Nucleon Mean Free Path Research Articles

The thermal self-consistent semiclassical approach and microscopic nucleon-nucleus optical potentials at finite temperature

The nucleon densities ρ q ( q = n, p) of three hot nuclei — 40Ca, 90Zr and 208Pb — at several temperatures are determined by a thermal self-consistent semiclassical (TSCSC) calculation. These densities are utilized, together with the nuclear matter approach and local density approximation (LDA), to evaluate nucleon-nucleus optical potentials at finite temperature. The potentials obtained in this way are fully self-consistent and microscopic at the level of nucleon density, since the same Skyrme force SKa is employed in determining the nucleon densities of target nuclei and in calculating the potentials. The temperature dependence of the nucleon mean free path (MFP) is evaluated and analysed using this optical potential. The influence of temperature on the potential and MFP is better taken care of by the present approach than by previous calculations with Negele's temperature-independent empirical densities. The extension of the present calculation to the high-energy region and the approximate evaluation of the optical potentials, using the low-temperature expansion to the Fermi-Dirac integrals, are also discussed in this paper.

Evidence for an absorption effect in neutron emission in the20Ne +58Ni reaction at 30 MeV per nucleon

Neutron energy spectra were analysed at various angles in coincidence with projectile-like fragments in the reaction20Ne +58Ni at 30 MeV per nucleon. The data have been parametrized with a three moving source fit, taking into account the emission from discrete excited states of the coincident light fragments and the recoil effect due to the emission of neutrons by light nuclei. A nucleon-nucleon scattering description of the intermediate velocity source gives good fits to the data. However the necessity of introducing a reabsorption effect in the projectile-like and target-like nuclei for the nucleons from that source is demonstrated by testing the momentum and energy balances in the fitting procedure. The mean free path of nucleons in nuclear matter is determined. A good agreement is then obtained for the lowest momentum transfers where single scattering dominates. For the largest momentum transfer another mechanism such as double scattering or one-body friction must be introduced in order to reproduce the data.

SELF-CONSISTENT SEMI-CLASSICAL APPROACH FOR ANALYSING THE TEMPERATURE EFFECT ON NUCLEON MEAN FREE PATH

The effect of temperature on the nucleon mean free path is analysed by utilizing the nac-leon density ρq, determined by self-consistent semi-classical approach and the optical potential obtained in local density approximation

The temperature pulse propagation in interacting nuclear slabs

Following the method developed by R.J. Swenson a non-Fourier equation for heat transfer in nuclear matter is obtained. The velocity of heat propagation is calculated and the value ν s = ν F/√3 is obtained. For two interacting nuclear slabs the temperature as a function of time is calculated. For a nucleon mean free path λ ∼ 3 fm the temperature saturation time is calculated and the value ∼160 fm/ c is obtained.

Evaporation of particles from hot nuclei

For particle evaporation from hot nuclei a model is proposed which is applicable to high excitation energies where the mean free path of nucleons becomes comparable to or smaller than the size of the nucleus. The formalism allows to calculate the time evolution of the emitting system and the evaporation rates and spectra of the emitted particles. The nucleus 133Cs with an initial temperature of 18 MeV is studied as an example. Implications for intermediate-energy heavy-ion collisions are indicated.

Nuclear mean free path in the relativistic sigma - omega model.

The nucleon mean free path in the intermediate energy region is estimated using various relativistic nuclear potential models. While the small effective mass in the relativistic models significantly enhances the theoretical values for the mean free path through Negele-Yazaki effect, it does not resolve the deviation from the experimental values extracted from the proton reaction cross sections on various targets.

Instabilities in hot nuclear matter: A mechanism for nuclear fragmentation.

We analyze the process of fragmentation in heavy-ion interactions from the viewpoint of growth of instabilities in hot expanding nuclear matter. The growth rates of modes in a medium unstable to small density perturbations of finite wavelength are calculated from a kinetic equation. This enables us to treat the case where the nucleon mean free path is comparable to or greater than the wavelength of the fluctuation, and the temperature is arbitrary. We estimate for hot nuclear matter the initial conditions which, after expansion, will result in fragmentation, evaporation, or vaporization.

