1.α particle scattering theory
(1) Coulomb scattering deflection angle formula
Suppose that the nucleus has a mass of m, a positive charge of +Ze, and is at the O point, while α particles with a mass of m, an energy of e and a charge of 2e are incident at a speed. When the mass of the nucleus is much greater than that of the alpha particle, it can be considered that the former will not be pushed, and the alpha particle will change its direction and deflection angle under the action of coulomb force, as shown in Figure 3.3- 1. The figure shows the original velocity of alpha particles, and b is the vertical distance between the nucleus and the extension line of the original motion path of alpha particles, that is, the minimum linear distance when the incident particles have no interaction with the nucleus, which is called the aiming distance.
Fig. 3.3 Path Deflection of-1α Particles in Coulomb Field of Nucleus
When α particles enter the Coulomb field of the nucleus, some kinetic energy will be converted into Coulomb potential energy. Let the initial kinetic energy and angular momentum of α particles be E and L, respectively. According to the law of conservation of energy and momentum:
( 1)
(2)
From (1) and (2), it can be proved that the path of α particles is hyperbola, and the deflection angle θ has the following relationship with the aiming distance b:
(3)
That is all right
(4)
This is the Coulomb scattering deflection angle formula.
(2) Rutherford scattering formula
There is a parameter b in the above Coulomb scattering deflection formula that cannot be measured in the experiment, so we must find a measurable quantity to replace the measurement of parameter B.
In fact, the aiming distance between alpha particles and atoms can be large or small, but the scattering of a large number of alpha particles has certain statistical laws. It can be seen from the scattering formula (4) that there is a corresponding relationship with B. The larger B is, the smaller B is, as shown in Figure 3.3-2. Those alpha particles whose aiming distance is between b and must scatter to the angle between θ and. Therefore, all α particles passing through the ring with B as the inner radius and B as the outer radius shown in the figure must be scattered into a spatial cone between angles.
Fig. 3.3-2 Relationship between Scattering Angle of α Particles and Aiming Distance
Suppose the target is a very thin foil with a thickness of t and an area of s, then the probability that α particles are scattered by the target atoms in the direction range of Figure 3.3- 1, that is, the probability that α particles hit the ring, that is
(5)
If represented by a solid angle,
because
Then there is
(6)
In order to obtain the actual number of scattered α particles and compare it with the experiment, the number of atoms on the target and the number of incident α particles must also be considered.
Because there are many nuclei in the thin foil, each nucleus corresponds to such a ring. If there is no shielding between nuclei, the number of atoms in unit volume is, the number of atoms in volume is, and the scattering angle of alpha particles hitting these rings is, then the probability that an alpha particle hits the thin foil and scatters in the sum direction is.
If n alpha particles are vertically incident on the thin foil per unit time, the alpha particles measured in the direction and solid angle per unit time are:
(7)
The differential scattering cross section formula is often used. The differential scattering cross section
Its physical meaning is the probability that when a particle (n= 1) is vertically incident on a unit area, it will be scattered by a target atom () in this area to a unit solid angle near the corner.
Therefore,
(8)
This is the famous Rutherford scattering formula.
Substituting each constant value, e represents the energy of the incident particle, and the formula is obtained:
(9)
Where, the unit of is, and the unit of e is MeV.
1. Experimental verification method of Rutherford theory
In order to verify Rutherford scattering formula, that is, to verify the nuclear structure, the core instrument used in the experiment is the detector.
Assuming that the solid angle of the sensitive plane of the detector to the target is, Rutherford scattering formula shows that the total number of α particles observed in a certain time interval should be:
( 10)
Where is the total number of alpha particles incident on the target during this time. Since all the formulas are measurable, the formula (10) can be compared with the experimental data. It can be seen from this formula that the number of α particles observed in the above aspects is related to the nuclear charge of the scattering target, the kinetic energy of α particles and the scattering angle.
Rutherford scattering formula (9) or (10) can be verified from the following aspects.
(1) Fixed the scattering angle, changed the thickness of the gold target, and verified the linear relationship between the scattering counting rate and the target thickness.
(2) Change the alpha particle source and the alpha particle energy, and verify the inverse square relationship between the scattering counting rate and the alpha particle energy.
(3) Change the scattering angle and verify the relationship between the scattering counting rate and the scattering angle. This is the most prominent and important feature of Rutherford scattering hit.
(4) Fixed scattering angle, using scattering targets with the same thickness but different materials, and verifying the square relationship between scattering counting rate and nuclear charge number of target materials. Because it is difficult to find scattering targets with the same thickness and the atomic number density needs to be corrected, this experiment is difficult.
This experiment only involves the third aspect, which is the most powerful verification of Rutherford's scattering theory.
3. Rutherford scattering experimental device
Rutherford scattering experimental device includes scattering vacuum chamber, electronic system and stepping motor control system. The mechanical structure of the experimental device is shown in Figure 3.3-3.
Figure 3.3-3 Mechanical Structure of Rutherford Scattering Experimental Device
Structure of (1) scattering vacuum chamber
The scattering vacuum chamber mainly includes radioactive source, scattering sample table, particle detector, stepping motor and rotating mechanism. The radioactive source is an or source, the main particle energy of the source is 0, and the main particle energy of the source is 0.
(2) Electronic system structure
In order to measure the differential scattering cross section of particles, it is necessary to measure the counting rate of particles emitted at different angles from Equation (9). The particle detector used is a gold-silicon barrier silicon (gold) detector. The particle detection system also includes a charge-sensitive preamplifier, a main amplifier, a counter, a detector bias power supply, a NIM box and a low-voltage power supply.
(3) Stepping motor and its control system
During the experiment, it is necessary to measure the counting rate of emergent particles with different scattering angles in vacuum, so it is necessary to change the scattering angles frequently. In this experimental device, the stepping motor is used to control the scattering angle, which makes the experimental process very convenient. You don't need to open the vacuum chamber to change the angle every time you measure the data of an angle, just control the stepping motor to rotate the corresponding angle outside the vacuum chamber; In addition, because the stepper motor has the characteristics of precise positioning, simple open-loop control can achieve the required precise control. E Rutherford et al., also known as Rutherford alpha particle scattering experiment. J.J. Tang Musun discovered that electrons revealed the internal structure of atoms, and put forward the raisin bun model of atoms in 1903. He believes that the positive charge and mass of an atom are connected, uniformly and continuously distributed in the atomic range, and electrons are embedded in it, which can slightly vibrate at its equilibrium position.
1909, Rutherford's assistants, H. Geiger and E. marsden, made an alpha particle scattering experiment at Rutherford's suggestion, and bombarded gold foil with collimated alpha rays. It is found that most α particles pass straight through the thin gold foil with little deflection, but the deflection angle of a few α particles is much larger than that predicted by Thomson model, and the deflection angle is about 1/8000. 19 1 1 year, Rutherford proposed nuclear models, in which the mass related to positive charge is concentrated in the center to form a nucleus, and electrons move around the nucleus outside the nucleus, from which the scattering formula of alpha particles is derived, which explains the large-angle scattering of alpha particles. Rutherford's scattering formula was later systematically verified by Geiger and marsden's improved experiments. According to the data of large angle scattering, it can be concluded that the upper limit of the nuclear radius is10-14m. This experiment initiated the study of atomic structure. The experimental results show that the vast majority of α particles still move in the original direction after passing through the gold foil, but a few α particles deflect greatly, and a few α particles deflect more than 90, and some even almost reach180 and bounce back, which is the scattering phenomenon of α particles.