Lithium atom scattering cross section calculation method, device and system and storage medium
By calculating the ultrafine structure and isotopic abundance of lithium atoms, the problem of traditional lidar in detecting the density of lithium atoms in the middle and upper atmosphere has been solved, enabling accurate detection of lithium atom density and environmental monitoring of space activities.
Patent Information
- Application Number
- CN202511836055.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-08
- Publication Date
- 2026-02-13
AI Technical Summary
Traditional lidar has difficulty in effectively detecting the density of lithium atoms in the middle and upper atmosphere, especially because the density of lithium atoms is low and the resonant scattering signal is weak, making it significantly susceptible to background noise interference. Existing technologies have insufficient calculation of the lithium atom scattering cross section, which affects the accuracy of density calculation.
A method for calculating the scattering cross section of lithium atoms is provided. Considering the hyperfine structure and isotopic abundance of lithium atoms, the method calculates the relationship between the scattering cross section and frequency of lithium atoms by calculating the relative transition intensity, offset frequency, Doppler broadening and absorption cross section of each transition line of the D2 line of lithium atoms. The method also considers the abundance ratio of lithium isotopes in nature to calculate the total scattering cross section.
It enables precise detection of lithium atom density in the middle and upper atmosphere, improves detection accuracy and signal-to-noise ratio, quantifies the environmental footprint of space activities, and provides data support for the formulation of environmental protection standards.
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Figure CN121521814A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of fluorescence scattering lidar for detecting atomic density, specifically relating to a method, device, system, and storage medium for calculating the scattering cross section of lithium atoms in the middle and upper atmosphere based on fluorescence scattering lidar. Background Technology
[0002] When meteoroids enter Earth's atmosphere, high-speed friction causes their metallic components to vaporize and ionize, forming a "metallic layer" diffused in the middle and upper atmosphere (80-105 km altitude). These metallic components are ideal "tracers" for studying the upper and middle atmosphere. Scientists have been observing metallic components in the atmosphere for nearly a century. The earliest observation was of sodium (Na) atmospheric glow about 100 years ago [Slipher, 1929]. Subsequently, sodium atoms were first observed using sodium resonance lidar [Bowman et al., 1969], leading to the development of sodium atom fluorescence scattering lidar detection. Since then, various lidars for iron, potassium, calcium, nickel, etc., have been developed, achieving numerous results in studying the dynamics and thermodynamic processes of the upper and middle atmosphere, as well as the coupling mechanisms between atmospheric layers. Sodium atoms have become a widely used target for scientists due to their high density, large backscattering cross section, and easily obtainable wavelengths. With the continuous advancement of observation technology, the single-pulse energy of lasers has been continuously increased, and the aperture of telescopes has been gradually enlarged, allowing for the precise detection of metallic elements that were previously difficult to detect.
[0003] With the development of aerospace, space activities (such as spacecraft launches and recoveries) release metallic components into the atmosphere, causing abnormal fluctuations in their concentration. These signals can serve as important indicators for monitoring space activities. Lithium atoms, as a crucial material for spacecraft, can be used to quantify the environmental footprint of space activities by monitoring changes in their concentration. This monitoring can also provide data support for the development of environmental standards. Monitoring persistent areas of abnormal lithium concentration can also be linked to specific types of debris, providing a basis for debris cleanup strategies. Lithium atoms are a trace component of the metallic layer in the middle and upper atmosphere. Their abundance is more than two orders of magnitude lower than that of sodium. Furthermore, lithium atoms are lightweight and diffuse rapidly in the atmosphere, making their distribution more sensitive to fluctuations in the mesosphere (such as tidal waves and gravity waves). Therefore, detecting lithium atom concentrations in the middle and upper atmosphere is of great significance. However, the low density and weak resonant scattering of lithium atoms make them susceptible to significant background noise interference, hindering effective detection by traditional lidar. Previous research in this area has been relatively limited.
