Light Nuclei
Cluster Models for Light Nuclei N. Itagaki, T. Otsuka, University of Tokyo S. Aoyama, Niigata University K. Ikeda, RIKEN S. Okabe, Hokkaido University Purpose of the present study Cluster model explore
More informationSOTANCP4. Is the Hoyle state condensed? Probing nuclear structure via 3-body decays. University of Birmingham, United Kingdom SOTANCP4.
Is the condensed? Probing nuclear structure via 3-body decays University of Birmingham, United Kingdom 1/29 Overview 1 2 3 4 1/29 Trinity of? 12 C 2/29 Cluster description of the 12 C as an equilateral
More informationNUCLEAR STRUCTURE AB INITIO
December, 6:8 WSPC/Trim Size: 9in x 6in for Proceedings master NUCLEAR STRUCTURE AB INITIO H. FELDMEIER AND T. NEFF Gesellschaft für Schwerionenforschung mbh Planckstr., D-69 Darmstadt, Germany E-mail:
More informationLow-lying dipole response in stable and unstable nuclei
Low-lying dipole response in stable and unstable nuclei Marco Brenna Xavier Roca-Maza, Giacomo Pozzi Kazuhito Mizuyama, Gianluca Colò and Pier Francesco Bortignon X. Roca-Maza, G. Pozzi, M.B., K. Mizuyama,
More informationMulti-cluster problems: resonances, scattering and condensed states
Journal of Physics: Conference Series OPEN ACCESS Multi-cluster problems: resonances, scattering and condensed states To cite this article: K Kat et al 2013 J. Phys.: Conf. Ser. 436 012026 View the article
More informationNuclear Symmetry Energy Constrained by Cluster Radioactivity. Chang Xu ( 许昌 ) Department of Physics, Nanjing University
Nuclear Symmetry Energy Constrained by Cluster Radioactivity Chang Xu ( 许昌 ) Department of Physics, Nanjing University 2016.6.13-18@NuSym2016 Outline 1. Cluster radioactivity: brief review and our recent
More informationChiral effective field theory on the lattice: Ab initio calculations of nuclei
Chiral effective field theory on the lattice: Ab initio calculations of nuclei Nuclear Lattice EFT Collaboration Evgeny Epelbaum (Bochum) Hermann Krebs (Bochum) Timo Lähde (Jülich) Dean Lee (NC State)
More informationThe Nuclear Many-Body Problem
The Nuclear Many-Body Problem relativistic heavy ions vacuum electron scattering quarks gluons radioactive beams heavy few nuclei body quark-gluon soup QCD nucleon QCD few body systems many body systems
More informationin covariant density functional theory.
Nuclear Particle ISTANBUL-06 Density vibrational Functional coupling Theory for Excited States. in covariant density functional theory. Beijing, Sept. 8, 2011 Beijing, May 9, 2011 Peter Peter Ring Ring
More informationFine structure of nuclear spin-dipole excitations in covariant density functional theory
1 o3iø(œ April 12 16, 2012, Huzhou, China Fine structure of nuclear spin-dipole excitations in covariant density functional theory ùíî (Haozhao Liang) ŒÆÔnÆ 2012 c 4 13 F ÜŠöµ Š # Ç!Nguyen Van Giai Ç!ë+
More informationarxiv: v1 [nucl-th] 9 Feb 2012
1 Antisymmetrized molecular dynamics and its applications to cluster phenomena Yoshiko Kanada-En yo 1, Masaaki Kimura 2, and Akira Ono 3 1 Department of Physics, Kyoto University, Kyoto 66-852, Japan 2
More informationCollective excitations of Λ hypernuclei
Collective excitations of Λ hypernuclei Kouichi Hagino (Tohoku Univ.) J.M. Yao (Southwest Univ.) Z.P. Li (Southwest Univ.) F. Minato (JAEA) 1. Introduction 2. Deformation of Lambda hypernuclei 3. Collective
More informationJoint ICTP-IAEA Workshop on Nuclear Structure Decay Data: Theory and Evaluation August Introduction to Nuclear Physics - 1
2358-19 Joint ICTP-IAEA Workshop on Nuclear Structure Decay Data: Theory and Evaluation 6-17 August 2012 Introduction to Nuclear Physics - 1 P. Van Isacker GANIL, Grand Accelerateur National d'ions Lourds
More informationFeatures of nuclear many-body dynamics: from pairing to clustering
Features of nuclear many-body dynamics: from pairing to clustering Alexander Volya Florida State University Collaborators: K. Kravvaris, Yu. Tchuvil sky Outline Configuration interaction approach SU(3)
