g -ray spectroscopy of (well deformed) sd -shell hypernuclei

1. 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

2. 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)

3. L Coupling of L to nuclear collectivity Low-lying elementary excitation mode Symmetry of nuclear vacuum SSB Collective motion Accessible via g-ray spectroscopy with a few keV sensitivity Shape of a nucleus at the ground state

4. Single particle excitation v.s. collective excitation From E.S. Paul, Univ. Liverpool, U.K.

5. Spontaneous deformation (SSB of rotational invariance) 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) H = Hintrinsic+Hcollective Symmetry restoring term Rotation/Vibration Deformed potential (Nilsson potential)

6. Shape parameterization Axially symmetric quadrupole Axially symmetric octapole l=2 a20≠0, a2±1=a2±2=0 l=3 a30≠0, a3±1,2,3 =0 a20≠0, a2±1,2 =0

7. Quadrupole deformation (l=2) • Five parameters (a2,0,±1,±2) • →Euler angles + a20, a22 • (body-fixed frame axes are chosen to coincide with principal axes) • Further parameterization of a20, a22 • b2: asphericity • (deviation from spherical shape) • g: triaxiality • (difference in length along principal axis) nuclear surface described by (b2, g)

8. Non collective oblate (b, g=60°) triaxial g spherical b Collective prolate (0,0) (b, g=0°)

9. Classical collective Hamiltonian of Bohr-Mottelson for quadrupole deformation vibration moment of inertia rotation potential Axial rotation: 1D Triaxial rotation: 3D

10. Axially symmetric shape Z (laboratory fixed) M 3 (body-fixed, axis of symmetry) K K: projection of total angular momentum I on the symmetry axis →a good quantum number

11. 42+ E(41+)/E(21+) 31+ 43+ 22+ 23+ g-band 02+ b-band Spectra of a deformed even-even nucleus (collective excitation mode) 41+ g 21+ vibrational v.s. rotational 0+ K=0, nb=1, ng=0 b2, J K=2, nb=0, ng=1 K=0, nb=0, ng=0

12. Collective excitation (Lab. frame)E(4+)/E(2+): Rotational v.s Vibrational • Rotational (deformed): • E(4)/E(2)=10/3 • Vibrational (spherical): • E(4)/E(2)=2 3.1 2.1

13. b , Q0 (intrinsic frame)and 21+, B(E2)(Lab. frame) Intrinsic Quadrupole moment: Experimentally b:

14. 22+ and experimental estimate of g A rigid triaxial rotor model Davydov and Filippov, Nucl. Phys. 8, 237 (1958) Meyer-Ter-Vehn, Nucl. Phys. A249, 111 (1975)

15. Target: AZ A-1Z+L Gating on missing mass spectrum p (n) p- (p0) A-1LZ-1 g High resolution g-ray spectroscopy A-1LZ p n g Bp Bn g ALZ (K-,p-) qp >>0O Weak decay mostly via non-mesonic in sd-shell hypernuclei

16. even-even mirror Possible sd-shell L hypernuclei via g-ray spectroscopy 39Ca 40Ca Z=20 38K 39K 38Ar 39Ar 40Ar 37Cl 34Cl 35Cl 36Cl 39Cl 31S 34S 36S 32S Z 30P 31P 28Si 30Si 27Si 26Al 27Al Most abundant isotopes (target) 26Mg 23Mg 24Mg 25Mg ~10% abundance 23Na 24Na 25Na 22Na proton decay 20Ne 22Ne 19Ne 21Ne neutron decay 18F 19F 21F N Z=9

18. even-even mirror Possible sd-shell L hypernuclei via g-ray spectroscopy 40Ca Z=20 39K 38Ar 39Ar 40Ar 37Cl 35Cl 36Cl 39Cl 34S 32S Z 31P 28Si 30Si 27Al Most abundant isotopes (target) 26Mg 24Mg 25Mg ~10% abundance 23Na 24Na proton decay 20Ne 22Ne 21Ne neutron decay 18F 19F N Z=9

19. (e2fm4)

20. Rotational 24Mg 38Ca 20Ne 26Si 38Ar 22Mg Vibrational 18Ne Rotational v.s. Vibrational

21. 18(▲) ,20Ne 22(▲) ,24Mg 26Si 30S 38Ar 38Ca 21+, 22+, and 02+

23. L hypernuclei shape with self-consistent mean field approach by Tohoku theory group Relativistic mean field & Skyrme HF+BCS

