Alkali metal mixture ratio measuring method based on alkali metal absorption spectrum C6-C8-C10 model

Abstract

The invention relates to an alkali metal mixture ratio measurement method based on an alkali metal absorption spectrum C6-C8-C10 model, which comprises the following steps: calculating a potential energy curve based on a first principle, and improving an absorption spectrum Lorentz fitting model; and according to the optimized alkali metal absorption spectrum model, deducing to obtain a related formula for calculating the alkali metal density, and obtaining the proportion of the alkali metal mixture based on absorption spectrum light intensity and broadening information obtained by collision of alkali metal atoms and buffer gas. According to the method, the accuracy of acquiring the spectral information is improved, so that the density calculation of different alkali metals in the alkali metal elementary substance and the alkali metal mixture is optimized, and the accuracy of the alkali metal mixture ratio calculation is further improved.

Description

Technical Field

[0001] The present invention belongs to the field of optical detection technology, and specifically relates to a method based on the absorption spectrum of alkali metals C6-C8-C 10 Model alkali metal mixture ratio measurement method. Background Art

[0002] Atomic gas cells, core components of precision measuring instruments such as atomic gyroscopes, atomic magnetometers, and atomic clocks, encapsulate a certain amount of alkali metals or noble gases. When used in inertial measurement and sensitive magnetic field measurements, optical pumping can be used to polarize the alkali metal atoms within the gas cell, and indirectly polarize the nuclear spins of the noble gas atoms through spin-exchange collisions. If the gas cell contains two or more alkali metal atoms, on the one hand, the pump light polarizes one atom, which can then polarize another atom through spin-exchange collisions. Ultimately, through spin-exchange collisions with noble gas atoms, the nuclear spin of the other atom is hyperpolarized, thereby increasing the polarizability of the entire system. On the other hand, hybrid pumping technology can be used to allow light to interact with alkali metal atoms with a smaller optical depth. The mutual collisions of the alkali metal atoms polarize the alkali metal atoms with a larger optical depth, thereby controlling the light intensity gradient within a smaller range and avoiding the problem of uneven polarizability caused by the light intensity gradient. Among the many factors that affect hybrid pumping efficiency, precisely controlling the ratio of the two alkali metal mixtures can improve the uniformity and efficiency of polarization, affect the life of the gas chamber, and is of great significance to the performance improvement of precision measuring equipment such as magnetometers.

[0003] To improve the efficiency of mixed pumping, it is necessary to study the ratio of the alkali metal mixture in the gas chamber. For the study of the components within the gas chamber, quantum chemical calculation tools can be used to analyze and calculate the interaction states of the main particles in the gas chamber, thereby better understanding the interactions and energy changes between particles from a microscopic perspective. After decomposing and analyzing the particle interactions within the entire gas chamber, the impact of various interactions on the overall performance of the gas chamber can be comprehensively considered. Potential energy curves and absorption spectra are macroscopic representations of microscopic interactions. By analyzing them, information about the composition of the gas chamber can be obtained.

[0004] Existing research experiments on gas cell composition have primarily focused on single-alkali metal gas cells, studying the measurement of alkali metal and noble gas densities. Current methods for measuring alkali metal density primarily include Faraday magneto-optical effect detection, magnetic resonance linewidth, and interferometry. However, when two or more alkali metals (or mixed components) are present in the gas cell, existing technologies often struggle to distinguish subtle differences between the components. Furthermore, existing technologies often require the introduction of an external magnetic field to excite or manipulate atomic polarization in order to improve signal detection capabilities. However, this external magnetic field introduces additional interference effects, potentially leading to inaccurate measurement results at low concentrations or with subtle compositional changes. These factors contribute to low accuracy in calculating the ratio of alkali metal mixtures in low-concentration materials. Summary of the Invention

[0005] The purpose of the invention is to provide a method based on the absorption spectrum of alkali metals C6-C8-C 10 A method for measuring the proportion of an alkali metal mixture based on a model is provided, in order to solve at least one technical problem existing in the prior art.