More informationNeutron Halo in Deformed Nuclei
Advances in Nuclear Many-Body Theory June 7-1, 211, Primosten, Croatia Neutron Halo in Deformed Nuclei Ó Li, Lulu Ò School of Physics, Peking University June 8, 211 Collaborators: Jie Meng (PKU) Peter
More informationPygmy dipole resonances in stable and unstable nuclei
Pygmy dipole resonances in stable and unstable nuclei Xavier Roca-Maza INFN, Sezione di Milano, Via Celoria 16, I-2133, Milano (Italy) Collaborators: Giacomo Pozzi, Marco Brenna, Kazhuito Mizuyama and
More informationTowards a microscopic theory for low-energy heavy-ion reactions
Towards a microscopic theory for low-energy heavy-ion reactions Role of internal degrees of freedom in low-energy nuclear reactions Kouichi Hagino (Tohoku University) 1. Introduction: Environmental Degrees
More informationNuclear Matter Incompressibility and Giant Monopole Resonances
Nuclear Matter Incompressibility and Giant Monopole Resonances C.A. Bertulani Department of Physics and Astronomy Texas A&M University-Commerce Collaborator: Paolo Avogadro 27th Texas Symposium on Relativistic
More informationFew-particle correlations in nuclear systems
Trento, 9. 4. 2014 Few-particle correlations in nuclear systems Gerd Röpke, Rostock Outline Quantum statistical approach to nuclear systems at subsaturation densities, spectral function Correlations and
More information4 November Master 2 APIM. Le problème à N corps nucléaire: structure nucléaire
4 November 2010. Master 2 APIM Le problème à N corps nucléaire: structure nucléaire The atomic nucleus is a self-bound quantum many-body (manynucleon) system Rich phenomenology for nuclei Mean field Which
More informationNucleon Pair Approximation to the nuclear Shell Model
Nucleon Pair Approximation to the nuclear Shell Model Yu-Min Zhao (Speaker: Yi-Yuan Cheng) 2 nd International Workshop & 12 th RIBF Discussion on Neutron-Proton Correlations, Hong Kong July 6-9, 2015 Outline
More informationBeyond-mean-field approach to low-lying spectra of Λ hypernuclei
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
More informationThe many facets of breakup reactions with exotic beams
Angela Bonaccorso The many facets of breakup reactions with exotic beams G Blanchon, DM Brink, F Carstoiu, A Garcia-Camacho, R Kumar, JMargueron, N Vinh Mau JAPAN-ITALY EFES Workshop on Correlations in
More information1 Introduction. 2 The hadronic many body problem
Models Lecture 18 1 Introduction In the next series of lectures we discuss various models, in particluar models that are used to describe strong interaction problems. We introduce this by discussing the
More informationTHEORY FOR QUARTET CONDENSATION IN FERMI SYSTEMS WITH APPLICATIONS TO NUCLEAR MATTER
THEORY FOR QUARTET CONDENSATION IN FERMI SYSTEMS WITH APPLICATIONS TO NUCLEAR MATTER P. SCHUCK 1,2,3 1 Institut de Physique Nucléaire, CNRS, UMR8608, Orsay, F-91406, France 2 Université Paris-Sud, Orsay,
More informationConfiguration interaction approach to nuclear clustering
Configuration interaction approach to nuclear clustering Alexander Volya Florida State University Configuration interaction approach A powerful tool in studies of nuclear many-body problems De-facto most
More informationMean-field concept. (Ref: Isotope Science Facility at Michigan State University, MSUCL-1345, p. 41, Nov. 2006) 1/5/16 Volker Oberacker, Vanderbilt 1
Mean-field concept (Ref: Isotope Science Facility at Michigan State University, MSUCL-1345, p. 41, Nov. 2006) 1/5/16 Volker Oberacker, Vanderbilt 1 Static Hartree-Fock (HF) theory Fundamental puzzle: The
More informationHeavy-ion sub-barrier fusion reactions: a sensitive tool to probe nuclear structure
Heavy-ion sub-barrier fusion reactions: a sensitive tool to probe nuclear structure Kouichi Hagino Tohoku University, Sendai, Japan 1. Introduction: heavy-ion fusion reactions 2. Fusion and Quasi-elastic