A new code system for the calculation of double differential reaction cross sections

Abstract The statistical exciton model following the master-equation approach has been improved and extended for application as an evaluation tool of double-differential reaction cross sections at incident nucleon energies of 5 to 50 MeV. For this purpose the code system GRAPE, centered around the exciton-model code GRYPHON has been developed, which combines a number of interesting features such as: unified treatment of pre-equilibrium and equilibrium processes, renormalized exciton state-densities summing up to the back-shifted Fermi gas formula, a new model for the internal transition rates based upon the nucleon mean free path in nuclear matter, angle-energy distributions based on intra-nuclear scattering in nuclear matter, account of discrete-level excitations, a new model for γ-ray competition, inclusion of multi-particle emission, and various sorting options with code output in the new ENDF-VI format. A major characteristic of the proposed model is that consistency with equilibrium models has been i...

Comments on the state densities and the transition rates in the pre-equilibrium exciton model

It is proposed to renormalize the exciton-state densities used in models for precompound decay such that the summed state densities agree with the expressions employed in equilibrium statistical models. In this way a close fit can be guaranteed between preequilibrium model calculations and the results of equilibrium statistical models for the evaporative stage of the reaction. The consequences of this proposal for the internal transition rates of the pre-equilibrium exciton model are analyzed. The matrix element for the residual interaction is obtained not from a phenomenological parametrization, but from the nucleon mean free path in nuclear matter. It is demonstrated that the proposed renormalization, from one-component Fermi-gas formulas to two-fermion expressions for the state densities, leads to strongly improved agreement of the effective exciton-model values for the nucleon mean free path in nuclear matter with realistic estimates. It is proved that the particle-hole state densities for a two-component Fermi gas, summed over the allowed exciton-state numbers, agree with the phenomenological state-density expressions used in statistical Hauser-Feshbach models.

The temperature dependence of the optical model potential and of the nucleon mean free path

The complex nuclear self energy is calculated in nuclear matter at full and half density semiclassically at higher temperatures including Pauli blocking. From this the nucleon mean free path λ mf is obtained in a wide energy region. For excitation energies per particle E ∗/A ⪡ 8 MeV, λ mf decreases drastically with higher temperature, whereas for E ∗/A ≫ 8 MeV it decreases only weakly from the value of λ mf ≈ 5 fm at T = 0.

Shortening of the nucleon's mean free path in heavy ion collisions

The mean free path of nucleons in heavy ion collisions is most essential for the development of nuclear collective phenomena. We discuss the effect of the nucleon Fermi motion in nuclei for shortening the mean free path. This Fermi motion together with the prior Pauli effect makes nuclei nontransparent for heavy ions in the medium energy domain.

Shortening of the nucleon's mean free path in heavy ion collisions

The mean free path of nucleons in heavy ion collisions is most essential for the development of nuclear collective phenomena. We discuss the effect of the nucleon Fermi motion in nuclei for shortening the mean free path. This Fermi motion together with the prior Pauli effect makes nuclei nontransparent for heavy ions in the medium energy domain.

Dissipative diabatic dynamics: A shell-model approach to large-amplitude collective nuclear motion

Starting from the discussion of isoscalar giant vibrations as small-amplitude diabatic modes, a time-dependent shell-model approach is introduced which simultaneously treats coherent and incoherent aspects of large-amplitude collective nuclear motion. The coherent coupling of the single-particle motion to the time-dependent mean field is treated in a diabatic approximation. The incoherent aspect is represented by residual two-body collisions which lead to statistical equilibrium within the intrinsic degrees of freedom (local equilibrium). An important consequence of the combined effects from diabatic single-particle motion and dissipative two-body collisions is a significant retardation of the friction force for realistic values of the mean free path of nucleons. The retarded-friction term describes an elastic response of the nucleus for perturbations fast compared to the local equilibration time, and a dissipative response for slow perturbations. This elastoplastic behaviour represents an interesting dynamical property of nuclear matter. A diabatic two-center shell model is introduced and results on diabatic single-particle levels and potentials are given and compared with corresponding quantities from TDHF calculations. Effects on cross-sections of nucleus-nucleus collisions (deeply inelastic reactions, extra-push for capture and fusion) are discussed. A specific finger print for the diabatic single-particle motion is the preequilibrium emission of neutrons from unbound diabatic levels in central nucleus-nucleus collisions.

