g-ray spectroscopy of (well deformed) sd-shell hypernuclei Graduate school of Science, Tohoku University T. Koike Hyperball-J collaboration K Hagino, Myaing Thi Win Three physics themes of g-ray spectroscopy of hypernuclei • LN interaction – Effective LN interaction • Spin doublet splitting • Impurity effects induced by a L hyperon – Change of core nucleus properties • Change of core energy levels • Electromagnetic properties: e.g. B(E2) • Nuclear medium effects of baryons – Change of L in nuclear medium • Single L particle →B(M1) Coupling of L to nuclear collectivity Low-lying elementary excitation mode Symmetry of nuclear vacuum SSB L Shape of a nucleus at the ground state Collective motion Accessible via g-ray spectroscopy with a few keV sensitivity Single particle excitation v.s. collective excitation From E.S. Paul, Univ. Liverpool, U.K. Nuclear deformation and collectivity • Nuclear shell effect – open shell→mass distribution anisotropy • uneven filling of magnetic sub-states • deformed shell model: Nilsson Model – modification of single particle energy levels • collective model by Bohr & Mottelson – collective elementary excitation (Nambu-Goldstone Mode) Spontaneous deformation (SSB of rotational invariance) Symmetry restoring term H = Hintrinsic+Hcollective Deformed potential (Nilsson potential) Rotation/Vibration Shape parameterization R , C ( ) 1 Axially symmetric quadrupole =2 20≠0, 2±1=2±2=0 Y , 0 Axially symmetric octapole =3 30≠0, 3±1,2,3 =0 20≠0, 2±1,2 =0 Quadrupole deformation (=2) • Five parameters (2,0,±1,±2) →Euler angles + a20, a22 (body-fixed frame axes are chosen to coincide with principal axes) • Further parameterization of a20, a22 a 20 b 2 cos g b2: asphericity 1 a 22 b 2 sin g (deviation from spherical shape) 2 g: triaxiality (difference in length along principal axis) nuclear surface described by (b2, g) R ( , ) R 0 1 b 5 16 (cos g ( 3 cos 2 1) 3 sin g sin 2 cos 2 ) Non collective oblate (b, g=60°) triaxial g spherical b Collective prolate (0,0) (b, g=0°) R ( , ) R 0 1 b 5 16 (cos g ( 3 cos 2 1) 3 sin g sin 2 cos 2 ) Classical collective Hamiltonian of Bohr- Mottelson for quadrupole deformation vibration H coll 1 2 B bb ( b , g ) b 2 1 2 moment of inertia 1 2 J ( b , g ) 2 V coll ( b , g ) 1 , 2 , 3 , rotation Axial rotation: 1D Triaxial rotation: 3D B gg ( b , g ) g B bg ( b , g ) b g 2 potential Axially symmetric shape E ( I , K , n b , ng ) 2 2J0 I ( I 1) K 2 b (nb 1 2 ) g ( n g 1) Z (laboratory fixed) M K 3 (body-fixed, axis of symmetry) K: projection of total angular momentum I on the symmetry axis → a good quantum number Spectra of a deformed even-even nucleus (collective excitation mode) 42+ E(41+)/E(21+) 31+ 43+ 22+ 23+ gband 02+ 41+ b-band 21+ 0+ K=0, nb=1, ng=0 b2, J K=0, nb=0, ng=0 g vibrational v.s. rotational K=2, nb=0, ng=1 Collective excitation (Lab. frame) E(4+)/E(2+): Rotational v.s Vibrational • Rotational (deformed): E x I I ( I 1) 2 2J – E(4)/E(2)=10/3 • Vibrational (spherical): E n n 2 – E(4)/E(2)=2 E (4 ) E (2 ) 2.1 3.1 b , Q0 (intrinsic frame) and 21+, Intrinsic Quadrupole moment: Experimentally E ( 2 1 ) B ( E 2 , 2 0 ) ( 25 8 ) [MeVe b: b 4 3 B(E2) (Lab. frame) B ( E 2) 2 2 Z 2 Q0 A 4 fm ] 3 5 R 0 Ze b 2 , R 0 Ze 1 2 R 0 ( 0 . 