激发能相关的能级密度参数和重核衰变性质

叶 巍

（东南大学物理系 南京 ）

内容

◆ 问题背景

◆ 理论模型

◆ 计算结果和结论

能级密度的重要性

● controlling the statistical decay of excited nuclei

● an crucial input for nucleosynthesis calculations (r-process), reactor science, etc.

Fermi-gas level-density expression

3/22

* *FG rot2

exp 2 aUa(E , J) 2J 1 , U E E (J)

2I 12 U

a

level-density parameter

It is employed in most statistical-model calculations

The level density parameter a is parametrized as:

d( ) [1 )) W / U]a U a （1-exp(-U/ E

d

U :W ::

a smoothed level-density parameter thermal energy

shell correction to the liquid-drop mass 18-20 MeV

E

1. Evaporation process: evaporation spectra

a

R.J.Charity, PRC82,014610(2010), and many other works

To fit energy spectra of evaporated particles, is large at low E* and small at higher E*, suggesting that must be dependent on E*

aa

2. Fission process: cross sections, particle yields

Critical factors that strongly influence the decay

mechanism of heavy nuclei at high energy

include:

A, E*, J, a(U) [af /an], , etc.

Experimental observation of enhanced emission of light particles prior to fission (with respect to predictions from standard statistical models) with increasing excitation energy in fusion-fission reactions. This is due to dissipation effects.

Theoretical Model

dq 1 dS(q,E*) T(t)

dt M dq M

The Langevin equation reads

q is the dimensionless fission coordinate and is definedas half of the distance between the center of mass of the future fission fragments divided by the radius of the compound nucleus. T is temperature, M is inertia parameter and is friction strength

(t) is a time-dependent stochastic variable which satisfies < (t) >=0 and < (t) (t’)> = 2δ(t-t’)

The driving force of the Langevin equation is calculated from the entropy:

E* is the total internal energy of the system, V(q) is potential energy.

deformation-dependent level density parameter

a(q) = a1A + a2 A2/3Bs(q)

where Bs(q) is the dimensionless surface area (for a sphereBs= 1). It is used to calculate af /an.

s(q,E*) 2 a(q)[E* V(q)]

● Evaporation residue cross section ER

Previous works on the role of the parameter af /an in the decay modes of thermal nuclei

B.Lott, et al. PRC 01, adjusting af /an to fit residue cross section data based on a statistical model

af /an changes with fissility

W.Ye, PRC81 (2010) 011603(R)

relativistic heavy-ion collisions vs. fusion reactions CN: (high E*,low L) vs. (low E*,high L)

W.Ye, PRC83 (2011) 044611

● spin distribution of evaporation residue

cross sections ER(L)

W.Ye, NPA853 (2011) 61

● prescission particle yields

role of spin: af /an (L)

Reactions systems

16O+181Ta 197Tl vs. 3,4He+197Au 200,201Tl

Scaling analysis of fission probability of systems 200Tl (right figure) and 201Tl (left figure) based on the standard statistical model

These figures are taken from L.G.Moretto et al., PRL75, 4186 (1995)and Th. Rubehn et al., PRC54, 3062 (1996)

16O+181Ta 197Tl

W.Ye, PRC84 (2011) 034617

Recent work on excitation-energy dependent af /an(E*) and its effects on the decay of hot nuclei

suggested probes: excitation energy at scission

E* = E*sc + V(q) + Ecoll + Eevap (tsc)

Ecoll is the kinetic energy of the collective degrees

of freedom, and Eevap(t) is the energy carried

away by all evaporated particles by the scission

time tsc

picture of fission process

Choose spallation reactions induced by

high energy protons

Models: QMD + SM, L.Ou, Z.X.Li, X.Z.Wu, etc.

BUU + SM, G.C.Yong, W.Zuo

INCL + SM , Belgium

main characteristics:

● the thermal excitation energy of the produced excited nuclei in spallation can reach 1 GeV

● significantly reduce side effects from compression, deformation and high spins. These distortions complicate the description of de-excitation process of excited nuclear systems

W.Ye, PRC85 (2012) 011601(R)

● The sensitivity of E*sc to nuclear friction depends on the af /an (E*).

● Experimentally, to probe information of af /an (E*), populating heavy systems with spallation reactions can significantly lower side effects associated with angular momentum, deformation, etc.

● Applications to spallation-induced reactions and the decay of superheavy nuclei.

Conclusions

Thanks for your attentions

W.Ye, High Energy Phys. Nucl. Phys. 26 (2000) 52

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