Systematic Study of Survival Probability of Excited Superheavy Nucleus

Transcription

1 Systematic Study of Survival Probability of Excited Superheavy Nucleus Cheng-Jun Xia Supervisor: Bao-Xi Sun Mathematical and Physical Sciences Department, Beijing University of Technology Collaborators: Shan-Gui Zhou, En-Guang Zhao Institute of Theoretical Physics, Chinese Academy of Sciences

2 Outline Introduction 1 Introduction 2 The formula for the survival probability The decay widths 3 Ground-state properties of superheavy nuclei The survival probability 4

3 Outline Introduction 1 Introduction 2 The formula for the survival probability The decay widths 3 Ground-state properties of superheavy nuclei The survival probability 4

4 The stability island Introduction Based on modern nuclear theories, larger shell gaps were predicted at Z = 114, 120, 126 etc., and N = 172, 184 etc., which give an island of long-lived superheavy nuclei.

5 Cold fusion reaction Introduction At GSI, JINR and RIKEN tremendous efforts were made trying to synthesis superheavy nuclei. Superheavy nuclei with Z = were synthesized for the first time in cold fusion reactions by Hofmann et al., with the excitation energy of compound nuclei around MeV.

6 Introduction Calculations done for survival probability There are a lot of calculations done in superheavy region using statistical methods for the survival probability with computer programs GROGIF, HIVAP and other programs. Due to the large ambiguity of fusion probability and nuclear properties for superheavy nuclei, the statistical models used for calculating the survival probability of superheavy elements are far from finished. A. S. Zubov, G. G. Adamian, and N. V. Antonenko Phys. Part. Nuclei, 2009, 40,

7 Motivation Introduction So far most studies about the stability of superheavy nuclei are done for ground-state, less calculations were made on excited superheavy nuclei. The question of how the shell structure affects excited superheavy nuclei is rather intriguing. Due to the prominent role of the deexcitation process of compound nuclei played in cold fusion reactions, it is important to study survival probability for 1n-channel of excited superheavy nuclei with the excitation energy around MeV systematically.

8 Motivation Introduction So far most studies about the stability of superheavy nuclei are done for ground-state, less calculations were made on excited superheavy nuclei. The question of how the shell structure affects excited superheavy nuclei is rather intriguing. Due to the prominent role of the deexcitation process of compound nuclei played in cold fusion reactions, it is important to study survival probability for 1n-channel of excited superheavy nuclei with the excitation energy around MeV systematically.

9 Motivation Introduction So far most studies about the stability of superheavy nuclei are done for ground-state, less calculations were made on excited superheavy nuclei. The question of how the shell structure affects excited superheavy nuclei is rather intriguing. Due to the prominent role of the deexcitation process of compound nuclei played in cold fusion reactions, it is important to study survival probability for 1n-channel of excited superheavy nuclei with the excitation energy around MeV systematically.

10 Outline Introduction The formula for the survival probability The decay widths 1 Introduction 2 The formula for the survival probability The decay widths 3 Ground-state properties of superheavy nuclei The survival probability 4

11 Introduction The formula for the survival probability The formula for the survival probability The decay widths Since we only care about the 1n-channel in our calculation, the survival probability can be simplified like this: Survival probability The survival probability for 1n-channel, W sur(e, J) = P 1n (E Γ n(e, J), J) γ Γγ(E, J), where P 1n (E, J) = exp[ (E S n 2T ) 2 2σ 2 ] is the realization probability for 1n-emission. We take T = aE, σ = 2.2 MeV in our calculation and a is the level density 2a parameter of the nucleus.