[0004] Fluorescent scattering lidar can be used to accurately detect the density of lithium atoms, among which... The effective backscattering cross section of metal atoms and ions is an indispensable condition for calculating the density of metal atoms and ions, and it directly affects the accuracy of the density calculation. Due to the limited detection of lithium atoms, few articles have considered the characteristics of lithium atoms to perform detailed calculations of the lithium atom scattering cross section. Similar to the calculation method for sodium atoms, the calculation of the lithium atom scattering cross section must take into account its double fine structure, and in addition, the abundance ratio of different lithium isotopes must also be considered. Summary of the Invention
[0005] To address the problems existing in the prior art, this invention provides a method, apparatus, system, and storage medium for calculating the lithium atom scattering cross section.
[0006] To achieve the above objectives, the present invention provides the following solution: A method for calculating the lithium atom scattering cross section includes: Step S1: Calculate the relative transition intensities of each transition line in the lithium atom D2 line; lithium atom D2 includes: 7 Li's D2 line and 6 Li's D2 line; Step S2: Calculate the offset frequency of each transition line relative to the center line; Step S3: Calculate Doppler broadening based on each line frequency; Step S4: Calculate the absorption cross section at the peak based on Doppler broadening; Step S5: Based on the absorption cross section at the peak and the relative transition intensities of each transition line of the lithium atom D2 line, obtain... 7 The relationship between the scattering cross section of Li and frequency and 6 The relationship between the scattering cross section of Li and frequency; Step S6, 7 The relationship between the scattering cross section of Li and frequency and 6 The total scattering cross section is obtained by multiplying the scattering cross section of Li by the frequency, multiplying each frequency by its respective isotope abundance, and then summing the results.
[0007] In step S2, the offset frequency of each transition line relative to the center line is calculated based on the D2 line hyperfine structure of lithium atoms.
[0008] In step S6, in nature 6 The natural abundance of Li is approximately 7.5%. 7 The natural abundance of Li is approximately 92.5%, and its total scattering cross section is: .
[0009] The present invention also provides a lithium atom scattering cross section calculation device, comprising: The first processing module is used to calculate the relative transition intensities of each transition line in the lithium atom D2 line; the lithium atom D2 includes:7 Li's D2 line and 6 Li's D2 line; The second processing module is used to calculate the offset frequency of each transition line relative to the center line. The third processing module is used to calculate Doppler broadening based on each line frequency; The fourth processing module is used to calculate the absorption cross section at the peak based on Doppler broadening; The fifth processing module is used to obtain, based on the absorption cross-section at the peak and the relative transition intensities of each transition line of the lithium atom D2 line, the following: 7 The relationship between the scattering cross section of Li and frequency and 6 The relationship between the scattering cross section of Li and frequency; The sixth processing module is used to... 7 The relationship between the scattering cross section of Li and frequency and 6 The total scattering cross section is obtained by multiplying the scattering cross section of Li by the frequency, multiplying each frequency by its respective isotope abundance, and then summing the results.
[0010] The second processing module calculates the offset frequency of each transition line relative to the center line based on the D2 line hyperfine structure of lithium atoms.
[0011] The sixth processing module calculates the total scattering cross section as follows: .
[0012] The present invention also provides a lithium atom scattering cross section calculation system, comprising: a memory and a processor, wherein the memory stores a computer program executed by the processor, and the computer program executes a lithium atom scattering cross section calculation method when executed by the processor.
[0013] The present invention also provides a storage medium storing a computer program, which executes a method for calculating the lithium atom scattering cross section when running.
