Correlation between alpha-decay energies of superheavy nuclei J. M. Dong, W. Zuo*, W. Schied, J. Z. Gu Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou,China Institute for Theoretical Physics, Justus-Liebig- University, Giessen, Germany China Institute of Atomic Energy, Beijing, China
Outline 1. Introduction and Motivation 2. Alpha decay energies of SHN 3. Alpha decay half-lives of SHN 4. Summary
Introduction and Motivation Syntheses of superheavy nuclei (SHN) becomes an active and exciting field in modern nuclear physics. Up to now SHN with Z = 104 118 have been synthesized in experiments!
Z=107 112, cold-fusion reactions, GSI, Darmstadt S. Hofmann and G. Munzenberg, Rev. Mod. Phys. 72, 733 (2000). Z = 113 118, hot-fusion evaporation reactions, JINR- FLNR,Dubna Yu. Ts. Oganessian et al., PRC 69, 021601(R) (2004); PRC 70, 064609 (2004); PRC 72, 034611 (2005); PRC 74, 044602 (2006); PRC 76, 011601(R) (2007); PRL 104, 142502 (2010). Other new superheavy nuclides: Z=113, Z=114 L. Stavsetra et al., PRL 103, 132502 (2009) (LBNL, USA) Ch. E. Dullmann et al., PRL 104, 252701 (2010). (GSI Darmstadt) P. A. Ellison et al., PRL 105, 182701 (2010). (LBNL, USA) K. Morita et al., J. Phys. Soc. Jpn. 73, 2593 (2004); J. Phys. Soc. Jpn. 76, 045001 (2007) (RIKEN, Japan).
Alpha-decay properties of heavy nuclei and SHN Alpha-decay is closely related to nuclear structure properties, it may provide useful information on nuclear properties such as ground state energies, shell effects, Alpha decay is the most efficient approach to identify new nucleus via the observation of alpha-decay chain Theoretically, one of the major goals is to predict reliably the half-lives of SHN for the experimental design. It is extremely important and necessary to obtain an accurate theoretical Q value for a reliable half-life prediction
The cluster model B. Buck et al, PRL72(1994)1326; R. R. Xu et al, PLB72(2006)322 C. Xu et al, PRC73(2006)041301 The density-dependent M3Y effective interaction P.R. Chowdhury et al, PRC77(2008)044603; G.Samanta et al, NPA789(2007)142 G. L. Zhang et al, NPA823(2009)16 The generalized liqiud drop model G. Royer et al, NPA730(2004)355; J. M. Dong et al, NPA832(2010)198; H.F. Zhang et al, PRC74(2006)017304; C77(2008)054318 The coupled channel approach D.S. Delion et al, PRC73(2006)014315; S. Peltonen et al, PRC75(2007)054301
The existing microscopic nuclear many-body approaches, such as RMF, SHF, can not achieve a good accuracy to estimate the alpha decay Q values! A new approach to calculate the alpha decay energy with a high accuracy is required!
Magic numbers in superheavy region Model dependent: Macroscopic-microscopic models: Z=114, N=184 Moller and Nix,JPG 20, 1681 (1994); Baran et al., PRC 72, 044310 (2005) Skyrme-Hartree-Fock: Z =124, 126 and N =184 Cwiok et al., NPA 211 (1996); Kruppa et al.,prc 61, 034313 (2000) Relativistic mean field models: Z =120, N =172,184 Bender etal., PRC 60, 034304 (1999);Rutz etal.,prc 56, 238 (1997); Patra etal.,, NPA 117, (1999)
Alpha-decay Q values of superheavy nuclei We proposed a formula to directly calculate the alpha decay energy (Q value) for nuclei with Z 92 and N 140 for the first time based on a liquid drop model: Dong, Zuo, Gu, Wang, Peng, PRC 81, 064309 (2010)
The standard and average deviations for the 154 heavy and superheavy nuclei are: Fig. 1. The deviations between the experimental values and the formula for the 154 nuclei.
On the whole, the formula provides good results for Z=117 isotope chain.
Correlation between alpha-decay energies of neighboring Q values based on the correlation between a nucleus and its neighbors. Basic idea: Using a known Q value to deduce the other ones. 1 Once the decay energy Q 1 of a reference nucleus A Z 1 is known, the Q 2 value of the other nucleus A Z 2 (target nucleus) with the same mass number A can be estimated by: Dong, Zuo, and Scheid, PRL, 107, 012501 (2011)
2 The correlation between the Q values of the nuclei belonging to an isotope chain with a proton number Z is given by 3 The correlation between the Q values of the nuclei belonging to an isotone chain with a neutron number N is given by
4 In general, if one selects ξ=xz+yn and β as variables, the relationship between the Q values of decay can be written as
Since the Q values of the reference nuclei are taken from the experimental measurements in calculations, the agreement suggests that the experimental data themselves are consistent with each other, which indicates that the experimental observations and measurements of the SHN are reliable to a great extent. So, the agreement between the experimental and theoretical values has significant importance.
To confirm the existence of shell gaps positively is not easy but to confirm the nonexistence of shell closures should be much easier! For the eight nuclides of elements 116 and 114 together with the six nuclei with a neutron number N =174 and N =172, the experimental Q values can be reproduced very accurately that confirms Z =114 and N =172 are not shell closures for the presently observed superheavy region experimentally.
Effect of symmetry energy on the isospin dependence of the Q values along an isotope chain of SHN Due to the inclusion of the effect of symmetry energy, the Q values reduce much more rapidly as N increases, and hence a superheavy element becomes longerlived against alpha-decay with increasing N. It is the effect of symmetry energy that primarily enhances the stability against alpha decay with larger neutron number for these synthesized SHN not around shell closures.
Alpha decay half-lives A new approach: estimate the half-life of a nucleus with the help of its neighbors based on some simple formulas. (Based on Royer s formula) (Based on VSS formula) Dong, Zuo, Scheid, NPA, 861, 1 (2011)
The two formulas are found to work very well.
Summary A new idea has been proposed for predicting the Q values of SHN. A simple formula has been got for describing the correlation between the -decay energies of the SHN Our investigation indicates that the reliability of the experimental observations and measurements on these synthesized SHN It is shown that Z=114 and N=172 is not shell closures for the presently observed superheavy region experimentally. Our investigation indicates that the reliability of the experimental observations and measurements on these synthesized SHN The increased stability against alpha-decay for the SHN not around shell closures with larger neutron number, is primarily attributed to the effect of the symmetry energy.
Thanks for your attention!
These two formulas are found to work very well. Applicability of WKB approximation We calculated the barrier penetrability for alpha decay, proton and cluster emission accurately with the recursion formulas by dividing the potential barrier into a sequence of square barriers and the results are compared with those of the WKB approximation.
Classical turning points dividing the potential barrier into a sequence of square barriers We cut off the barrier at a sufficiently large distance of r 2 = 1000 fm.
The wave function u(r) (Ψ(r) = Y lm (θ,ϕ)u(r)/r) of the emitted particle with Q value in these n regions can be written as
The wave function outside of the barrier is given by By using the connection condition of wave function, one can deduce the transmission amplitude and reflection amplitude for the nth square barrier:
and for the j th (j <n) square barrier:
The penetration probability is given by: Relative deviation of penetrability caused by the WKB approximation:
WKB method produces relative deviations by about ( 40) ( 30)% for alpha decay of heavy and superheavy nuclei, ( 40) ( 20)% for proton emission and ( 5) 15% for cluster radioactivity. Also, in consideration of the deviations being nearly constants in each decay mode, indeed, the WKB approximation works well for these decays.