PROTECCIONES COLECTIVAS

An outline of the general theory and modeling of nuclear reactions can be given in many ways. A common classification is in terms of time scales: short reaction times are as- sociated with direct reactions and long reaction times with compound nucleus processes. At intermediate time scales, pre-equilibrium processes occur. An alternative, more or less equivalent, classification can be given with the number of intranuclear collisions, which is one or two for direct reactions, a few for pre-equilibrium reactions and many for compound reactions, respectively. As a consequence, the coupling between the incident and outgoing channels decreases with the number of collisions and the statistical nature of the nuclear reaction theories increases with the number of collisions. Fig. 10 explains the role of the different reaction mechanisms during an arbitrary nucleon-induced reaction in a schematic manner. The underlying nuclear models will be discussed later.

When discussing nuclear reactions in the context of a computer code, rather than a mathematically formal approach, we think Fig. 11 is an appropriate starting point. A parti- cle incident on a target nucleus will induce several binary reactions which are described by the various competing reaction mechanisms that were mentioned above. The end products of the binary reaction are the emitted particle and the corresponding recoiling residual nu- cleus. In general this is, however, not the end of the process. A total nuclear reaction may involve a whole sequence of residual nuclei, especially at higher energies, resulting from multiple particle emission. All these residual nuclides have their own separation energies, optical model parameters, level densities, fission barriers, gamma strength functions, etc., that must properly be taken into account along the reaction chain. The implementation of this entire reaction chain forms the backbone of TALYS. The program has been written in a way that enables a clear and easy inclusion of all possible nuclear model ingredients for any number of nuclides in the reaction chain. Of course, in this whole chain the target and primary compound nucleus have a special status, since they are subject to all reaction mechanisms, i.e. direct, pre-equilibrium, compound and fission and, at low incident ener- gies, width fluctuation corrections in compound nucleus decay. Also, at incident energies below a few MeV, only binary reactions take place and the target and compound nucleus are often the only two nuclei involved in the whole reaction. Historically, it is for the binary reactions that most of the theoretical methods have been developed and refined, mainly because their validity, and their relation with nuclear structure, could best be tested with

Multiple Pre-Eq. Emission Pre-Eq. Fission Fission Multiple Compound Emission discrete peaks Compound low-E hump Elastic Projectile Elastic Shape Reaction Particle Spectra Elastically Scattered Particles Nuclear Reaction Mechanisms

high-E tail

Compound

Direct

Figure 10. The role of direct, pre-equilibrium and compound processes in the description of a nuclear reaction and the outgoing particle spectra.

exclusive measurements. In general, however, Fig. 11 should serve as the illustration of a total nuclear reaction at any incident energy. The projectile, in this case a neutron, and the target(ZC, NC− 1) form a compound nucleus (ZC, NC) with a total energy

Etot= ECM+ Sn(ZCN, NCN) + Ex0, (1)

whereECM is the incident energy in the CM frame,Snis the neutron separation energy of the compound nucleus, andE0

xthe excitation energy of the target (which is usually zero, i.e. representing the ground state). The compound nucleus is described by a range of possible spin (J) and parity (Π) combinations, which for simplicity are left out of Fig. 11. From

this state, transitions to all open channels may occur by means of direct, pre-equilibrium and compound processes. The residual nuclei formed by these binary reactions may be populated in the discrete level part and in the continuum part of the available excitation energy range. In Fig. 11, we have only drawn three binary channels, namely the(ZC, NC−

1), (ZC − 1, NC) and (ZC − 1, NC − 1) nuclei that result from binary neutron, proton and deuteron emission, respectively. Each nucleus is characterized by a separation energy per possible ejectile. If the populated residual nucleus has a maximal excitation energy

E_xmax(Z, N ) that is still above the separation energies for one or more different particles

for that nucleus, further emission of these particles may occur and nuclei with lowerZ and N will be populated. At the end of the nuclear reaction (left bottom part of Fig. 11), all the

reaction population is below the lowest particle separation energy, and the residual nucleus

(ZC−x, NC−y) can only decay to its ground or isomeric states by means of gamma decay. In a computer program, the continuum must be discretized in excitation energy (Ex) bins.

We have taken these bins equidistant, although we already want to stress the important fact here that the emission energy grid for the outgoing particles is non-equidistant in TALYS. After the aforementioned binary reaction, every continuum excitation energy bin will be further depleted by means of particle emission, gamma decay or fission. Computationally, this process starts at the initial compound nucleus and its highest energy bin, i.e. the bin just belowE_xmax(ZC, NC) = Etot, and subsequently in order of decreasing energy bin/level, decreasingN and decreasing Z. Inside each continuum bin, there is an additional loop over

all possibleJ and Π, whereas for each discrete level, J and Π have unique values. Hence,

a bin/level is characterized by the set{Z, N, Ex, J, Π} and by means of gamma or particle emission, it can decay into all accessible{Z′, N′, Ex′, J′, Π′} bins/levels. In this way, the

whole reaction chain is followed until all bins and levels are depleted and thus all channels are closed. In the process, all particle production cross sections and residual production cross sections are accumulated to their final values.

We will now zoom in on the various parts of Fig. 11 to describe the various stages of the reaction, depending on the incident energy, and we will mention the nuclear reaction mechanisms that apply.