Single particle properties of heavy and superheavy nuclei. Aleksander Parkhomenko
Plan Intoduction Intoduction Metod of calculations Metod of calculations Phenomenological formula for α-decay half-lives Phenomenological formula for α-decay half-lives Results Results a) One-quasiparticle excitations a) One-quasiparticle excitations b) Systematic b) Systematic c) α-decay chains c) α-decay chains Conclusions Conclusions
3 Li 11 Na 19 K 37 Rb 1H1H 55 Cs 87 Fr 4 Be 12 Mg 38 Sr 20 Ca 56 Ba 88 Ra 39 Y 21 Sc 57 La * 89 Ac + 40 Zr 22 Ti 72 Hf 41 Nb 23 V 73 Ta 42 Mo 24 Cr 74 W 43 Tc 25 Mn 75 Re 44 Ru 26 Fe 76 Os 45 Rh 27 Co 77 Ir 46 Pd 28 Ni 78 Pt 47 Ag 29 Cu 79 Au 48 Cd 30 Zn 80 Hg 5B5B 5B5B 31 Ga 13 Al 49 In 81 Tl 6C6C 6C6C 32 Ge 14 Si 50 Sn 82 Pb 7N7N 7N7N 33 As 15 P 51 Sb 83 Bi 8O8O 8O8O 34 Se 16 S 52 Te 84 Po 9F9F 9F9F 35 Br 17 Cl 53 I 85 At 10 Ne 18 Ar 36 Kr 54 Xe 2 He 86 Rn 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Es 104 Rf 105 Db 106 Sg 107 Bh 108 Hs 109 Mt 110 Ds 111 Rg 112 Cn Fm 101 Md 102 No 103 Lr 68 Er 69 Tm 70 Yb 71 Lu + Actinides * Lanthanides MENDELEYEV PERIODIC TABLE OF THE ELEMENTS Transactinides 89 Ac Db
ZXNZXN A Z-2 X N-2 A-4 γ Q th Q t,th E p E d α g.s. α
Method of the calculations Yukawa-plus-exponetial model Strutinski shell correction BCS pairing approximation Woods-Saxon potential MacroscopicMicroscopic
The shape of a nucleus Axial symmetric nuclei:
β 3 = β 4 = β 5 = β 6 = β 7 = β 8 =0. β 2 = 0
β 3 = β 4 = β 5 = β 6 = β 7 = β 8 =0. β 2 = 0.2
β 3 = β 4 = β 5 = β 6 = β 7 = β 8 =0. β 2 = 0.3
β 3 = β 4 = β 5 = β 6 = β 7 = β 8 =0. β 2 = 0.4
β 3 = β 5 = β 6 = β 7 = β 8 =0. β 2 = 0.4 β 4 = 0.1
β 3 = β 5 = β 6 = β 7 = β 8 =0. β 2 = 0.4 β 4 = 0.2
β 3 = β 5 = β 7 = β 8 =0. β 2 = 0.4 β 4 = 0.2 β 6 = 0.1
β 3 = β 5 = β 7 =0. β 2 = 0.4 β 4 = 0.2 β 6 = 0.1 β 8 =0.1
Shell efects
One-quasiparticle excitations λnλnλnλn 249 Cf E MeV
One-quasiparticle excitations λnλnλnλn 249 Cf E MeV
Phenomenological formula for α-decay half-lives log 10 T α (Z,N) = a Z (Q α ) -1/2 + b Z + c log 10 T α (Z,N) = a Z (Q α - E p ) -1/2 + b Z + c log 10 T α (Z,N) = (a Z + d) (Q α ) -1/2 + b Z + c Viola-Seaborg formula : for e-e for o-e log 10 T α (Z,N) = a Z (Q α - E n ) -1/2 + b Z + c for e-o log 10 T α (Z,N) = a Z (Q α - E np ) -1/2 + b Z + c for o-o E np = E n + E p E np = E n + E p
Results
Nuclein rmsnpe-e o-e e-o o-o Z = N =
Nuclein rms e-e o-e e-o o-o
Z=93 Ns.p. (teor)s.p. (eksp) 1385[642](5) 1405[642](5+) 1425[642] [642] [642] [642](5+) 1505[642](5-) Z=95 Ns.p. (teor)s.p. (eksp) 1425[523]5(-) 1445[523](5)- 1465[523] [523] [642](5+) 1523[521](5) Z=105 Ns.p. (teor)s.p. (eksp) 1529[624](9+) Theoretical and experimental spins in a ground state
T α exp T α th Q α exp MeV Q α th MeV Q α tr th MeV 271 Ds 1.1 ms 0.39 ms Hs 59 ms 0.25 s Sg 0.31 s 0.93 s Rf 3.1 s 0.59 s
T α exp T α th Q α exp MeV Q α th MeV Q α tr th MeV 269 Ds 179 µs 40 µs Hs 701 µs 4.7 ms Sg 61 ms 96 ms Rf 9.4 s 64 s No 92.4 s 90.8 s
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. Q α exp 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 α exp is taken. Q α th The accuracy of the mentioned above phenomenological formula decreases by a factor of about 4, when theoretical values of Q α th are used. 269 Ds and 271 Ds It is found that description of the 269 Ds and 271 Ds chains data is rather good.