Outline: 1. Brief review of alpha cluster decay in chart of nuclides

1. Alpha Cluster Formation and Decay in the Quartetting Wave Function Approach Chang Xu School of Physics, Nanjing University, China Outline: 1. Brief review of alpha cluster decay in chart of nuclides 2. Quartetting wave function approach for alpha emitters 3. Symmetry energy constrained by nuclear particle decay 4. Short summary

2. Brief review of alpha decay in chart of nuclides Superheavy island Light island Doubly magic:100Sn Heavy nuclei Doubly magic: 208Pb Yellow color: alpha decay

3. Alpha cluster formation in 104Te 104Te

4. N=Z line

5. University of Tennessee

6. The Fastest Alpha Emitter “Tellurium-104 is now also the fastest known alpha emitter—though this finding is more fun than fundamental. ”

7. 2018:104Te <18ns (experiment)

10. Alpha cluster formation and decay in 212Po Spherical Doubly magic Only one decay channel Accurate experimental data …… Microscopic calculation of alpha cluster formation and decay in 212Po

11. 1998 2006

12. Alpha cluster formation and decay ——Quartetting wave function approach 1. Quantum 5-body problem (2p+2n+core) 2. Subdivide the W.F into an intrinsic part and a c.o.m part

13. Alpha cluster formation and decay ——Quartetting wave function approach 3. Intrinsic bound-state W. F. transforms at critical density into an unbound 4 nucleon shell-model state Pauli blocking Surface Region Inner Region

14. Alpha cluster formation and decay ——Quartetting wave function approach 4. First-principle approach to nuclear many-body system: several approximations performed to make the approach practicable 5. Alpha cluster preformation, pre-factor and penetration probability simultaneously calculated

15. Four-nucleon w.f. is subdivided in the c.m. part and the intrinsic part Potential A: Thomas-Fermi model for the core region. Potential B: Discrete energy level structure of the core nucleus.

17. c.m. wavefunction

18. Experimental data: Qa and Ta (well measured) c and d fitted to Qa and Ta Preformation probabilities are obtained for each nucleus shell effect: further improments describing a short-range repulsion (c) and a long-range attraction (d); S denotes the nucleon-nucleon distance.

19. Comparison of alpha cluster formation between 210Po and 212Po

20. Alpha cluster preformation probabilities Daughter nuclei: N=126 isotones Experimental data: Qa and Ta (well measured) c and d fitted to Qa and Ta Preformation probabilities are obtained for each nucleus shell effect: important describing a short-range repulsion (c) and a long-range attraction (d); S denotes the nucleon-nucleon distance.

21. Alpha cluster formation and decay ——Quartetting wave function approach preliminary results

22. Effective c.o.m potential for 102Sn, 102Te, and 104Te

23. Effective c.o.m potential for 210Pb, 210Po, and 212Po

24. Effective c.o.m wave function for 102Sn, 102Te, and 104Te

25. Effective c.o.m wave function for 210Pb, 210Po, and 212Po

26. Alpha cluster formation and decay in 104Te, 210Pb, 210Po, and 212Po preliminary results

27. Alpha cluster formation and decay in superheavy nuclei

28. Symmetry energy constrained by nuclear particle decay Symmetry energy Density slope

29. The symmetry energy can be characterized by the Esym(ρ0) and its slope parameter L(ρ0) Isospin effect in nuclear decay—symmetry energy • Using the Hugenholtz–Van Hove (HVH) theorem • N. M. Hugenholtz and L. Van Hove, Physica 24, 363 (1958) The single-particle potential of proton and neutron: Un and Up

30. The HVH theorem

31. Decomposition of symmetry energy and its density slope Lane potential isoscalar isovector Derivative of density Derivative of momentum at 0 Xu et. al, Phys. Rev. C 81, 044603 (2010) ; Nucl. Phys. A 865, 1 (2011)

32. Extracting symmetry energy and its density slope Cluster formation

33. Symmetry energy from optical potential Systematics based on world data accumulated since 1969: Single particle energy levels from pick-up and stripping reaction Neutron and proton scattering on the same target at about the same energy Proton scattering on isotopes of the same element (p,n) charge exchange reactions L(0) = 52.722.5 MeV Esym= 31.34.5 MeV

34. Symmetry energy from radioactivity data Proton emitters: 208Pb Cluster emitters: correlation Esym Spherical Large asymmetry δ

35. (I) Symmetry energy from proton radioactivity • L(ρ0) increases with the increasing neutron skin thickness S for each proton emitter • The upper limit 59.0 MeV and the lower limit 44.6 MeV are taken into account in the error bar of S Proton radioactivity: 19 emitters Esym= 29.3 MeV L=51.8 MeV

36. (I) Symmetry energy from proton radioactivity The uncertainty in the spectroscopic factor does notaffect the value of L(ρ0) significantly

37. (II) Symmetry energy from cluster radioactivity Cluster radioactivity: 22 emitters Esym= 30.4 MeV L= 57.2 MeV

38. (III) Symmetry energy from double beta decay energy A is invariable for the nuclei (A, Z) and (A, Z + 2), contribution from volume and surface terms are neglected Contribution from the pairing term has been removed Candidate nuclei are carefully chosen under several conditions:

39. (III) Symmetry energy from double beta decay energy Double beta decay energy: totally 449 data Esym = 29.3 MeV Esym4 = 3.6 MeV

40. Constrains of symmetry energy Decay data: (1)majority of nuclei (2) close to drip lines (3) large isospin symmetry (4) accurate data Phys. Rev. C 97, 051302 (2018)   Phys. Rev. C 96, 044331 (2017)  Phys. Rev. C 94, 044322 (2016) Phys. Rev. C 92, 024301 (2015)  Phys. Rev. C 90, 064310 (2014) 

41. Short summary 1. Alpha decay: an important problem with renewed interest • Light island (doubly magic 100Sn) • doubly magic 208Pb • Superheavy island (next doubly magic nucleus) 2. Recent calculations on alpha emitters around Z=50,Z=82, N=126 regions and superheavy nuclei 3. A quartetting wave function approach for alpha cluster formation and decay: derivative term neglected, local approximation for the effective c.o. m. potential…… 4. Esym from cluster, proton, and double beta decay

42. Thanks! Collaborators : Z. Ren, G. Roepke, P. Schuck, A. Tohsaki, Y. Funaki, T. Yamada, H. Horiuchi, B. Zhou, M. J. Lyu, Bao-An Li, L. W. Chen, T. Myo

44. Alpha cluster formation and decay ——Quartetting wave function approach Quartetting wave function C.o.m motion equation of the quartet

45. Tcal/Texp alpha cluster preformation systematics 210Po 212Po N=126 Po isotopes

46. Neutron shell proton shell Case I alpha cluster preformation Z=82 Case II N=126

47. Extracting symmetry energy from decay data Constrain both the symmetry energy and its density slope by radioactivity data Phys. Rev. C 97, 051302 (2018)   Phys. Rev. C 96, 044331 (2017)  Phys. Rev. C 94, 044322 (2016) Phys. Rev. C 92, 024301 (2015)  Phys. Rev. C 90, 064310 (2014) 

48. (III) Symmetry energy from double beta decay energy Double beta decay energy: totally 449 data

49. (I) Symmetry energy from proton radioactivity As an example • Effect of deformation on L(ρ0): increase with the neutron skin thickness S • Deformation effect: limited for small S