12 A 3 ) [ b ] 2 B ( E 2) Q0 2 b 2 1 E ( 21 ) 22+ and experimental estimate of g A rigid triaxial rotor model r E2 2 E2 1 1 1 8 sin ( 3g ) 2 9 1 1 8 sin ( 3g ) 2 9 Davydov and Filippov, Nucl. Phys. 8, 237 (1958) r v.s. g 9 8 E(22)/E(21) 7 6 5 4 3 2 1 0 10 15 20 25 g (degree) 30 35 Meyer-Ter-Vehn, Nucl. Phys. A249, 111 (1975) Target: AZ A-1Z+L p (n) Gating on missing mass spectrum - (0) p g A-1 LZ-1 n g Bp Bn g A Z L High resolution g-ray spectroscopy (K-,-) >>0O Weak decay mostly via non-mesonic in sd-shell hypernuclei A-1 LZ Z=20 Possible sd-shell L hypernuclei via g-ray spectroscopy 34Cl even-even 32S 30P 31P mirror Z 27Si 28Si 26Al 27Al 23Mg 24 Mg 25Mg 26Mg 22Na 19Ne 20Ne 18F Z=9 31S 19F 23Na 21Ne 22Ne 21F 24Na 25Na 39Ca 40Ca 38K 39K 38Ar 35Cl 36Cl 34S 37Cl 39Ar 40Ar 39Cl 36S 30Si Most abundant isotopes (target) ~10% abundance proton decay neutron decay N direct core 18 F Sn (MeV) 9150 Sp (MeV) 5607 19 Ne 23 Mg 24 Mg 11639 13147 16532 6412 7579 11693 25 Mg 26 Al 27 Si 30 P 7331 11366 13312 11320 12064 6307 7464 5595 32 S 34 Cl 39 Ar 15042 11508 6598 8864 5142 10733 38 12074 13289 5143 5764 K 39 Ca Z=20 40Ca Possible sd-shell L hypernuclei 39K via g-ray spectroscopy 35Cl even-even 32S mirror Z 36Cl 37Cl 39Ar 40Ar 39Cl 34S 31P 28Si 27Al 24Mg 25Mg 26Mg 23Na 20Ne 18F Z=9 38Ar 19F 21Ne 22Ne 24Na 30Si Most abundant isotopes (target) ~10% abundance proton decay neutron decay N ev-ev core 18 21 41 22 02 2021） tps 269±24 0.64(4) 340±30 1.04(9) 10Ne8 1887.3 3376.2 3616.4 3576.3 10Ne10 1633.7 4247.7 7833.4 22 12Mg10 1246.3 3308.2 4402 5965 370±13 4.2(15) 24 12Mg10 1368.7 4123 4238 6432.5 432±11 1.97(5) 26 14Si12 1795.9 4446 2783.5 3332.5 356±34 0.62(6) 30 2210.6 N.O 3402.6 324±41 0.242(30) 130±10 0.66(5) 96±21 0.86(20) 20 38 38 16S14 18Ar20 20Ca18 (e2fm4) N.O 2167.5 5349.5 3936.7 3377.5 2206 N.O 3685 3057 Rotational v.s. Vibrational E(4)/E(2) 3.4 3.2 Rotational 24Mg 3 E(4)/E(2) 2.8 38Ca 20Ne 2.6 22Mg 2.4 26Si 38Ar 2.2 Vibrational 2 1.8 18Ne 1.6 1.4 8 10 12 14 16 Z 18 20 22 Excitation enrgy (MeV) 21+, 22+, and 02+ 18(▲) ,20Ne 8 22(▲) ,24Mg 1st 2+ 2nd 2+ 2nd 0+ 6 26Si 4 30S 38Ar 38Ca 2 0 8 10 12 14 Z 16 18 20 b b/bs.p. g 10Ne8 0.694 4.36 r<2 10Ne10 0.727 4.57 17.8o 22 12Mg10 0.58 4.4 21o 24 12Mg10 0.605 4.57 22o 0.446 3.93 r<2 16S14 0.338 3.40 r<2 18Ar20 0.163 1.84 r<2 20Ca18 0.125 1.58 r<2 ev-ev core 18 20 26 14Si12 30 38 38 L hypernuclei shape with self-consistent mean field approach by Tohoku theory group Relativistic mean field & Skyrme HF+BCS Relativistic Mean Field calculations • self-consistent mean field • Exchange of s, r, and