[0014] For atmospheric metallic layers present in the mesopause region, the interaction between the laser and metal atoms and molecules is resonant fluorescence scattering. When using lidar to detect the concentration of metallic elements in the atmosphere... The effective backscattering cross section of a metal atom ion is an indispensable condition for calculating the density of metal elements. This invention calculates the scattering cross section of lithium atoms in the middle and upper atmosphere based on fluorescence scattering lidar. Considering the special hyperfine structure of lithium atoms, the backscattering cross section of lithium atoms is made more accurate. The laser wavelength usually selected for detecting lithium atoms in the middle and upper atmosphere is the D2 line wavelength of Li atoms, which is from... 2 S 1 / 2 Energy level transition to 2 P 3 / 2The wavelength of the energy level, since the hyperfine structure D2 line is further divided into multiple transition lines, is first calculated as follows: 7 The relative oscillator strengths of the six Li transition lines are plotted, showing the relationship between the frequency and absorption cross section of each line. Multiplying these values by the transition weight of each line and summing them gives the result. 7 The relationship between the total scattering cross section of Li and frequency is calculated in the same way. 6 The relationship between the Li scattering cross section and frequency. In nature... 6 The natural abundance of Li is approximately 7.5%. 7 The natural abundance of Li is approximately 92.5%, and its isotopic abundance needs to be considered. 7 Li and 6 The total scattering cross section is obtained by multiplying the two Li function graphs by their respective isotopic abundances and then adding them together. Attached Figure Description
[0015] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0016] Figure 1 This is a flowchart of the lithium atom scattering cross section calculation method according to an embodiment of the present invention; Figure 2 for 7 A schematic diagram of the double fine structure of the D2 line of Li; Figure 3 for 6 A schematic diagram of the double fine structure of the D2 line of Li; Figure 4 for 7 A schematic diagram of the total absorption cross section of Li and its absorption cross section along its six ultra-fine transition lines; Figure 5 for 6 A schematic diagram of the total absorption cross section of Li and the absorption cross sections of its five hyperfine transition lines; Figure 6 This is a schematic diagram of the total scattering cross section of line D2. Detailed Implementation
[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0019] Example 1 like Figure 1 As shown, the present invention provides a method for calculating the lithium atom scattering cross section, comprising: Step S1: Calculate the relative transition intensities of each transition line in the lithium atom D2 line; lithium atom D2 includes: 7 Li's D2 line and 6 Li's D2 line; Step S2: Calculate the offset frequency of each transition line relative to the center line; Step S3: Calculate Doppler broadening based on each line frequency; Step S4: Calculate the absorption cross section at the peak based on Doppler broadening; Step S5: Based on the absorption cross section at the peak and the relative transition intensities of each transition line of the lithium atom D2 line, obtain... 7 The relationship between the scattering cross section of Li and frequency and 6 The relationship between the scattering cross section of Li and frequency; Step S6, 7 The relationship between the scattering cross section of Li and frequency and 6 The total scattering cross section is obtained by multiplying the scattering cross section of Li by the frequency, multiplying each frequency by its respective isotope abundance, and then summing the results.
[0020] As one embodiment of the present invention, in step S1, the transition intensity of each line and the electric dipole matrix element are... It is proportional to the square of . This indicates the coupling of two hyperfineon levels. and (in , Excited state, F, The matrix element (referring to the ground state).
[0021] To calculate the electric dipole matrix elements, the matrix elements can be represented as the product of the Clebsch-Gordan coefficients and the reduced matrix elements. ; in, For the reduced matrix elements. Kleibusch-Gordon coefficient The Kleibusch-Gordon coefficient is represented using the Wigner 3-j notation: ; Where F is the hyperfine total angular momentum quantum number of the ground state (7 The values of LiD2 are 1, 2, 6 LiD2 can take values of 1 / 2 and 3 / 2. F' is the magnetic quantum number of the hyperfine total angular momentum of the ground state, with values ranging from (-F, -F + 1, ..., F); F' is the hyperfine total angular momentum quantum number of the excited state. 7 The values of LiD2 are 0, 1, 2, and 3. 6 The values of LiD2 are 1 / 2, 3 / 2, and 5 / 2. The magnetic quantum number of the hyperfine total angular momentum of the excited state is denoted by , with values ranging from (-F', -F' + 1, ..., F'); q is the quantum number identifier of the electric dipole moment component, used to describe the component direction of the electric dipole moment in the spherical coordinate system basis set. (The values of q, 0, 1, and -1 correspond to...) ); Let Wigner 3-j be the notation, which describes the selection rule for angular momentum coupling.
[0022] It can be decomposed into ; in, The elements of the total angular momentum reduction matrix are... 7 Li and 6 Li's D2 line total angular momentum reduction matrix element It is a constant value; This is the Wigner 6-j notation, where J is the total angular momentum quantum number of the electron and I is the spin quantum number of the atomic nucleus.
