5.3 THE EXPERIMENTAL APPROACH TO NUCLEAR REACTIONS .sx Having defined the quantities that are normally measured in a nuclear reaction we here outline the typical experimental procedures which are followed for studying the symbolic reaction A(a , b)B .sx No details are given of the apparatus other than to mention very briefly the underlying physical principles .sx Details of low energy nuclear physics apparatus are given , for example , in Burcham ( 1988 ) and of high energy elementary particle apparatus in a book in this series by Kenyon ( 1988) .sx Referring to Fig. 5.3 , charged ions of the particle a are produced in some form of accelerator ( described later in this section ) and , by use of bending magnets for example , will emerge with a particular energy .sx These ions then pass through a collimator in order to define their direction with some precision and strike a target containing the nuclei A. As the beam particles move through the target they will mainly lose energy by ionizing target atoms and so , if precise energy measurements are to be made , a thin target must be used .sx This , however , increases the difficulty of the experiment since few interactions will take place .sx Choice of target thickness is clearly a crucial decision in planning an experiment .sx diagram&caption .sx The reaction product particles b move off in all directions and their angular distribution can be studied by detecting them after passage through another collimator set at a particular angle theta .sx Various types of detector are used ( discussed later ) - sometimes in combination - and these can determine the type of particle as well as its energy .sx But experimenters have to contend with many complications of interpretation , impurities in targets and , not least , the stability of their apparatus .sx In the end , detailed information becomes available about sigma , d sigma /d OMEGA and their energy dependence for the reaction under study .sx 5.3.1 Accelerators .sx Most important for nuclear reaction studies are Van de Graaff accelerators in which ions are accelerated in an evacuated tube by an electrostatic field maintained between a high voltage terminal and an earth terminal , charge being conveyed to the high voltage terminal by a rotating belt or chain .sx In early forms of this accelerator , positive ions from a gaseous discharge tube were accelerated from the high voltage terminal to earth .sx But , in modern 'tandem' accelerators , negative ions are accelerated from earth to the high voltage terminal where they are then stripped of some electrons and the resultant positive ions are further accelerated down to earth potential .sx The effective accelerating potential is thus twice the potential difference in the machine .sx High flux proton beams with energies up to around 30MeV can be produced in this way .sx The machines can also be used to accelerate heavy ions such as 16 O. At higher energies use is generally made of orbital accelerators in which charged particles are confined to move in circular orbits by a magnetic field .sx At non-relativistic energies the angular frequency of rotation omega , known as the cyclotron frequency , is constant depending only on the strength of the field .sx In a cyclotron , the particles rotate in a circular metallic box split into two halves , known as Ds , between which an oscillating electric field is maintained .sx Its frequency matches omega and so the particle is continually accelerated .sx In a fixed magnetic field the orbital radius increases as the energy increases and , at some maximum radius , the particles are extracted using an electrostatic deflecting field .sx However , as the energy becomes relativistic ( remember formula ) , omega decreases with energy and it becomes necessary to decrease steadily the frequency of the oscillating electric field with energy to preserve synchronization .sx Such a machine is known as a synchrocyclotron and protons with energies in the region of 100 MeV have been produced in this way .sx For energies higher than this gigantic magnets would be needed and so the approach is to accelerate bunches of particles in orbits of essentially constant radius using annular magnets producing magnetic fields which increase as the particle energy increases :sx This energy increase is provided by passing the particles through radio - frequency cavities whose frequency also changes slightly as the particles are accelerated to ensure synchronization .sx Such devices are called synchrotrons and can be physically very large .sx For example , the so-called Super Proton Synchrotron ( SPS ) at CERN ( Geneva ) has a circumference around 6 km and can produce protons with energies up to around 450 GeV .sx LEP ( the Large Electron-Positron Collider ) has a circumference of 27 km and accelerates electrons ( and positrons in the opposite direction ) to energies of approximate-sign 60 GeV or more .sx Finally , the Superconducting Super Collider ( SCC ) , which uses superconducting magnets , and which is being built in the USA , has a circumference of 87 km and will produce proton and antiproton beams with energies approximate-sign 20 000 GeV !sx .sx Electrons can also be accelerated in synchrotrons but , because of their small mass , large amounts of energy are radiated ( synchrotron radiation ) owing to the circular acceleration .sx At energies beyond a few GeV this loss becomes prohibitive and use has to be made of linear accelerators in which electrons are accelerated down a long evacuated tube by a travelling electromagnetic wave .sx The Stanford Linear Accelerator ( SLAC ) in the USA , for example , is around 3 km long and can produce pulses of electrons with energies up to 50 GeV .sx 5.3.2 Detectors .sx Although in the early days much use was made of ionization chambers , for example the Geiger counter ( section 1.4 ) , the detectors currently in use for nuclear physics experiments are usually either scintillation counters or semiconductor detectors or some combination .sx The former are developments of the approach of Rutherford , Geiger and Marsden ( section 1.3 ) using the scintillations produced in a ZnS screen to detect alpha -particles .sx Various scintillators are in current use such as NaI activated by an impurity ( usually thallium for detection of gamma -particles ) , or some organic material dissolved in a transparent plastic or liquid .sx The scintillations are detected by a photomultiplier tube producing a pulse of photo - electrons .sx The size of the pulse - the pulse height - gives a measure of the energy of the incident particle .sx Semiconductor detectors depend on an incident particle or photon exciting an electron from the valence band to the conduction band .sx The resultant increase in conductivity - a conduction pulse - then produces a signal which is processed electronically and which enables the energy of the incident radiation to be measured .sx In the field of very high energy physics , considerable use is made of bubble chambers and wire chambers .sx The former follows on from the Wilson cloud chamber and consists essentially of a large chamber , possibly several metres in diameter , containing liquid ( e.g. hydrogen , helium , propane , .sx .. ) near its boiling point .sx The chamber is expanded as charged particles pass through it , leading to the formation of bubbles , as a result of boiling , along the particle tracks which can be stereo flash photographed .sx The lengths of the tracks and their curvature in a magnetic field enable particle lifetimes , masses and energies to be deduced .sx Wire chambers consist of stacks of positively and negatively charged wire grids in a low pressure gas .sx An incident charged particle ionizes the gas and acceleration of the resultant electrons near the anode wires leads to further ionization and an electrical pulse .sx The physical location of the pulse can be determined electronically so that track measurements can be made .sx Using an applied magnetic field to bend the tracks again enables information to be obtained about the properties of the detected particle .sx 5.4 NUCLEAR REACTION PROCESSES .sx In the previous chapter some understanding of nuclear structure has been achieved in terms of a nuclear model in which nucleons move around fairly independently in a potential well .sx To give some intuitive understanding of nuclear reaction processes we stay with this description of the nucleus and follow a very illuminating discussion given by Weisskopf ( 1957) .sx An incident particle , a , approaching a nucleus , A , will , if it is charged , first experience the long-range Coulomb potential and if its energy is low will be elastically scattered by this before coming within the range of the nuclear force .sx In this case it undergoes Rutherford or Coulomb scattering as described in section 1.3. For higher energies , or if the particle is uncharged , it will come within the range of the nuclear force due to the nucleons .sx This can be represented by a potential energy curve of the form already discussed and shown in Fig. 4.2 for an incident neutron or proton .sx As a result of this interaction the incident particle may again be elastically scattered without colliding directly with a nucleon in the nucleus .sx The form of this scattering will obviously depend on the shape and size of the nucleus and its associated potential well , and is referred to as shape elastic scattering .sx All of these processes are symbolized by .sx formula .sx If a direct collision with a nucleon takes place then there are various possibilities .sx The nucleon may be excited to a higher ( unoccupied ) state and the incident particle leaves the nucleus with reduced energy .sx This in an inelastic scattering process and the nucleus is left in an excited state .sx Another variant of this is that , instead of exciting a nucleon , the incident particle excites a collective mode - a vibrational or a rotational state ( section ) .sx Such processes are symbolized by .sx formula .sx where A* signifies an excited state of the nucleus A. Alternatively the incident particle may give enough energy to the nucleon with which it collides so that this nucleon , b , is knocked out from the nucleus ( Fig. ) .sx There are two possibilities here , depending on how much energy is lost by the incident particle .sx If the incident particle , a , retains enough energy to escape from the nucleus after the collision we have the process .sx formula .sx where B is the residual nucleus remaining after the nucleon b has been knocked out of A. However , the incident particle may lose so much energy that it is captured , resulting in the formation of a nucleus B' , i.e. formula .sx Reactions of the various kinds just discussed are referred to as direct reactions since there is direct interaction with a single nucleon rather than with the nucleus as a whole .sx Other variants illustrated in Figs 5.4b and 5.4c are stripping and pick-up reactions .sx In the former a composite incident particle , usually a deuteron ( 2 H ) , is stripped of one of its component nucleons which remains in the target nucleus and the remaining nucleon(s ) escape .sx Conversely , in the latter , the incident particle , usually a nucleon , picks up another nucleon from the target nucleus and carries it away , emerging as a deuteron .sx diagram&caption .sx The next possibility is that the incident particle collides with a nucleon in the target nucleus , perhaps one lying in a very low shell model level , and neither has sufficient energy to escape .sx There will then be a series of further random collisions in the nucleus ( Fig. 5.5 ) until eventually enough energy is concentrated by chance on one particle to enable it to escape ; or the nucleus may lose its energy by emitting electromagnetic radiation .sx This state of the nucleus after it has captured the incident particle and in which many internal collision processes are occurring was first discussed by Niels Bohr in 1936 and is referred to as the compound nucleus .sx Whereas a direct reaction , for an incident particle of several MeV , takes place in a time of the order of that taken by a nucleon to cross a nucleus ( formula ) the compound nucleus exists for a much longer period and we shall see in section 5.8 that it can exist for times in the approximate region from 10 -14 s to 10 -20 s. A compound nucleus process can thus be represented as taking place in two stages - formation of the compound nucleus and , after a considerable time , its decay .sx Symbolically , .sx formula .sx where C* represents the excited compound nucleus .sx Because of the long life of the compound nucleus little information about its mode of formation is carried forward to influence the way in which it disintegrates .sx diagram&caption .sx Finally , one other approach to coping with the complexities of nuclear reaction processes should be mentioned , namely , the optical model which was developed by Feshback , Porter and Weisskopf in 1954 and which is useful in giving a broad understanding of nuclear reactions .sx