between N and L • Potential Energy Surface (PES) of a L hypernucleus with axially symmetric deformation: Eb • Angular momentum not a good quantum number Skyrme Hartree-Fock +BCS Myaing Thi Win et al., submitted to PRC • • • • self-consistent mean field Skyrme-type LN interaction PES of L hypernuclei with triaxial deformation: E(b,g) Angular momentum not good quantum number 24Mg, 24Mg+L L A rough estimate based on energy expansion around the PES minimum (b0,g0) in terms of g E (b 0 ,g ) E (b 0 ,g 0 ) EL E " " L 1 D g 2 2 2 + 4.238MeV 4.11MeV 22 22+ ћ 0 . 97 0+ numerical value ћL 0+ 24Mg 25 LMg Energy difference between core and hypernuclei E 28 L Si ( b , g ) E 28 Si ( b , g ) E 26 L Si ( b , g ) E 26 Si ( b , g ) E 24 L Mg (b , g ) E 24 Mg (b , g ) E 26 L Mg (b , g ) E 26 Mg (b , g ) Towards spherical shape, but through with energetically favorable path in (b,g) plane → g deformation is important in L hypernucleus L as a probe of a core nucleus shape (vacuum) stability in (b,g) plane Effects can be cleanly observed from L hypernucleus with even-even core Rigid No/small changes (Weak coupling limit) Nuclear medium effect on L Soft Large changes (Impurity effect) Property of core nucleus Hyperncuelar g-ray spectroscopy of 25LMg • Mg is the most deformed in the sd-shell • Non-yrast state population → 22+, 02+ • Response of core to L in the sd-shell – Change in the (b, g) plane ? • b softness (g-ray transition ½2+→ ½1+ ) • g softness – Similar shrinkage (no change in b and g) ? • Possible to produce by using natural target Use of an natural Mg target Target DL=1,2 (20>>5°) Abundance DL=0 ( <5°) direct 24Mg 0.79 (0+) 25Mg 0.10 (5/2+) 26Mg (0+) 0.11 L 24 Mg L core 23Mg L 25 Mg L core 24Mg L 26 Mg L core 25Mg 24 LMg> 26 LMg >25LMg n p 23 LMg 22Mg LMg 23Mg 24 LNa 23Na 25 LMg 24Mg LNa> LNa 22Na 24 23 23 25 LNa 25 24Na LMg >24LNa Use of natural Mg target and identification of five L hypernuclei (I) 20>>5 ∩ 5>>0 20>>5 → 5>>0 → 24 LMg 25 LMg 26 LMg 79% 10% 11% 23 LNa 24 23Na(K-,-)→23 LNa LNa Natural Mg 27Al 23Na 27Al(K-,-)→p+26 LMg Use of natural Mg target and identification of five L hypernuclei (II) Use of two targets in one experiment 1. Enriched Mg target run: A • ID of 24LMg, 23LNa 2. Natural Mg target run: B • ID of 25LMg 3. Spectrum subtraction of B-A • ID of 26LMg, 24LNa • gg coincidence is essential → Hyperball-J • gray spectroscopy of five hypernuclear spectroscopy in the transitional mass region in the sd-shell – 25LMg: even-even core 24Mg – Mirror hypernuclei : 24LNa ⇔24LMg – 23LNa: N=Z core – 24LMg and 26LMg: isotope study (neutron dependence) J-PARC E13 experimental setup (K-, - ) reaction @ pK = 1.5 GeV/c Hyperball-J Ge array Compact arrangement Ge detector x32 (full set) 60% relative eff., N-type, Transistor reset type (150MeV/reset) Total photo peak eff. ~6% for 1-MeV γray High modularity Adjustable geometry E13 & E03,07 (X x-ray) Radiation