Random-walk model of precompound decay II: Stochastic uncertainties in the lifetimes and cross-sections

The uncertainties arising from the stochastic nature of precompound decay nuclear reactions are analyzed in the framework of the preequilibrium exciton and random-walk models. It is demonstrated that the standard deviations and the mean values of the exciton-state lifetimes are of the same order of magnitude. Their correlations are weakly positive, except for exciton states near the equilibrium number, where the correlations are significant. The usefulness and the limitations of the never-come-back approximation are discussed. A general proof is presented of the conditions under which the master-equation and random-walk approaches to Markov processes are equivalent. Connections between different preequilibrium models, e.g. the multi-step compound model and the microscopic statistical theory of precompound decay, are pointed out. It is shown that the waiting time between subsequent collisions is governed by a Poisson process, suggesting that the variance associated with the nucleon mean free path in nuclear matter, as estimated from preequilibrium models, is considerable. The stochastic uncertainties in the emission cross-sections correspond to those of a Bernoulli process.

Dissipative diabatic dynamics

A time-dependent shell-model approach to large-amplitude collective nuclear motion is introduced which simultaneously treats the coherent (diabatic) single-particle motion in the time-dependent mean field and the in coherent two-body collisions which lead to statistical equilibrium within the intrinsic degrees of freedom. An important feature of the combined effects from diabatic single-particle motion and dissipative two-body collisions is the retardation of dissipation for realistic values of the mean free path of nucleons. This elastoplastic behaviour represents an interesting dynamical property of nuclear matter. A diabatic two-center shell-model is introduced and results on diabatic single-particle level s and potentials are given and compared with corresponding quantities from TDHF calculations. Effects on cross-sections of heavy-ion collisions are discussed and preliminary results on the diabatic pre-equilibrium emission of nucleons in central collisions are presented.

Nuclear mean free paths and transparency at intermediate energies

The soft-spheres model of nuclear reaction cross sections incorporating tapered density distributions is used to evaluate nucleon mean free paths and transparencies at intermediate energies. Comparison with similar calculations employing uniform density distributions shows the latter to give misleading results that nevertheless have been used in recent years as evidence that the physics of the nucleon–nucleon interaction within nuclei is incompletely understood.

A study of the formation of compound nucleus states by absorption of 30 to 90 MeV photons in Sn, Ce, Ta and Pb nuclei

From measurements σ ( j) ( E γ ) = Σ i = j i max σ( γ, in…) on four heavy nuclei (Sn, Ce, Ta, Pb) from 30 to 90 MeV with monochromatic photons one obtains the cross section for the formation of a compound nucleus state excited with the full energy of the absorbed photon. This cross section is compared with high energy extrapolation of the Lorentz line which fits σ(tot: E γ ) on the giant dipole resonance and with the absorption on a quasideuteron pair. A value 3.5 fm <λ < 8.5 fm is deduced for the mean free path of a fast nucleon in these heavy nuclei.

On the mean free path of medium-energy nucleons in nuclear matter

We show that the “experimental” value of the mean free path of nucleons in nuclear matter deduced from elastic nucleon—nucleus scattering is ambiguous and depends critically on the parametrization chosen for the radial shape of the optical potentials. We find that a realistic choice of radial potential shapes, based on recent theoretical advances in nucleon optical models, leads to derived values for the mean free path at medium energies which are compatible with a simple microscopic expectation.

Mean Free Path in a Nucleus

It is shown that proper treatment of the nonlocality of the nuclear optical potential resolves much of the apparent discrepancy between previous theoretical calculations and empirical values of the nucleon mean free path.

Is the concept of a mean free path relevant to nucleons in nuclei?

Computes realistic nucleon mean free paths in 12C and 208Pb nuclei by including the effects of Fermi motion, Pauli blocking and the Coulomb and nuclear interaction potentials. These local (i.e. radius-dependent) mean free paths can differ enormously from the nuclear matter value. The meaning of a mean free path in finite nuclei is discussed and an alternative quantity, the absorption probability as a function of impact parameter, is defined.