Ernest Rutherford made experiments where he used energetic alpha particles which he obtained from a radioactive source. He let alpha particles hit a gold foil and observed how they were scattered. These experiments showed that the main part of the mass of the atom was concentrated to the centre of the atom. Eventually these findings led Niels Bohr to create a new model for the atom.

However in the long run it's neither very "healthy" nor "flexible" to use strong radioactivity as source of energetic alpha particles. Therefore some persons started to think about how to accelerate ions to high velocities artificially. The very first accelerator in which ions could be accelerated to energies high enough to induce nuclear reactions was built 1930 by Cockroft and Walton This accelerator was a linear accelerator and the principle to create a high energy was based on cascade generation of high voltage. At about the same time Ernest Lawrence had started to think in another direction. He invented the cyclotron. He and M. Stanley Livingstone built the first at Berkeley 1931.

Swedish scientists became highly interested in the new physics that was emerging during the first decades of the century. According to some unofficial sources two Nobel prizes (one in physics and one in chemistry) were "confiscated" and used to create the Nobel Institute of Physics. Manne Siegbahn became the first director of this institute and his first task was to build a cyclotron. (Today what's remaining of the former Nobel Institute of Physics is called the Manne Siegbahn Laboratory and that's where this laboration takes place).

The cyclotron was ready during autumn 1939. With it protons, deuterons and alpha particles could be accelerated. Cyclotrons are often characterised by their pole diameter. It tells to what energy particles can be accelerated for a given magnetic field strength. The cyclotron of the Nobel Institute had a diameter of 80 cm.

Already 1944 Manne Siegbahn presented plans to build a bigger cyclotron. Within half a year he received 500000 Swedish kronor from the Rockefeller foundation in USA. This money was enough to start a project to build a 225 cm cyclotron. Hard labour and economical grants from the Knut and Alice Wallenberg foundation, the Nobel foundation and the government made it possible to reach the goal; deuterons accelerated to 25 MeV, already in autumn 1951.

The 225 cm cyclotron was a "classical" cyclotron working at a fixed frequency. The frequency had to be set for each ion and experiment and could not be varied in short time. This meant that one could not adjust the frequency when ions became relativistic. Another limiting factor was that the ion sources that were placed at the centre of the cyclotron could not produce highly charged ions. This limited the ions that could be accelerated to be lighter or equal to oxygen. Gradually it became evident that the institute needed a new accelerator and during the end of the 80s a new accelerator project was started. On the day of St Lucia 1990 we had our first ion beam circulating in our new accelerator and storage ring CRYRING 1990. Today it's used for atomic and molecular physics studies and for applications like the testing of micro electronics circuits for outer space and other surroundings with intense radiation. Today accelerator techniques are used in many fields of physics and also for applications of many kinds.

Since the very beginning the institute also had smaller accelerators. The accelerator we are using to make nuclear reactions is a single ended Van de Graaff. It's a linear accelerator and the accelerating voltage is obtained by charging a rubber belt, which in turn charges the so-called terminal. You have probably seen a small desktop version of a Van de Graaff during your studies of physics. Our Van de Graaff can be charged to a maximum voltage of about 2.5 MV. Singly charged ions can therefore reach a maximum of 2.5 MeV. An ion with charge 2⁺ can consequently reach 5 MeV.

In a tandem Van de Graaff negative ions are injected at the low energy end and are accelerated towards the terminal which is charged to a voltage V. Inside the terminal, the singly charged ions have reached V eV. The relatively high energy at the terminal is utilised to strip off a number of electrons = q. This is done with a thin carbon foil or a gas at low pressure. On the way out the ions thereafter gain an energy of qV eV and reach a total energy of (q+1)V eV.

Our single ended Van de Graaff is equipped with a radio frequency ion source in the terminal. The ion source is fed with gases like H₂ or mixtures of ³He and ⁴He. The ion source can be remotely controlled.

In the following we will describe nuclear reactions from a general point of view. After that we will consider a few important aspects of nuclear reactions.

A nuclear reaction between a projectile nucleus x and a target nucleus X might result in one or more new nuclei. Here we consider production of two new nuclei y and Y and we write the nuclear reaction as:

x + X ® Y + y

One can also write X(x,y)Y to describe the same reaction. If y = x and Y = X we call what has happened "scattering".

At low projectile energy only electromagnetic interactions play a role. Since nuclei in our world all are positively charged they are repelling each other by Coulomb forces. At higher energy when the projectile "touches" the target nucleus the strong force start to play a role. A simple estimate of how much energy is needed to overcome the Coulomb repulsion can be obtained if one considers the projectile and target nuclei as two charged spheres.

The following 5 tasks should be done in advance.

Task 1: Calculate the kinetic energy which is required to overcome the repulsive energy at a distance between two spheres representing a proton and a ¹⁹F nucleus. Use reasonable estimates of the radii of the proton and the ¹⁹F nucleus.

Another important property in nuclear reactions is the equivalence of energy and mass. The Q-value is defined by equation 11.2 in Krane, here numbered (1)

where M and m are masses, indices refer to the formulas above and T_s are kinetic energies of respective particles. c is of course the speed of light.

The Q-value is important because it tells us how much energy is available or needed for the reaction to take place. If Q> 0 energy is released in the reaction and this energy is shared as kinetic energy by the two new nuclei.

The kinetics of a nuclear reaction can be calculated if one knows the initial energy of the projectile and the masses of the initial and final nuclei involved in the reaction.

Task 2: Calculate the Q-values of the reactions:

p + ¹⁹F ® ²⁰Ne and p + ¹⁹F ® ¹⁶O + a