24. Relativistic Mean Field calculations • self-consistent mean field • Exchange of s, r, and w between N and L • Potential Energy Surface (PES) of a L hypernucleus with axially symmetric deformation: E(b) • Angular momentum not a good quantum number

25. 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

26. 4.238MeV 4.11MeV 22+ 22+ ћw ћwL 0+ 0+ 24Mg 25LMg A rough estimate based on energy expansion around the PES minimum (b0,g0) in terms of g numerical value

27. Energy difference between core and hypernuclei Towards spherical shape, but through with energetically favorable path in (b,g) plane　→　g deformation is important in L hypernucleus

28. 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 Soft Large changes (Weak coupling limit) (Impurity effect) Nuclear medium effect on L Property of core nucleus

29. 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 Hyperncuelar g-ray spectroscopy of 25LMg

30. Use of an natural Mg target 24LMg> 26LMg >25LMg 23LNa> 25LMg >24LNa

31. 26LMg 25LMg 24LMg 11% 10% 79% 23LNa 24LNa Use of natural Mg target and identification of five L hypernuclei (I) Natural Mg 27Al 23Na 20>q>5 ∩ 5>q>0 27Al(K-,p-)→p+26LMg 20>q>5 → 5>q>0 → 23Na(K-,p-)→23LNa

32. Use of natural Mg target and identification of five L hypernuclei (II) Use of two targets in one experiment • Enriched Mg target run: A • ID of 24LMg, 23LNa • Natural Mg target run: B • ID of 25LMg • Spectrum subtraction of B-A • ID of 26LMg, 24LNa

33. g-g coincidence is essential → Hyperball-J • g-ray 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)

34. J-PARC E13 experimental setup (K-, p- ) reaction @ pK = 1.5 GeV/c

35. 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) Half the array shown • Radiation hardness: • 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 R&D

36. 電子光理学センターでの作業風景 2010年9月

37. Single particle energy level From a text book by Ring and Schuck

38. Nilsson Hamiltonian (deformed S.H.O) Anisotropic HO (axially symmetric) Kp[NnzL] (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

39. Odd-A Core • 23Mg11(3) → g.s=3/2 • 2311(3)Na→ g.s=3/2 • 25Mg13(5) → g.s=5/2 Shape driving From Table of Isotope

40. 24, 25, 26LMg(20>q>5) d3/2 1/2 1/2 2S1/2 5/2 3/2 d5/2 1/2 K=1/2+ K=3/2 K=1/2 K=5/2+ K=1/2+ K=0 3/2[211] 1/2[211] 1/2[200] 1/2[211] 5/2[202] 23Mg 24Mg 25Mg

41. Even-core hypernucleus : 25LMg 5/2, 3/2 7/2, 9/2 5/2,3/2 T=0 2412Mg12 25LMg

42. 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 6a 9LBe (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 2a 13LC (g.s. 0+ ,T=0) 126C6 E(4)/E(2)=3.17 B(E2)↑=397(e2fm4) b=0.582, b/bs.p.=2.2 E(2+)-EL(2+) ≈-90keV 3a Even-even core hypernucleus : 25LMg • 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)

43. Mirror hypernuclei: 24LNa & 24LMg K=1/2 K=1/2 1/2[211] 1/2[211] 2311Na12 2312Mg11 K=3/2 K=3/2 3/2[211] 3/2[211]

44. Core: 63Li3 4He+p+n a + d g.s. 1+ Z=N odd-odd core: 23LNa • Core: 2211Na11 • 20Ne +p+n • 16O+a+d • g.s. 3+ Kp=3+ • Core: 189F9 • 16O+p+n • 4a+d • g.s. 1+ 2211Na11 K=0+, T=1 K=0+, T=0 • Core: 105B5 • 8Be+p+n • 2a + d • g.s. 1+ 3/2[211] 3/2[211] K=3+, T=0 3/2[211] • Core: 147N7 • 12C+p+n • 3a + d • g.s. 1+ R.H. Spear et al., PRC 11 742 (1975)

45. 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 • …….

46. 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-,p-) 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