Spin dependence of the modified Kramers width of nuclear fission

Abstract

A statistical model calculation for the decay of a compound nucleus is presented where the compound nuclear spin dependence of the Kramers modified fission width is included. Specifically, the spin dependences of the frequencies of the harmonic oscillator potentials osculating the rotating liquid-drop model potential at equilibrium and saddle regions are considered. Results for the 16 O+ 208 Pb system show that the energy dependence of the dissipation strength extracted from fitting experimental data is substantially reduced when the spin dependence of the frequencies is properly taken into account.During the last two decades, experimental and theoretical investigations of heavy ion induced fusion-fission reactions at beam energies above Coulomb barriers have made significant contributions to the understanding of the nuclear bulk dynamics at high excitation energies. Specifically, careful analyses of experimental values of multiplicities of pre-scission light particles (mainly neutrons and γ 's) [1-8], evaporation residue cross sections [9-11] and mass and kinetic energy distributions of fission fragments [1][2][3] have established that the fission dynamics of a hot compound nucleus is dissipative in nature. The theoretical analyses are usually performed either by employing the Langevin equation in a dynamical model of nuclear fission [12][13][14] or by using the statistical model where the fission width includes the effects of dissipation [15]. The later approach is used more frequently [6-9,11] since it is rather straightforward to implement it in a standard statistical model code for the decay of a compound nucleus.Considering fission as a diffusive process of a Brownian particle across the fission barrier in a viscous medium, Kramers solved the corresponding Fokker-Planck equation with a few simplifying approximations which finally yielded the so-called Kramers modified Bohr-Wheeler expression for fission width as [15,16] whereIn the above, BW is the fission width due to Bohr and Wheeler [17] and β is the strength of the reduced dissipation coefficient. ω gs and ω sad are the local frequencies of the harmonic oscillator potentials which osculate the liquid drop model nuclear potential at the ground state and the saddle configurations, respectively, while m gs and m sad are the corresponding inertia parameters. T is the nuclear temperature. The dimensionless quantity η = β/2ω sad is often used as a free parameter in order to fit experimental data. * Corresponding author: santanu@veccal.ernet.in A number of assumptions are usually made while applying Eq. (1) in statistical model calculations. A constant value for the parameter η is usually assumed for all spin values of the compound nucleus (CN). The centrifugal barrier however changes the potential profile at higher values of spin of a CN, which consequently results in a spin dependence of the frequencies ω gs and ω sad of the osculating harmonic oscillator potentials [18]. Figure 1 shows the frequencies as a function of spin for the compound nucleus 224 Th. ...

Spallation reaction versus heavy-ion fusion: Fission excitation functions as a fundamental probe of presaddle nuclear dissipation

“…It has been found in numerous experiments [1][2][3][4][5][6][7][8][9] that when excitation energy deposited into the compound system is increased, the measured prescission particle multiplicity exceeds that estimated by standard statistical models (SMs). This discrepancy has been demonstrated [10][11][12][13][14][15][16][17][18][19][20][21] to arise from dissipation effects that are not accounted for in theoretical calculations. Nuclear dissipation retards the fission process that affects the competition of fission with evaporation, two principle decay modes of highly excited nuclei.…”

“…Towards that goal, we compare the sensitivity of fission cross sections to β for different E * and c in the framework of Langevin models. The stochastic approach [10,[12][13][14][16][17][18]21,38,39] has been utilized to successfully reproduce a great number of experimental data on fission excitation functions and prescission particle multiplicities for a lot of fissioning systems over a wide range of excitation energy, angular momentum, and fissility.…”

Significant role of deformation in probing postsaddle nuclear dissipation with light particle emission

“…This is because of its importance for understanding experimental data involving fusion-fission, fusion-evaporation and quasifission processes [1][2][3][4][5][6] as well as because of its relevance to the synthesis of superheavy nuclei [7,8]. Due to dissipation, fission is delayed.…”

“…This results in an enhanced emission of the prescission light particles and a large evaporation residue cross section with respect to that predicted by standard statistical models. Accordingly, information on the dissipation strength is extracted by comparing theory and experiment [3,[9][10][11][12][13]. It has been shown that dynamical Langevin models can give a rather good description for a great number of experimental observables associated with dissipative fission [14][15][16].…”