in order toexplainThe coordinate system must be selected for the position, speed and direction of the particle.stayFrame of referenceIn order to determine the position of a point in space, a set of orderly data selected according to the specified method is called "coordinates".The method of specifying coordinates in a problem is the coordinate system used in the problem.[1]Laboratory coordinate system is a commonly used coordinate system for experimental analysis and data processing, which reflects the direct description of experimental results.
Chinese name
Laboratory coordinate system
Foreign name
laboratory coordinates
Features
Direct reaction experiment results based on experimental device
Static relative to the laboratory (or experimental device)Coordinate system。All experimental results are obtained on the experimental device, so if you want to verify the correctness of the theory, you need to give the theoretical results in the laboratory coordinate system.If the theoretical calculation is not carried out in the laboratory coordinate system (for example, in the centroid coordinate system), the calculation results should be converted to the laboratory coordinate system in order to compare with the experimental results.[2]
Conversion relationship with centroid coordinate system
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First, find the velocity v of the center of mass in the laboratory systemc。According to the definition of the center of mass, the total momentum of the group of particles should be equal to the product of the total mass of the group of particles and the speed of the center of mass, which is obtained from Figure 1 (mone+mtwo）vc=mv1。From this, the velocity v of the center of mass relative to the laboratory system can be obtainedcEqual to vc=mvone/（mone+mtwo）。Because particle m1，mtwoIt is not subject to external force except interaction, so particle m1，mtwoThe total momentum of the particle group is conserved, that is, during the whole collision process, the particle m1，mtwoThe total kinetic energy of is always equal to monev1。Therefore, the centroid velocity v during the whole collision processcThe direction of is always parallel to the incident velocity v of the incident particle1，That is, the direction parallel to the x axis.
Figure 1 Collision Diagram in Centroid Coordinate System
Figure 2 Collision diagram under laboratory system
according toGalileo transformationThe velocity composition theorem is obtained, and the relationship between the incident velocity and the exit velocity of the incident particle and the target particle relative to the laboratory system and the centroid system can be obtained: vone=vone'+vc',0=vtwo'+vc,u1=u1'+vc,u2'=u2'+vc
From Figure 2
calculation
andcentroidSpeed relative to laboratory department
The scattering angle θ of the incoming and outgoing particles in the laboratory system is thus obtainedoneAnd in the centroid coordinate systemScattering angleThe relation of θ is tg θone=sinθ/(mone/mtwo+Cos θ), while the scattering angle θ of the target particle in the experimental coordinate systemtwoAnd the scattering angle θ in the center of mass coordinate system is tg θtwo=﹣sinθ/(1+cosθ)。[3]
