Pre-equilibrium Nuclear Reactions Research Articles

Calculation of excitation functions and isomeric cross section ratio of the58Ni(n,p)58Com,greactions in the 1–20 MeV energy range

Calculation of the excitation functions and isomeric cross section ratio of ${}^{58}\mathrm{Ni}{(n,p)}^{58}{\mathrm{Co}}^{m,g}$ reactions has been carried out using Hauser-Feshbach and preequilibrium nuclear reaction model codes in the 1--20 MeV energy range, and compared with measurements and previous calculations. The structure in the isomeric cross section ratio curve in the low-energy region has been investigated. The anomaly of the branching ratio of the 53 keV ${(4}^{+})$ state to the isomeric states has been resolved by using more precise formalism of the $\ensuremath{\gamma}$-ray transition probabilities available in the literature for the continuum and discrete levels.

Calculations for the excitation functions of the [formula omitted], [formula omitted] and [formula omitted] reactions

Calculations for the excitation functions of 63 Cu p, n 63 Zn , 63 Cu p, 2 n 62 Zn and 65 Cu p, n 65 Zn reactions have been carried out in 3–30 MeV energy range using statistical and pre-equilibrium nuclear reaction models. The calculations have been compared with reported measurements and discussed.

Partial level densities for nuclear data calculations

The main formalisms of partial level densities (PLD) used in preequilibrium nuclear reaction models, based on the equidistant spacing model (ESM), are considered. A collection of FORTRAN77 functions for PLD calculation by using 14 formalisms for the related partial-state densities is provided and 28 sample cases (73 versions) are described. The results are given in graphic form too. Composite (recommended) formulas, which include the optional use of various corrections, i.e. the advanced pairing and shell correction in addition to the Pauli effect, and average energy-dependent single-particle level densities for the excited particles and holes are also given. The formalism comprises the density of particle—hole bound states, and the effects of an exact correction for the Pauli-exclusion principle are considered.

Closed-form evaluation of pre-equilibrium light-cluster emission in heavy ion reactions

Abstract A formalism is developed to evaluate pre-equilibrium cluster emission spectra in heavy ion reactions using a closed form expression obtained by extending the hybrid model of pre-equilibrium nuclear reactions.

Preemission cluster energies in preequilibrium nuclear reactions

A formalism is developed to evaluate the energy distribution of light clusters inside an excited nucleus. Its importance in predicting emitted cluster spectra is demonstrated by comparison with experiment and other models. {copyright} {ital 1997} {ital The American Physical Society}

Continuum angular distributions in preequilibrium nuclear reactions: Physical basis for Kalbach systematics.

We show how momentum conservation is fundamental to the description of angular distributions in preequilibrium nuclear reactions. By using state densities with linear momentum to describe the phase space during the preequilibrium cascade, angular distributions can be derived in a transparent way. Fermi-motion and Pauli-blocking effects are included, and correlations between the emission particle's energy and angle are obtained for all orders of scattering. Our model provides a physical basis for many features of widely used phenomenological systematics of Kalbach, and provides a framework for understanding the systematical properties of continuum angular distributions.

Energy-dependent single-particle state density effects in the hybrid model of pre-equilibrium nuclear reactions

Different energy dependences of the single-hole and excited-particle state densities, of Fermi-gas model type and a linear dependence respectively, are adopted in accordance with recent proofs of accurate shell-model Hamiltonian eigenvalues. The respective different values at the Fermi level also make possible both the correct prediction of the bound nucleon number, for a Fermi energy value of 40 MeV, and the agreement with the average neutron resonance spacing data. An attempt to distinguish between the surface effects and the influences attributable to the energy dependence of the single-particle state density is made within the geometry-dependent hybrid model of the pre-equilibrium emission. Comparisons with the large amount of data existing for fast-neutron reactions on the 51V and 56Fe target nuclei at incident energies up to 20 MeV support the model assumptions.

Neutron skin effect in preequilibrium nucleon emissions.

The geometry-dependent hybrid model of preequilibrium nuclear reactions is used together with the droplet model description of neutron and proton densities to investigate the effect of excess surface neutrons on the nucleon emission spectra. It is found that in alpha-particle--induced reactions the effect of neutron-skin on nucleon emission spectra is negligible. For nucleon-induced reactions the effect is more significant but not strong enough to remove the discrepancies between calculation and experiment.

