History of Rutherford Experiment

In Ernest Rutherford's laboratory, Hans Geiger and Ernest Marsden (a 20 yr old undergraduate student) carried out experiments to study the scattering of alpha particles by thin metal foils. In 1909 they observed that alpha particles from radioactive decays occasionally scatter at angles greater than 90°, which is physically impossible unless they are scattering off something more massive than themselves. This led Rutherford to deduce that the positive charge in an atom is concentrated into a small compact nucleus. During the period 1911-1913 in a table-top apparatus, they bombarded the foils with high energy alpha particles and observed the number of scattered alpha particles as a function of angle. Based on the Thomson model of the atom, all of the alpha particles should have been found within a small fraction of a degree from the beam, but Geiger and Marsden found a few scattered alphas at angles over 140 degrees from the beam. Rutherford's remark "It was quite the most incredible event that ever happened to me in my life. It was almost as incredible as if you had fired a 15-inch shell at a piece of tissue paper and it came back and hit you." The scattering data was consistent with a small positive nucleus which repelled the incoming positively charged alpha particles. Rutherford worked out a detailed formula for the scattering (Rutherford formula), which matched the Geiger-Marsden data to high precision.

The source used in the Rutherford experiments was purifed radium contained in a thin-walled 1-mm diameter glass tube. The source strength was about 0.1 Curie, or about 4 billion nuclear decays per second. The alpha particles were allowed to pass through a small diaphragm and were directed toward a thin foil target. The detector was a small (10^-6 m²) zinc sulfide screen mounted a few centimeters away from the target. (Rohlf)

Rutherford Scattering Questions

	1. Why was the observation of large angle scattering of alpha particles surprising? 为什么观察到α粒子的大角度散射是令人惊讶的？
	2. Under what conditions can you get scattering at angles greater than 90 degrees? 在什么条件下可以得到大于90度的散射角？
	3. Besides the mass of the target, what else determines the scattering angle? 除了靶的质量之外，什么还决定了散射角？
	4. How can you determine the distance of closest approach to the target? 如何确定粒子接近靶的最近距离？
	5. What was the evidence of a new type of force from the observation of the scattering? 观察到的散射现象是什么证据表明了一种新类型的力？

Geiger-Marsden Data on Alpha Scattering

Geiger and Marsden showed that the number of scattered alpha particles as a function of scattering angle was consistent with a small, concentrated positive nucleus. To angles above 140 degrees, the nucleus appeared as a point positive charge, so this data did not measure the nuclear size. When the scattering departed from that predicted from Coulomb's law, it could be inferred that another force was coming into play and you could claim to have "hit" the nucleus. At 140 degrees, they still hadn't hit it. 盖革和马斯登证明，散射角与散射α粒子数的关系与一个小而集中正电荷的核是一致的。对于大于140度的角度，核表现为一个点正电荷，因此这些数据并未测量核的大小。当散射偏离库仑定律预测的范围时，可以推断另一种力起作用，你可以说已经“击中”了核。在140度时，他们仍然没有击中它。 Sketch of experiment 实验示意图

Since they had used the most energetic alpha particles at their disposal, 7.7 MeV, and still hadn't seen the departure from Coulomb scattering which would signal a direct interaction with the nucleus, they had to look for other alternatives to get a measure of nuclear size. This led to a famous remark by Rutherford to his graduate students "There is no money for apparatus -. we shall have to use our heads!"(Keller) The form that "using their heads" took was the study of lighter target nuclei, and finally the use of aluminum target nuclei yielded measurable direct backscatter of alpha particles, at least establishing an upper bound for the nuclear size.

Conditions for large angle scattering

Regardless of the nature of the force in an elastic collision, to get a scattering angle greater than 90 degrees, the target must be more massive than the projectile.

Determining the Impact Parameter

Besides the masses of the target and projectile, the scattering angle depends upon the force and upon the impact parameter. The impact parameter is the perpendicular distance to the closest approach if the projectile were undeflected.

Show 显示	For the special case of alpha scattering from a nucleus of atomic number Z, the relationship is more convenient in the form to the right. 对于原子序数为Z的核的α粒子散射特殊情况，更方便的形式如右所示。

For alpha particle scattering off a nucleus of atomic number Z =, an observed scattering angle of degrees for an alpha particle of kinetic energy MeV corresponds to an impact parameter of

b = x10^ m = fermi.

Determining the closest approach to the nucleus amounts to calculating the minimum distance for the hyperbolic orbit which is produced by the coulomb repulsive force. The expression for the closest approach as a function of the impact parameter b is given by:

Which has a limit for back-scattering which is just determined by setting the initial kinetic energy equal to the final potential energy. This corresponds to stopping the projectile and sending it backward, so at its closest approach, all the energy is in electric potential energy. 哪种情况的反散射有极限，其极限由将初始动能等于最终势能来确定。这对应于使弹体停止并反向发射，因此在最接近时，所有能量都转化为电势能。

The closest approach for the trajectory described above is then

上述轨迹的最近接近点则是

rmin=x10^ m = fermi. r min = x10^ m = fermi.（专名或术语） 中文译文中的待填/计算数值依次对应：1：rmb 2：rmp 3：rmf。实际数值以上方原输入框为准。

确定粒子接近核的最近距离，相当于计算由库仑斥力产生的双曲线轨道的最小距离。该最近距离作为冲击参数b的函数表达式为：

Rutherford scattering was the first method used to measure the size of nuclei. More precise measurements are made with electron scattering, and it was discovered that the density of nuclei is approximately constant. This has made possible the modeling of nuclear radii from just their mass numbers. As a comparison for the calculated parameters above, if we assume a mass number of twice Z above, an approximate nuclear radius can be calculated.

estimated nuclear radius for A=2Z is r = fermi.

This will always be an underestimate because of the neutron excess of heavy nuclei, but a more accurate value can be obtained by using the nuclear mass in the nuclear radius relationship.

这将始终是一个低估，因为重核中中子过剩，但可以通过使用核质量来获得更准确的值。

卢瑟福散射是测量核尺寸的第一种方法。更精确的测量则使用电子散射，发现核的密度近似是恒定的。这使得仅通过核的质数就能建模核半径成为可能。作为上述计算参数的比较，如果假设质量数是Z的两倍，可以估算出核半径。对于A=2Z的情况，核半径约为r = fermi。

中文译文中的待填/计算数值依次对应：1：nr。实际数值以上方原输入框为准。

The default calculation above will be the calculation of the impact parameter b and the radius of closest approach. However, if you substitute a number for the radius of closest approach, it will calculate the kinetic energy necessary to produce that value, given the angle and other parameters.