The ground state structure and alpha decay of Hs super- heavy isotopes Junqing Li (Institute of Modern Physics, CAS,Lanzhou) KITPC-CAS Relativistic many-body problems for heavy and superheavy nuclei : Jun 8-Jun 27, 2009

Collaborators Ma Long (Institute of Modern Physics, CAS) Hongfei Zhang (Lanzhou University) Xiaohong Zhou (Institute of Modern Physics, CAS) Zaiguo Gan (Institute of Modern Physics, CAS)

超锕新核素 259 Db 及 265 Bh 在核素图上端部分的位置 —— IMP CAS 265 Bh 0.94 s 9.24  259 Db 0. 5 s 9.47 

INTRODUCTION --About 85 super-heavy nuclei with Z =104–118 (except Z = 117)(14) super heavy elements have been synthesized in experiments. --There is a large gap of unknown isotopes between the neutron deficit super heavies obtained in cold fusion and the heaviest isotopes formed in hot fusion -- The latter isotopes underwent the spontaneous fission before reaching known nuclei. --Hs isotope chain passes through the region, and owns a double magic deformed nucleus 270 Hs, and nuclei 263,264,265,266,267,269,270,275,277 Hs were synthesized. Spontaneous fission 277 Hs, 278 Hs

270 Hs is the unique sub-double magic SHN produced so far. The study of the structures, decay properties, and stabilities of the unknown nuclei in the Hs chain, is useful to give some information as how to synthesize and to detect these nuclei, and at which characters they may connect with the decay chain of upper heavier nuclei.

Reaction mechanism to be studied

II. The model The effective Lagrangian we are using:

Axially symmetric deformation is assumed, the nuclear spinors and meson fields are expanded in an axially deformed harmonic oscillator basis The major shell is chosen for SHN as Nf=Nb=20 for nucleons and mesons, respectively. Pairing effect: BCS. ♠ Two important points for the microscopic study of the pairing interaction are the role of the finite range and of the density dependence A density-dependent delta interaction BCS calculation is carried out

The BCS-type pairing with density-dependent delta function interaction (DDDI) in the relativistic mean field theory Based on the single-particle spectrum calculated with the RMF method, the DDDI is introduced(850MeVfm 3 ): For either neutrons or protons, the pairing matrix elements may be written as: H.F.Zhang,J.Q.Li et al., Euro. Phys. Jour. A30,(2006)

prevent the unrealistic pairing of highly excited states confine the region of influence of the pairing potential to the vicinity of the Fermi surface defining the pairing contribution E pair to the total energy as Cutoff factor State dependent energy gap The particle number condition

IV. Ground state properties of the superheavy nucleus Hs NL-Z2 parameter

Binding energies 262 Hs- 270 Hs 277 HS…. Spontaneous fission …

Alpha-decay energy 277 Hs 268 Hs

The quadrupole deformation in the ground state of Hs nuclei Zhingzhou Ren, et al., Phys. Rev. C66, (2002). N=184 N=162 N=176

The single particle level diagram of nucleus 270 Hs Gap 1.679MeV Gap 1.298Mev

Two-neutron separation energies S 2n of Hs isotopes

The one proton separation energy of Hs isotopes 256 Hs

The level diagram of nucleus 254,256 Hs 2p 100% － 0.35MeV

The improvement of the DDDI pairing p N 256 Hs

Alpha decay half-lives (WKB) The decay barriers are determined in the quasi-molecular shape path within generalized liquid drop model including proximity effects(GLDM) For a deformed nucleus, the macroscopic energy is defined as E = E V + E S + E C + E Rot + E Prox When the colliding nuclei are separated, E V = −15.494[(1 − 1.8I 1 2 )A 1 + (1 − 1.8I 2 2 )A 2 ] MeV, E S = [(1−2.6I 1 2 )A 1 2/3 +(1−2.6I 2 2 )A 2 3/2 ] MeV, E C =0.6e 2 Z 1 2 /R e 2 Z 2 2 /R 2 + e 2 Z 1 Z 2 /r For one body shapes A i, Z i,R i and I i are the masses, charges, radii and relative neutron excesses of the two nuclei

For the alpha emission where the proximity between the two separated alpha and daughter nucleus plays the central role, a very accurate formula is Potential barrier by GLDM against emission of alpha from the mother nucleus. r is the centre-of- mass distance. ZHANG H.F, LI J.Q. et al., Commu. Theo. Phys. Vol. 48, No. 3 (2007) pp. 545–552, PRC74(2006)017304,PRC76(2007)047304

The WKB barrier penetration probability the decay constant of the alpha emitter The assault frequency the reduced mass G.Royer et al., NPA444,477(1985), NPA697,630(2002), ), NPA683,182(2001), JPG26,1149(2000), NPA699,479(2002)

Comparison between experimental alpha-decay half-lives and results obtained with the GLDM, the DDM3Y effective interaction and the VSS formulae.

Alpha-decay half-lives of Hs isotopes using the GLDM and compared with those from the VSS formulae

Half-lives of spontaneous fission C1= ,c2= ,c3= ,c4= The seniority number v is v = 0 for the spontaneous fission of even– even nuclei and v = 2 for spontaneous fission of odd–A nuclei.

The half-lives of spontaneous fission and Alpha-decay of Hs nuclei Open square: spotaneous fission, Open circle: alpha decay

Summary The ground state properties of Hs nuclei was calculated to give an overview to the isotope chain. More stable isotopes are located on the proton abundant side of the chain. The proton drip line nucleus is 256 Hs The most stable unknown Hs nucleus may be 268 Hs In DDDI, the interaction between different paired nucleons is state dependent, the positive states whose wave functions are concentrated in the nuclear region, also contribute to the pairing matrix elements. This results in more reasonable single- particle energy level distributions and nucleon occupation. Therefore the theory by DDDI is generated to be available to describe the properties of nuclei closer to the drip line.

The possible existing Hs nuclides may in the range from A=263 to 274, nuclides beyond the area will undergo spontaneous fission

Alpha-decay can provide very clear signatures of the nuclear species at the beginning of the decay chain, whereas fission does not. Models of alpha-decay properties are therefore highly useful for designing and interpreting experiments that could explore the limits of stability of the heaviest elements. And the GLDM is one of the available method to describe the alpha decay.

Thanks for attention