hardness: R&D Mechanical cooling of Ge detector High background: PWO background suppressor High energy deposit and counting rate: Baseline restoration and pile up separation via waveform analysis Half the array shown 電子光理学センターでの作業風景 2010年9月 Single particle energy level h 2 2m D m r 2 2 2 C ( ) l s D( ) l 2 From a text book by Ring and Schuck Nilsson Hamiltonian (deformed S.H.O) Anisotropic HO (axially symmetric) h 2 2m D m 2 (x y ) 2 2 2 m 2 KNnzL] (asymptotic Q.N.) • K: projection of total angular momentum along the symmetry axis • N: HO principal quantum number • nz : number of nodes along the symmetry (quantization) axis • L: orbital angular momentum projection onto the symmetry axis From Table of Isotopes 2 z C ( ) l s D( ) l 2 z 2 Odd-A Core • • • g.s=3/2 23 11(3)Na → g.s=3/2 25Mg 13(5) → g.s=5/2 23Mg 11(3) → Shape driving 24, 25, 26 LMg d3/2 (20>>5) 1/2 1/2 5/2 2S1/2 3/2 d5/2 1/2 K=3/2 K=1/2 3/2[211] 1/2[211] 23Mg K=0 24Mg K=5/2+ K=1/2+ K=1/2+ 1/2[200] 1/2[211] 5/2[202] 25Mg Even-core hypernucleus : 25LMg 7/2, 9/2 5/2,3/2 T=0 24 12Mg12 25 Mg L 5/2, 3/2 Even-even core hypernucleus : 25LMg • 9 LBe (g.s. 0+ ,T=0) – 84Be4 (unbound) – E(4)/E(2)=3.75 • G(4+)=3.5MeV, G(2+)=1.5MeV – B(E2;2+→4+)=45±14(e2fm4) – Ec(2+)-EL(2+)=-9.8keV – 2 • 13 LC – – – – – – 12 • Core: 2412Mg12 (g.s. 0+ ,T=0) – – – – – – Bound (Ex<11.7MeV) E(4)/E(2)=3.1 B(E2)↑=432(11)(e2fm4) b=0.605, b/bs.p.=4.57 g=22o 6 (g.s. 0+ ,T=0) 6C6 E(4)/E(2)=3.17 B(E2)↑=397(e2fm4) b=0.582, b/bs.p.=2.2 E(2+)-EL(2+) ≈-90keV 3 •Measurements of : • DE=E(3/2+)-E(5/2+) •spin-orbit in sd-shell •Radial dependence • DE(21+)=Ec(21+)-EL(21+)→b • DE(22+)=Ec(22+)-EL(22+)→g • EL(41)/EL(21) Mirror hypernuclei: 24LNa & 24LMg K=1/2 K=1/2 1/2[211] 1/2[211] 23 Na 11 12 23 Mg 12 11 K=3/2 K=3/2 3/2[211] 3/2[211] Z=N odd-odd core: 23LNa • Core: 2211Na11 – – 20Ne +p+n 16O++d • Core: 189F9 • g.s. 1+ • Core: 3Li3 • Core: – 4He+p+n – +d • g.s. 1+ • Core: 147N7 – 12C+p+n – 3 + d • g.s. 1+ 11Na11 – 16O+p+n – 4+d • g.s. 3+ K3 6 22 10 5B5 – – 2 + d 8Be+p+n • g.s. 1+ K=0+, T=0 K=0+, T=1 3/2[211] 3/2[211] K=3+, T=0 3/2[211] R.H. Spear et al., PRC 11 742 (1975) Things to do Experimental feasibility studies • Cross section for hyper-fragments (help needed form theory side) • Yield estimates • SKSMinus resolution (larger Z of a target) • Target thickness • Stopping time and DSAM simulation • ……. Summary • L as a probe of ground state (vacuum) of sd-shell nuclei via detection of elementary excitation mode (collective mode) with a Ge detector sensitivity • Importance of triaxial deformation (g) – theoretical prediction by Myaing et al. – detection of 22+ • Use of a natural Mg target experiment at J-PARC – (K-,-) reaction with SKS and Hyperball-J – g-ray spectroscopy of 25LMg • Well deformed even-even core • Experimental feasibility study needed – cross section calculations are appreciated
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