[0023] The ratio of the relative oscillator strengths of the transition lines is the electric dipole matrix element. The ratio of the squares of, in 7 Taking the LiD2 line as an example, for calculation The F=1 energy level transitions to F'=0,1,2 and The F=2 energy level transitions to The relative oscillator strengths of the six transition lines F'=1,2,3 need to be determined by considering the three transitions of each transition line ( )of Adding the squares of the values and then normalizing them yields the lithium atom. 7 The relative oscillator strengths of each of the six LiD2 lines, 1 / 16, 5 / 32, 5 / 32, 1 / 32, 5 / 32, and 7 / 16, are shown in Table 1. Table 1
[0024] Calculate in the same form 6The relative oscillator strengths of the five lines of the LiD2 line are shown in Table 2. Table 2
[0025] In one embodiment of the present invention, in step S2, based on the D2 line hyperfine structure of lithium atoms, the offset frequency of each transition line relative to the center line is calculated, thereby calculating the frequency of each line. ; 7 Li and 6 The double fine structure of Li's D2 line, as shown in... Figure 2 , 3 As shown.
[0026] Frequency of each line in the ultra-fine structure Equals the D2 line frequency minus the offset frequency ; The calculation results for each line frequency are shown in Tables 3 and 4: Table 3 ( 7 Li)
[0027] Table 4 ( 6 Li)
[0028] As one embodiment of the present invention, in step S3, Doppler broadening is calculated based on each line frequency, using the following formula: ; Where v0 is the resonance fluorescence center frequency of the atom or ion; k b is Boltzmann constant; c is the speed of light; M is the absolute mass of an atom or ion; T is the absolute temperature, specifically calculated based on measured temperature. In this invention, the average temperature at 100 km is 200 K.
[0029] In one embodiment of the present invention, in step S4, the absorption cross section at the peak value can be calculated based on Doppler broadening, i.e. ; Where e is the electron charge; ε0 is the vacuum permittivity; m e denoted as electron mass; c is the speed of light; f (Oscillator Strength) is the oscillator strength of a metal atom or ion.
[0030] As one embodiment of the present invention, in step S5, based on the absorption cross-section at the peak value... Substitute the following formula relating the incident photon frequency to the absorption cross section: ; Plot using MATLAB 7 The relationship between the absorption cross-section and frequency of the six LiD2 transition lines, multiplied by their respective relative oscillator strengths. Then, by adding the graphs of the six functions together, we get the graph showing the relationship between the total incident photon frequency and the absorption cross section.
[0031] ; 6 The absorption cross section of Li is the sum of the five transition lines of D2. ; 7 The total absorption cross section of Li and the absorption cross sections of its six ultrafine transition lines are as follows: Figure 4 As shown, it can be seen 7 The maximum absorption cross section of Li is approximately 0.63 × 10⁻⁶. -16 m 2 .
[0032] 6 The total absorption cross section of Li and the absorption cross sections of its five hyperfine transition lines are as follows: Figure 5 As shown, it can be seen 6 The maximum absorption cross section of Li is approximately 0.72 × 10⁻⁶. -16 m 2 .
[0033] In nature 6 The natural abundance of Li is approximately 7.5%. 7 The natural abundance of Li is approximately 92.5%. Its isotopic abundance needs to be considered. Therefore, the formula for calculating its absorption cross-section is as follows: ; Where I(A) represents the isotopic abundance; N represents the total number of transition lines in the hyperfine structure; f is the frequency of the i-th transition line; i Let be the relative oscillator strength of the i-th transition line.
[0034] Based on the above relationships, the function graph represented in MATLAB is as follows: Figure 6 As shown.
[0035] Example 2 The present invention also provides a lithium atom scattering cross section calculation device, comprising: The first processing module is used to calculate the relative transition intensities of each transition line in the D2 line of lithium atoms; 7 Li's D2 line and 6 Li's D2 line; The second processing module is used to calculate the offset frequency of each transition line relative to the center line. The third processing module is used to calculate Doppler broadening based on each line frequency; The fourth processing module is used to calculate the absorption cross section at the peak based on Doppler broadening; The fifth processing module is used to obtain, based on the absorption cross section at the peak and the relative oscillator strength of each transition line of the lithium atom D2 line, the following: 7 The relationship between the scattering cross section of Li and frequency and 6 The relationship between the scattering cross section of Li and frequency; The sixth processing module is used to... 7 The relationship between the scattering cross section of Li and frequency and 6 The total scattering cross section is obtained by multiplying the scattering cross section of Li by the frequency, multiplying each frequency by its respective isotope abundance, and then summing the results.