More informationValence quark contributions for the γn P 11 (1440) transition
Valence quark contributions for the γn P 11 (144) transition Gilberto Ramalho (Instituto Superior Técnico, Lisbon) In collaboration with Kazuo Tsushima 12th International Conference on Meson-Nucleon Physics
More information1. Introduction. 2. Recent results of various studies of K pp. 3. Variational cal. vsfaddeev
Theoretical studies of K - pp Akinobu Doté (KEK Theory Center) 1. Introduction 2. Recent results of various studies of K pp DHW (Variational with Chiral-based) vs AY (Variational with phenomenological)
More informationarxiv:nucl-th/ v2 4 Apr 2003
Collective Properties of Low-lying Octupole Excitations in 28 82 Pb 126, 2 Ca 4 and 8 O 2 XR Zhou a,b, EG Zhao a,b,d, BG Dong c, XZ Zhang c, GL Long a,d arxiv:nucl-th/21132v2 4 Apr 23 a Department of Physics,
More informationLisheng Geng. Ground state properties of finite nuclei in the relativistic mean field model
Ground state properties of finite nuclei in the relativistic mean field model Lisheng Geng Research Center for Nuclear Physics, Osaka University School of Physics, Beijing University Long-time collaborators
More informationProbing shell evolution with large scale shell model calculations
Probing shell evolution with large scale shell model calculations Yutaka Utsuno Advanced Science Research Center, Japan Atomic Energy Agency Center for Nuclear Study, University of Tokyo Nuclear structure
More informationLow- and High-Energy Excitations in the Unitary Fermi Gas
Low- and High-Energy Excitations in the Unitary Fermi Gas Introduction / Motivation Homogeneous Gas Momentum Distribution Quasi-Particle Spectrum Low Energy Excitations and Static Structure Function Inhomogeneous
More informationCalculating β Decay for the r Process
Calculating β Decay for the r Process J. Engel with M. Mustonen, T. Shafer C. Fröhlich, G. McLaughlin, M. Mumpower, R. Surman D. Gambacurta, M. Grasso June 3, 26 Nuclear Landscape To convincingly locate
More informationShell Eects in Atomic Nuclei
L. Gaudefroy, A. Obertelli Shell Eects in Atomic Nuclei 1/37 Shell Eects in Atomic Nuclei Laurent Gaudefroy 1 Alexandre Obertelli 2 1 CEA, DAM, DIF - France 2 CEA, Irfu - France Shell Eects in Finite Quantum
More informationNature of low-energy dipole states in exotic nuclei
Nature of low-energy dipole states in exotic nuclei Xavier Roca-Maza Università degli Studi di Milano, Via Celoria 16, I-133, Milano SPES One-day Workshop on "Collective Excitations of Exotic Nuclei" December
More informationMulti-configuration calculations of hypernuclear photoproduction spectra to shed light on new capability
Multi-configuration calculations of hypernuclear photoproduction spectra to shed light on new capability T. Motoba (Osaka E-C Univ. / Yukawa Inst., Kyoto Univ.) A. Umeya (Nippon Institute of Technology)
More informationNuclear structure aspects of Schiff Moments. N.Auerbach Tel Aviv University and MSU
Nuclear structure aspects of Schiff Moments N.Auerbach Tel Aviv University and MSU T-P-odd electromagnetic moments In the absence of parity (P) and time (T) reversal violation the T P-odd moments for a
More informationEffective Field Theory for light nuclear systems
Effective Field Theory for light nuclear systems Jimmy Rotureau Chalmers University of Technology, Göteborg, Sweden B. Barrett, University of Arizona, Tucson I. Stetcu, University of Washington, Seattle
More informationStudy of the tensor correlation using a mean-field-type model. Satoru Sugimoto Kyoto University
Study of the tensor correlation using a mean-field-type model Satoru Sugimoto Kyoto University The content. Introduction. Charge- and parity-projected Hartree- Fock method 3. pplication to the sub-closed
More informationNew Frontiers in Nuclear Structure Theory
