Single particle properties of heavy and superheavy nuclei.

1. Single particle properties of heavy and superheavy nuclei. Aleksander Parkhomenko

2. Plan • Intoduction • Metod of calculations • Phenomenological formula for α-decay half-lives • Results a) One-quasiparticle excitations b) Systematic c) α-decay chains • Conclusions

3. MENDELEYEV PERIODIC TABLE OF THE ELEMENTS 1H 2He 3Li 4Be 5B 6C 7N 8O 9F 10Ne 11Na 12Mg 13Al 14Si 15P 16S 17Cl 18Ar 19K 20Ca 21Sc 22Ti 23V 24Cr 25Mn 26Fe 27Co 28Ni 29Cu 30Zn 31Ga 32Ge 33As 34Se 35Br 36Kr 37Rb 38Sr 39Y 40Zr 41Nb 42Mo 43Tc 44Ru 45Rh 46Pd 47Ag 48Cd 49In 50Sn 51Sb 52Te 53I 54Xe 105Db 55Cs 56Ba 57La* 72Hf 73Ta 74W 75Re 76Os 77Ir 78Pt 79Au 80Hg 81Tl 82Pb 83Bi 84Po 85At 86Rn 89Ac+ 87Fr 88Ra 89Ac+ 104Rf 105Db 106Sg 107Bh 108Hs 109Mt 110Ds 111Rg 112Cn 113113 114114 115115 116116 118118 Transactinides 90Th 91Pa 92U 93Np 94Pu 95Am 96Cm 97Bk 98Cf 99Es 100Fm 101Md 102No 103Lr +Actinides 58Ce 59Pr 60Nd 61Pm 62Sm 63Eu 64Gd 65Tb 66Dy 67Ho 68Er 69Tm 70Yb 71Lu *Lanthanides

4. ZXN A E p Z-2XN-2 A-4 γ Qt,th α g.s. E d Qth α g.s.

5. Method of the calculations Macroscopic Microscopic Yukawa-plus-exponetial model Strutinski shell correction BCS pairing approximation Woods-Saxon potential

6. The shape of a nucleus Axial symmetric nuclei:

7. β2= 0 β3= β4= β5= β6= β7= β8=0.

8. β2= 0.2 β3= β4= β5= β6= β7= β8=0.

9. β2= 0.3 β3= β4= β5= β6= β7= β8=0.

10. β2= 0.4 β3= β4= β5= β6= β7= β8=0.

11. β2= 0.4 β4= 0.1 β3= β5= β6= β7= β8=0.

12. β2= 0.4 β4= 0.2 β3= β5= β6= β7= β8=0.

13. β2= 0.4 β4= 0.2 β6= 0.1 β3= β5= β7= β8=0.

14. β2= 0.4 β4= 0.2 β6= 0.1 β8 =0.1 β3= β5= β7=0.

15. 249Cf151 E MeV -6.0 λn One-quasiparticle excitations -8.0

16. 249Cf151 -6.0 λn -8.0 One-quasiparticle excitations E MeV

17. Phenomenological formula for α-decay half-lives Viola-Seaborg formula : log10Tα(Z,N) = a Z (Qα )-1/2 + b Z + c log10Tα(Z,N) = (a Z + d) (Qα )-1/2 + b Z + c for e-e log10Tα(Z,N) = a Z (Qα - Ep)-1/2 + b Z + c for o-e log10Tα(Z,N) = a Z (Qα - En)-1/2 + b Z + c for e-o log10Tα(Z,N) = a Z (Qα - Enp)-1/2 + b Z + c for o-o Enp = En + Ep

18. Results

19. Z = 84-110 N = 128-171

20. Z = 84-110 N = 128-171

27. Theoretical and experimental spins in a ground state

32. Summary • Quantum characteristics of most experimentally known ground states of analyzed here odd-A nuclei (in 24 of 38 cases for proton-odd and in 23 for 34 cases for neutron-odd nuclei) are reproduced by the calculations. • Energy of known lowest nucleon excited states are reproduced by the applied model within an average accuracy of about 200 keV. • Sensitivity of single-particle excitation energies to changes of such a quantity as the equilibrium deformation of a nucleus is rather large. • A new, simple phenomenological formula for description of α-decay half-lives of heaviest e-e, o-e, e-o and o-o nuclei uses only 5 adjustable parameters. The formula allows one to describe Texp of 61 e-e nuclei roughly within a factor of 1.3, 45 o-e nuclei within a factor of 2.1, 55 e-o nuclei within a factor of 3.2 and 40 o-o nuclei within a factor of 4.0, on the average, when Q αexpis taken. • The accuracy of the mentioned above phenomenological formula decreases by a factor of about 4, when theoretical values of Q αthare used. • It is found that description of the 269Ds and 271Ds chains data is rather good.