[0036] In one embodiment of the present invention, the second processing module calculates the offset frequency of each transition line relative to the center line based on the D2 line hyperfine structure of lithium atoms. In one embodiment of the present invention, the sixth processing module calculates the total scattering cross section as follows: .
[0037] Example 3 The present invention also provides a lithium atom scattering cross section calculation system, comprising: a memory and a processor, wherein the memory stores a computer program executed by the processor, and the computer program executes a lithium atom scattering cross section calculation method when executed by the processor.
[0038] Example 4 The present invention also provides a storage medium storing a computer program, which executes a method for calculating the lithium atom scattering cross section when running.
[0039] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.
Claims
1. A method for calculating the scattering cross section of a lithium atom, characterized in that, include: Step S1: Calculate the relative transition intensities of each transition line in the D2 line of lithium atoms; The lithium atom D2 line includes: 7 Li's D2 line and 6 Li's D2 line; Step S2: Calculate the offset frequency of each transition line relative to the center line; Step S3: Calculate Doppler broadening based on each line frequency; Step S4: Calculate the absorption cross section at the peak based on Doppler broadening; Step S5: Based on the absorption cross section at the peak and the relative transition intensities of each transition line of the lithium atom D2 line, obtain... 7 The relationship between the scattering cross section of Li and frequency and 6 The relationship between the scattering cross section of Li and frequency; Step S6, 7 The relationship between the scattering cross section of Li and frequency and 6 The total scattering cross section is obtained by multiplying the scattering cross section of Li by the frequency, multiplying each frequency by its respective isotope abundance, and then summing the results.
2. The method for calculating the lithium atom scattering cross section as described in claim 1, characterized in that, In step S2, the offset frequency of each transition line relative to the center line is calculated based on the D2 line hyperfine structure of lithium atoms.
3. The method for calculating the lithium atom scattering cross section as described in claim 2, characterized in that, In step S6, in nature 6 The natural abundance of Li is approximately 7.5%. 7 The natural abundance of Li is approximately 92.5%, and its total scattering cross section is: 。 4. A lithium atom scattering cross section calculation device, characterized in that, include: The first processing module is used to calculate the relative transition intensities of each transition line in the D2 line of lithium atoms; Lithium atom D2 includes: 7 Li's D2 line and 6 Li's D2 line; The second processing module is used to calculate the offset frequency of each transition line relative to the center line. The third processing module is used to calculate Doppler broadening based on each line frequency; The fourth processing module is used to calculate the absorption cross section at the peak based on Doppler broadening; The fifth processing module is used to obtain, based on the absorption cross-section at the peak and the relative transition intensities of each transition line of the lithium atom D2 line, the following: 7 The relationship between the scattering cross section of Li and frequency and 6 The relationship between the scattering cross section of Li and frequency; The sixth processing module is used to... 7 The relationship between the scattering cross section of Li and frequency and 6 The total scattering cross section is obtained by multiplying the scattering cross section of Li by the frequency, multiplying each frequency by its respective isotope abundance, and then summing the results.
5. The lithium atom scattering cross section calculation device as described in claim 4, characterized in that, The second processing module calculates the offset frequency of each transition line relative to the center line based on the D2 line hyperfine structure of lithium atoms.
6. The lithium atom scattering cross section calculation device as described in claim 5, characterized in that, The sixth processing module calculates the total scattering cross section as follows: 。 7. A lithium atom scattering cross section calculation system, characterized in that, include: A memory and a processor, wherein the memory stores a computer program executed by the processor, the computer program performing the lithium atom scattering cross section calculation method as described in any one of claims 1-3 when executed by the processor.
8. A storage medium, characterized in that, The storage medium stores a computer program that, when executed, performs the lithium atom scattering cross section calculation method as described in any one of claims 1-3.