New Frontiers in Nuclear Structure Theory From Realistic Interactions to the Nuclear Chart Robert Roth Institut für Kernphysik Technical University Darmstadt Overview Motivation Nucleon-Nucleon Interactions
More informationarxiv:nucl-th/ v1 27 Nov 2002
1 arxiv:nucl-th/21185v1 27 Nov 22 Medium effects to the N(1535) resonance and η mesic nuclei D. Jido a, H. Nagahiro b and S. Hirenzaki b a Research Center for Nuclear Physics, Osaka University, Ibaraki,
More informationOverview of Nuclear Structure and Excitations
Overview of Nuclear Structure and Excitations MAJOR FEATURES OF OUR SUN -the 3rd lecture- SS Jyvaskyla August 06-12, 2014 T= ~10 7 K at the core = ~1 kev Yoshitaka Fujita Osaka University Layer Structure
More informationTDHF Basic Facts. Advantages. Shortcomings
TDHF Basic Facts Advantages! Fully microscopic, parameter-free description of nuclear collisions! Use same microscopic interaction used in static calculations! Successful in describing low-energy fusion,
More informationRepulsive aspects of pairing correlation in nuclear fusion reaction
4C EOS and Heavy Nuclei, ARIS2014 2014.6.6 (Fri.) @ Univ. of Tokyo Repulsive aspects of pairing correlation in nuclear fusion reaction Shuichiro Ebata Meme Media Laboratory, Hokkaido Univ. Nuclear Reaction
More informationQuantum Theory of Many-Particle Systems, Phys. 540
Quantum Theory of Many-Particle Systems, Phys. 540 IPM? Atoms? Nuclei: more now Other questions about last class? Assignment for next week Wednesday ---> Comments? Nuclear shell structure Ground-state
More informationE. Fermi: Notes on Thermodynamics and Statistics (1953))
E. Fermi: Notes on Thermodynamics and Statistics (1953)) Neutron stars below the surface Surface is liquid. Expect primarily 56 Fe with some 4 He T» 10 7 K ' 1 KeV >> T melting ( 56 Fe) Ionization: r Thomas-Fermi
More informationAlpha Clustering in Nuclear Reactions Induced by Light Ions
Alpha Clustering in Nuclear Reactions Induced by Light Ions C. Beck (IPHC Strasbourg) Introduction : alpha clustering in 12 C, 16 O, 20 Ne clusters in light neutron-rich nuclei Highly deformed shapes in
More information14. Structure of Nuclei
14. Structure of Nuclei Particle and Nuclear Physics Dr. Tina Potter Dr. Tina Potter 14. Structure of Nuclei 1 In this section... Magic Numbers The Nuclear Shell Model Excited States Dr. Tina Potter 14.
More informationCalculation of Energy Spectrum of 12 C Isotope. by Relativistic Cluster model
Calculation of Energy Spectrum of C Isotope by Relativistic Cluster model Nafiseh Roshanbakht, Mohammad Reza Shojaei. Department of physics, Shahrood University of Technology P.O. Box 655-6, Shahrood,
More informationDi-neutron correlation in Borromean nuclei
Di-neutron correlation in Borromean nuclei K. Hagino (Tohoku University) H. Sagawa (University of Aizu) 11 Li, 6 He What is the spatial structure of valence neutrons? Compact? Or Extended? 1. Introduction:
More informationShell evolution and pairing in calcium isotopes with two- and three-body forces
Shell evolution and pairing in calcium isotopes with two- and three-body forces Javier Menéndez Institut für Kernphysik, TU Darmstadt ExtreMe Matter Institute (EMMI) with Jason D. Holt, Achim Schwenk and
More informationNuclear physics around the unitarity limit
Nuclear physics around the unitarity limit Sebastian König Nuclear Theory Workshop TRIUMF, Vancouver, BC February 28, 2017 SK, H.W. Grießhammer, H.-W. Hammer, U. van Kolck, arxiv:1607.04623 [nucl-th] SK,
More informationPHYSICAL REVIEW C 70, (2004)
PHYSICAL REVIEW C 70, 014307 (2004) Giant resonances in 112 Sn and 124 Sn: Isotopic dependence of monopole resonance energies Y.-W. Lui, D. H. Youngblood, Y. Tokimoto, H. L. Clark, and B. John* Cyclotron
More informationSummary Int n ro r d o u d c u tion o Th T e h o e r o e r t e ical a fra r m a ew e o w r o k r Re R s e ul u ts Co C n o c n lus u ion o s n