Renormalization for optical model and unified model of nuclear reactions.

A unified model of nuclear reactions taking account of both the compound and preequilibrium nuclear reactions is proposed in terms of a renormalization of the wave functions generated by the optical model potential. The cross sections of the nuclear reactions including preequilibrium processes are formulated, which are especially suited for calculations of cross sections of those nuclear reactions in which the residual nuclei are in discrete levels or isomeric states. The model is used to investigate the reactions [sup 59]Co([ital n],2[ital n])[sup 58]Co and [sup 93]Nb([ital n],2[ital n])[sup 92]Nb. The results are in good agreement with the experimental data.

Non-equilibrium entropy in excited nuclei

We investigate the time-dependent behaviour of entropy in excited nuclei. In distinction to recent claims, it is shown that no self-organisation is involved in pre-equilibrium nuclear reactions.

Studies of nuclear second moments for pre-equilibrium nuclear reaction theories ? Extension to finite-range residual interaction

Study of the nuclear second moments, important inputs to pre-equilibrium reaction theories, is extended to residual interactions of finite range. The interactions are assumed to have general spin and isospin dependence. The second moments are found to be always positive definite for commonly used values of the interaction parameters. They seem to support the strong coupling limit of the pre-equilibrium reaction theory by Nishioka et al. [1], which would imply the modification of the phenomenological model used in analyzing experimental data. As an application of the second moments, it is also investigated how the nuclear level densities change with the parameter values of the residual interaction. The results show the important role of the residual interaction especially in the low energy region, which may greatly improve the agreement with experimental data at thermal neutron resonances.

Studies of nuclear second moments for pre-equilibrium nuclear reaction theories

The nuclear second moments, important inputs to pre-equilibrium reaction theories, are evaluated by assuming a simple model. The positive definite nature of the second moments is examined, and the nuclear level densities are calculated using positive definite second moments.

Study of the mechanisms of pre-equilibrium nuclear reactions in the microscopic approach

The mechanisms of pre-equilibrium nuclear reactions are investigated within the Statistical Multistep Direct Process (SMDP) + Statistical Multistep Compound Process (SMCP) formalism. It has been shown that from an analysis of linear part in such dependences as $$\ln \left[ {{{\frac{{d^2 \sigma }}{{d\varepsilon _b d\Omega _b }}} \mathord{\left/ {\vphantom {{\frac{{d^2 \sigma }}{{d\varepsilon _b d\Omega _b }}} {\varepsilon _b^{1/2} }}} \right. \kern-\nulldelimiterspace} {\varepsilon _b^{1/2} }}} \right]upon\varepsilon _b $$ and $$\ln \left[ {{{\frac{{d\sigma ^{SMDP \to SMCP} }}{{d\varepsilon _b }}} \mathord{\left/ {\vphantom {{\frac{{d\sigma ^{SMDP \to SMCP} }}{{d\varepsilon _b }}} {\frac{{d\sigma ^{SMDP} }}{{d\varepsilon _b }}}}} \right. \kern-\nulldelimiterspace} {\frac{{d\sigma ^{SMDP} }}{{d\varepsilon _b }}}}} \right]upon{{U_B } \mathord{\left/ {\vphantom {{U_B } {\left( {E_a - B_b } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {E_a - B_b } \right)}}$$ one can extract information about the type of mechanism (SMDP, SMCP, SMDP→SMCP) and the number of stages of the multistep emission of secondary particles. In the above approach, we have discussed the experimental data for a broad class of reactions in various entrance and exit channels.

Surface effects in the exciton model of preequilibrium nuclear reactions.

Surface effects on direct particle emission in the exciton model of preequilibrium nuclear reactions are described in terms of the mean effective well depth in the region of the first target-projectile interaction. A simple parametrization for this quantity as a function of the bombarding energy is derived, and its predictive ability is demonstrated. There is no evidence for a mass dependence of the parameter values. The question of surface effects is found to be tied to the assumed energy dependence of the single particle state density. A Fermi gas model square root dependence is used in this work. Only (nucleon, nucleon) reactions are considered, but sizable effects on complex particle spectra are anticipated.