12 Introduction The formula for the survival probability The decay widths The decay widths for particle emission and fission Decay widths For particle emission, E Sβ Γ β (E 1/a δ 2i β + 1, J) = 0 π 2 2 m βε β σ β (ε β ) ρ(e S β ε β, J) ρ(e dε β., J) For fission, Γ f (E ; J) = 1 E Bf 1/a δ ρ s.d. (E B f ε f ; J)T f (ε f )dε f. 2πρ s.d. (E ; J) B f Here we subtract [1/a + δ] in the upper limit of the integral because of the irregular behavior of the level density ρ(e, J) when E < 1/a + δ, and σ β (ε β ) is the absorption cross section for the particle. The level density is adopted from Fermi-gas model. Z. Q. Feng, G. M. Jin, F. Fu and J. Q. Li Nucl. Phys. A, 2006, 771, 50 67

13 The fission barrier Introduction The formula for the survival probability The decay widths The fission barrier used here includes the washing out effect of shell effects with the excitation energy. Fission barrier The fission barrier, B f (E ) = Bf DM + Bf M exp( E 2 /E D ) ( 2 )J(J + 1), 2J g.s. 2J s.d. where E D = 5.48A1/ /A 1/3. The momentum of inertia, J g.s.;s.d. = k 2 5 MR2 (1 + β g.s.;s.d. 2 /3). The macroscopic part of the fission barrier Bf DM is calculated using the formula proposed by Dahlinger et al, and the microscopic part Bf M = E mic, where E mic is the shell correction energy calculated in FRDM by Möller et al.

14 Outline Introduction Ground-state properties of superheavy nuclei The survival probability 1 Introduction 2 The formula for the survival probability The decay widths 3 Ground-state properties of superheavy nuclei The survival probability 4

15 Introduction Ground-state properties of superheavy nuclei The survival probability Ground-state properties of superheavy nuclei Nuclear characteristics The nuclear characteristics (particle separation energy S β, shell correction energy E mic ) from the results of finite-range droplet model (FRDM) are adopted here as our input parameters for calculating the survival probability, which predicted the nucleus with Z = 114, N = 184 to be the centre of the island of stability. P. Möller, J. R. Nix, W. D. Myers and W. J. Swiatecki At. Data & Nucl. Data Tables., 1995, 59,

16 Z The fission barrier Introduction Ground-state properties of superheavy nuclei The survival probability B f (M e V ) N Fission barrier The fission barriers are mainly decided by the shell effect in superheavy area. The island of fission barrier is the main reason for the existence of the island of stability.

17 Introduction Ground-state properties of superheavy nuclei The survival probability The survival probability of the nucleus with dependence of excitation energy W (1 1 4,2 9 8 ) s u r Here is a typical example of the behavior of the survival probability with the dependence of excitation energy in 1n-channel. W s u r Definition of optimum excitation energy E * (M e V ) The optimum excitation energy is defined at where the survival probability is the biggest in 1n-channel, which is 7.3 MeV here.

18 Z The survival probability Introduction Ground-state properties of superheavy nuclei The survival probability W s u rv The survival probability at optimum excitation energy There are three major stability islands with higher survival probability. The survival probability of the odd nuclei is systematically higher than the neighboring even-even nuclei. The neutron rich islands may not be as stable as the other two. N

19 Outline Introduction 1 Introduction 2 The formula for the survival probability The decay widths 3 Ground-state properties of superheavy nuclei The survival probability 4

20 Introduction Survival probability We present theoretical estimates for the survival probability in 1n-channel (with J = 0) of 1845 excited superheavy elements from Z = 100 to Z = 134 using statistical methods. 1 Three major islands emerged with higher survival probability. 2 The stability island still preserved when the nucleus in superheavy area is excited with the centre to be around Z = 114, N = The existence of neutron rich island is induced by low neutron separation energy in neutron rich area. 4 The survival probability of the odd nuclei is systematically higher than the neighboring even-even nuclei. 5 The connection of shell correction, fission barrier and survival probability is clearly shown graphicly.

21 Introduction Decay widths The decay branching ratios and widths are given. 1 The branching ratios for charged particle emission are very small, which confirm the statement that the charged particle emission can be omitted during the deexcitation process of excited superheavy nucleus. 2 In the neutron-rich area nuclei with very low neutron separation energy become very unstable against neutron emission.

22 Problems Introduction We still have limited theoretical data concerns the fission barriers and the ground-state properties of superheavy nuclei let along the experimental results. A great deal of assumptions and approximations were made in our calculation here, more refined calculations are required.

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