Isospin mixing and parity- violating electron scattering O. Moreno, P. Sarriguren, E. Moya de Guerra and J. M. Udías (IEM-CSIC Madrid and UCM Madrid) T. W. Donnelly (M.I.T.),.), I. Sick (Univ. Basel) Summary
More informationMicroscopic calculation of the. in the FMD approach. 3 He(α,γ) 7 Be capture reaction
Microscopic calculation of the 3 He(α,γ) 7 Be capture reaction in the FMD approach S-factor [kev b].7.6.5.4.3 Weizmann 4 LUNA 6 LUNA 7 Seattle 7 ERNA 9 FMD Thomas Neff Interfaces between structure and
More informationLow-energy reactions involving halo nuclei: a microscopic version of CDCC
Low-energy reactions involving halo nuclei: a microscopic version of CDCC P. Descouvemont Université Libre de Bruxelles, Belgium In collaboration with M.S. Hussein (USP) E.C. Pinilla (ULB) J. Grineviciute
More informationStructure of halo nuclei and transfer reactions
Structure of halo nuclei and transfer reactions F. Barranco and G. Potel Sevilla University R.A. Broglia Milano University and INFN The Niels Bohr Institute, Copenhagen E. Vigezzi INFN Milano DCEN 2011,
More informationPARTICLE-NUMBER CONSERVING
PARTICLE-NUMBER CONSERVING MICROSCOPIC APPROACH AND APPLICATION TO ISOSPIN MIXING L. Bonneau, J. Le Bloas, H. Naidja, P. Quentin, K. Sieja (CENBG/Université Bordeaux 1) J. Bartel (IPHC/Université Louis
More informationFolding model analysis of the inelastic α+ 12 C scattering at medium energies, and the isoscalar transition strengths of the cluster states of 12 C
Folding model analysis of the inelastic α+ 12 C scattering at medium energies, and the isoscalar transition strengths of the cluster states of 12 C Do Cong Cuong 1, Dao T. Khoa 1a, and Yoshiko Kanada-En
More informationAMD. Skyrme ( ) 2009/03/ / 22
2009 3 25 26 AMD Skyrme ( ) 2009/03/25 26 1 / 22 (?) ( ) 2009/03/25 26 2 / 22 Nuclear Matter in Nuclear Collisions and Neutron Stars 0 60 E sym [MeV] 40 20 0 0 NL3 ChPT DBHF DD ρδ DD TW var AV18+ δ V+3
More informationExcitations in light deformed nuclei investigated by self consistent quasiparticle random phase approximation
Excitations in light deformed nuclei investigated by self consistent quasiparticle random phase approximation C. Losa, A. Pastore, T. Døssing, E. Vigezzi, R. A. Broglia SISSA, Trieste Trento, December
More informationQuantum three-body calculation of the nonresonant triple-α reaction rate at low temperatures
Quantum three-body calculation of the nonresonant triple- reaction rate at low temperatures Kazuyuki Ogata (in collaboration with M. Kan and M. Kamimura) Department of Physics, Kyushu University Kyushu
More informationSchiff Moments. J. Engel. May 9, 2017
Schiff Moments J. Engel May 9, 2017 Connection Between EDMs and T Violation Consider non-degenerate ground state g.s. : J, M. Symmetry under rotations R y (π) for vector operator like d i e i r i implies:
More informationSpin Cut-off Parameter of Nuclear Level Density and Effective Moment of Inertia
Commun. Theor. Phys. (Beijing, China) 43 (005) pp. 709 718 c International Academic Publishers Vol. 43, No. 4, April 15, 005 Spin Cut-off Parameter of Nuclear Level Density and Effective Moment of Inertia
More informationIsoscalar dipole mode in relativistic random phase approximation
Isoscalar dipole mode in relativistic random phase approximation arxiv:nucl-th/0003041v1 20 Mar 2000 D. Vretenar 1,2, A. Wandelt 1, and P. Ring 1 1 Physik-Department der Technischen Universität München,
More informationStability of heavy elements against alpha and cluster radioactivity
CHAPTER III Stability of heavy elements against alpha and cluster radioactivity The stability of heavy and super heavy elements via alpha and cluster decay for the isotopes in the heavy region is discussed
More informationPionless EFT for Few-Body Systems
Pionless EFT for Few-Body Systems Betzalel Bazak Physique Theorique Institut de Physique Nucleaire d Orsay Nuclear Physics from Lattice QCD Insitute for Nuclear Theory April 7, 2016 Seattle Betzalel Bazak
More information