Analysis of intermediate structures of spectral emission in pre-equilibrium nuclear reactions in the microscopic approach

The quasi-particle-phonon model of pre-equilibrium decay (QP Ph M PED) is proposed. Within this model, intermediate states are specified by the number of quasi-particles, quasi-holes and phonons. In describing nuclear relaxation we consider two types of internuclear transitions with the change in exciton number byΔNex=0, ±2 and number of phononΔNph=±1. The mixed densities of intermediate statesϱ(Nex,Nph,E) have been determined. An analysis has been made of the structure of the hard part of the emission spectrum in the60Ni(p,p′) and120Sn(p,p′) reaction at ɛp=62 MeV. This analysis suggests the importance of taking into account the transitions withΔNph=+1, along with the transitions withΔNex= +2.

A study of pre-equilibrium nuclear reactions with composite particles

A study of pre-equilibrium nuclear reactions with composite particles

Phenomenology of continuum angular distributions. I. Systematics and parametrization

A large number of experimental angular distributions have been studied for particles emitted into the continuum in preequilibrium nuclear reactions in order to study their systematics. For pure multistep direct reactions it has been found that to first order the shapes of these angular distributions are determined by the energy of the outgoing particle. In addition, there is evidence that the division of the cross section into multistep direct and multistep compound components with the latter having a symmetric angular distribution is a meaningful one. The shapes of the angular distributions can be described in terms of Legendre polynomials. The polynomial coefficients are given by simple phenomenological relations involving the energy of the outgoing particle. The same reduced coefficients are used for multistep direct and multistep compound processes except that only even order polynomials are considered in the latter case. The present formulation has been shown to have significant predictive ability for light ion reactions.NUCLEAR REACTIONS $A(a,b)$, $A=^{12}\mathrm{C} \mathrm{to} ^{232}\mathrm{Th}$, $a=p,d,^{3}\mathrm{He},^{4}\mathrm{He}$, $b=n,p,d,t,^{3}\mathrm{He},^{4}\mathrm{He}$, $E=18\ensuremath{-}80$ MeV, ${E}_{b}=4\ensuremath{-}60$ MeV. Deduced systematics of $\frac{\ensuremath{\sigma}({E}_{b},\ensuremath{\theta})}{\ensuremath{\sigma}({E}_{b})}$ in continuum. Parametrized $\frac{\ensuremath{\sigma}({E}_{b},\ensuremath{\theta})}{\ensuremath{\sigma}({E}_{b})}$ in continuum with energy dependent Legendre polynomial coefficients.

Phenomenology of continuum angular distributions. II. Griffin preequilibrium model

The Griffin or exciton model for preequilibrium nuclear reactions has been extended so that particle unbound states in the equilibrating system are distinguished from bound states. This permits the preequilibrium cross section to be divided into components due to multistep direct and multistep compound processes for calculation of emitted particle angular distributions. Preequilibrium models traditionally assume that all states of a given particle-hole number are equally likely whereas present work indicates that unbound states are preferentially populated. Nevertheless, the emission energy spectra calculated are not significantly changed from earlier versions of the model.NUCLEAR REACTIONS Extended Griffin preequilibrium statistical model to calculate multistep direct and multistep compound cross sections separately. Tested equal a priori probabilities assumption.

On the fluctuations in the statistical theory of pre-equilibrium nuclear reactions

1. The dominant effect in the statistical theory of pre-equilibrium nuclear reactions at not too high excitation energies is the process of intranuclear cascade, in which at every step the number of exeitons n is increased by A n = + 2. In the approximations implicit in the theory, the process of exeiton multiplication is considered as a sequence of real transitions between states of the umperturbed singleparticle Hamiltonian having a definite number of particle-holes. One can therefore pass from one state to another state following different sequences, and the amplitudes for the various chains add together coherently. I t is very reasonable to treat statistically this interference phenomenon, and one obtains in this way a theory of fluctuations in the excitation function and in the spectra of the emitted particles, similar to the theory of the Ericson effect for compound nucleus, if I[D >> 1. We shall show that in the most common cases one has a condition equivalent to F/D>> 1, for medium and heavy nuclei.