1. ON E0 TRANSITIONS IN HEAVY EVEN – EVEN NUCLEI VLADIMIR GARISTOV, A. GEORGIEVA* Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria, garistov@mail.ru * Institute of Solid Physics, Sofia, Bulgaria Sofia 2015 This work was partially supported by the Bulgarian National Foundation for Scientific Research under Grant Number № ДФНИ-Е02/6

2. Scenario: To make You familiar with our approaches for the classification of the excited states energies with J p = 0 + in the same nucleus Parabolic distribution and classification of the excited states within the Interacting Vector Bosons Model (IVBM) : energies with the same set of model parameters and also the estimation of the E0 transition probabilities in this two approaches. Sofia 2015

4. Distribution function n

5. Редкоземельные элементы: 58 Ce 60 Nd 62 Sm 64 Gd 66 Dy 68 Er 70 Yb Актиниды: 90 Th 92 U 94 Pu 96 Cm 98 Cf 100 Fm 102 No Exploration of the energy distributions of excited states with arbitrary J p in the same nucleus Parabolic distribution E n = a n – b n 2 +C In the case of J p = 0 + C = 0

6. Dy isotopes E n = a n – b n 2

8. 114 Cd

9. 118 Sn

10. 132 Ba

11. 156 Gd

12. 2.9460 0(+),1,2,3+ 3.1789 0(+),1,2,3(+) 3.2120 0(+),1,2,3+ 3.3476 0(+),1,2,3+ 3.5050 0(+),1,2,3+ 3.5425 (0+),1,2,3,4(+) 3.5590 0(+),1,2,3(+) 3.5795 0+,1,2,3,4+ 3.6500 (0+),1,2,3,4(+) 3.6985 (0+),1,2,3,4(+) 3.8485 0(+),1,2,3+ 3.8595 0(+),1,2,3(+) 3.99254 0(+),1,2,3+ 4.0086 0(+),1,2,3(+) 136 Ba D = 1.46471 KeV 0 + ?? Ambiguous spins data

13. We also had a chance to drag into this affair the experimentalists from JINR - Dubna: Adam J, Solnyshkin A.A. Islamov T.A. and ITEP – Moscow: Bogachenko D.D., Egorov O.K., Kolesnikov V.V.,Silaev V.I.. As a result – trusting in our predictions the two new 0 + states in 160 Dy has been observed.

14. Time to blow ones own trumpet

16. 0.00+0+ 2+2+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 0+0+ 2+2+ 2+2+ 2503.8 2297.5 1952.3 1708.2 1456.7 1280.0 703.0 681.3 86.8 K1271.0 I K =0.024 g1594.5 Ig=0.8 g1822.5 Ig=0.24 g594.5 g 616.2 K681.3 I K =0.024 K703 I K =0.086 160 Dy Observed transitions in 160 Dy Sofia 2015 Adam J et.al. (2014) Bulg. J. Phys.} 41, 10–23.

17. Why did we impose the restrictions - positive and integer classification parameter? the application of the group theory in nuclear physics To draw attention of theoreticians that work with Sofia 2015 Ana Georgieva, Michael Ivanov, Svetla Drenska, Nikolay Minkov, Huben Ganev, Kalin Drumev We found a suitable approach - Interacting Vector Bosons Model (IVBM)

18. Philosophy of this approach Georgieva A I, Raychev P and Roussev R, (1982) J. Phys. G: Nucl. Phys., 8, 1377. Ganev H G, Garistov V P, Georgieva A I and Draayer J P, (2004), Phys. Rev., C70, 054317. Solnyshkin A A, Garistov V P, Georgieva A, Ganev H and Burov V V (2005) Phys. Rev., C72, 064321. Georgieva, A.I., Ganev, H.G., Draayer, J.P and Garistov V.P., Physics of Elementary Particles and Atomic Nuclei, 40, 461 (2009). Garistov V P, Georgieva A I and Shneidman T M, (2013), Bulg. J. Phys., 40, 1–16 Adam J et.al. (2014) Bulg. J. Phys.} 41, 10–23. Interacting Vector Bosons Model (IVBM) Peter Raychev, Roussy Roussev, Ana Georgieva

21. sp(4,R) and su(3) algebras are related through the u(2)  su(2)  u(1) algebra of the pseudo spin T, which is the same in both chains.

22. λ=2T μ=N/2 -T

23. To make the analysis of the structure of low lying excited states we need the description of several rotational bands. Classification of the excited states energies with arbitrary J p within the same set of model parameters and also the estimation of the transition probabilities IVBM confirmed it’s advantages in description of the rotational bands energies. To bind our new clssification to the predetermined parameters obtained from the description of rotational bands’ energies

24. Band’s energies Here K and N 0 marks the belonging to rotational band type

25. Band’s heads energies Here N 0 specifies the corresponding rotational band head’s type

27. β - type band’s heads energies Here N 0 specifies the position of rotational band head N 0 = 2,4, 6,8, … Rotational β - band energies

29. IVBM

31. Band’s head energy

32. Garistov’s approach IVBM

34. Band’s head energy

35. 160 Gd From b band IVBM 0 + states energies

38. Band’s head energy Here N 0 specifies the corresponding rotational band head’s type and for J p = 0 + N 0 = 2,4, 6,8, …

39. IVBM Parabola

41. Band’s head energy Here N 0 specifies the corresponding rotational band head’s type and for J p = 0 + N 0 = 2,4, 6,8, …

42. 160 Gd From b band IVBM 0 + states energies

44. Band’s head energy

46. 168 Yb

47. a = 0.485916 b = 0.0275156 D=0.002 MeV 0+0+ E 0+ = a n – b n 2 IVBM 0 + states energy distribution

53. Thank You !

55. Band’s heads energies Here N 0 specifies the corresponding rotational band head’s type

60. beta 2 + gamma 2 + 1-1- 3-3-

63. beta 2 + gamma 2 +

64. Dy isotopes E n = a n – b n 2 +c

65. 160 Gd From b band From g band IVBM 2 + states energies

66. 156 Gd From b band From g band IVBM 2 + states energies

67. 152 Gd 2 + states

69. gamma beta

70. 2→0 4→0 6→0 8→0 2→0 4→2 6→4 D N=N DN=2 r 2 /2000

71. 2 + gamma 2 + beta

77. N 0 =10 N 0 =4 N 0 =0

78. E 2+ = a n – b n 2 + c 168 Yb a = 0.55132 b = 0.0266917 c = - 0.450742 D = 0.002 MeV 2+2+ Ambiguous Spin Data

79. beta 2 + gamma 2 +

80. beta 2 + gamma 2 + 1-1- 3-3-

81. 168 Yb b type 2 + states g type 2 + states Ground band 2 + state E 2+ = a n – b n 2 + c 168 Yb a = 0.55132 b = 0.0266917 c = - 0.450742 D = 0.002 MeV 2+2+ Ambiguous Spin Data

82. sp(12,R)  sp(4,R)  so(3)   ∩ u(6)  u(2)  su(3) sp(4,R) and su(3) algebras are related through the u(2)  su(2)  u(1) algebra of the pseudo spin T, which is the same in both chains. This permits an investigation of the behavior of low lying collective states with the same angular momentum L in respect to the number of excitations N that build these states. mutual complementarity of sp(4,R) with the so(3)