[0006] Technical solution, based on alkali metal absorption spectrum C6-C8-C 10 A model alkali metal mixture ratio measurement method, including: S1, using quantum chemical calculation method to obtain the potential energy curve between alkali metal atoms and buffer gas atoms; S2, calculate the theoretical absorption spectrum based on the obtained potential energy curve and improve the Lorentz line shape of the absorption spectrum; S3: Based on the improved Lorentzian line shape of the absorption spectrum, an experimental device was built to obtain the absorption spectrum, and the pressure broadening and spectral intensity resulting from the collision of the alkali metal mixture with the buffer gas were fitted; S4, calculating the ratio information of the alkali metal mixture based on the obtained pressure broadening and spectral intensity.

[0007] According to one aspect of the present application, step S1 further comprises: S11, when the buffer gas is He, when the alkali metal atoms in the ground state or excited state collide with the buffer gas atoms in the gas chamber, the interaction between the atoms is expressed by C6-C8-C 10 The model is represented in the following basic form: V(R) = -C6 / R 6 -C8 / R 8 -C 10 / R 10 ; R is the distance between the two bodies; C6, C8, C 10 is the potential energy curve parameter; S12, based on C6-C8-C 10The NEVPT2 method is used to calculate the single point energy of the ground state and the first to third excited states of each point, and the potential energy curves of the ground state and excited state are obtained.

[0008] According to one aspect of the present application, when the potential energy curve is calculated using the NEVPT2 method, the CASSCF module is set to have an active electron number of 1, an active space size of 8, and a spin multiplicity of 2. A total of 10 excited states with energy from small to large are calculated, and the first four calculation results are taken.

[0009] According to one aspect of the present application, step S2 is further: Based on the potential energy curve and C6-C8-C 10 Model, perform potential energy curve fitting, and obtain potential energy curve parameters C6, C8, C 10 ; Based on this, the collision broadening is constructed through the Anderson-Talman collision model: γ(Δ)=n p v th 8πR th 2 I(ΔT d ); where v th =(2kT / μ) 1 / 2 The most probable rate is expressed as C6 in the potential energy curve parameter |C6|=R th 5 v th , then C8, C 10 They are: |C8|=(k1R th ) 7 v th ,|C 10 ∣=(k2R th ) 9 v th ; and T d =C6 1 / 5 v th -6 / 5 =R th / v th represents the characteristic collision duration; I(ΔT d ) is a dimensionless parameter related to the line shape derived from the collision broadening rate; when |ΔT d When ∣<1, γ(Δ) is written as γ(Δ)=γ(0)(1+p1ΔT d ); Based on this, the improved absorption spectrum Lorentz line shape is: I(Δ)=γ(0) (1+p1ΔT d ) / ((Δ-δ b ) 2 +γ 2 (0) / 4); where n p is the number density of buffer gas atoms, R this the characteristic distance, k is the Boltzmann constant, T is the temperature, μ is the reduced mass of the collision between atoms or molecules, Δ is the deviation between the laser frequency and the resonance frequency, ΔT d is the time scale of the collision effect relative to the spectral broadening, γ(0) is the basic line broadening, p1 is the correction factor, and δ b is the frequency shift of the Lorentz curve, k1 and k2 are correction coefficients.

[0010] According to one aspect of the present application, the correction coefficients k1 and k2 are based on C6-C8-C 10 Obtained by model fitting.

[0011] According to one aspect of the present application, step S3 further includes: Based on the improved Lorentzian line shape of the absorption spectrum, the optical depth OD and pressure broadening Ξ are obtained by fitting the absorption spectrum, and the density of the alkali metal element in the alkali metal mixture is calculated using the formula: N a =OD max ×Ξ / (2r e cfl); where r e is the classical electron radius, c is the speed of light, f is the oscillator strength, N a is the density of alkali metal a in the desired alkali metal mixture, l is the optical path length, OD max is the maximum optical depth, that is, the spectral light intensity.

[0012] According to one aspect of the present application, step S4 is further: If the mixture in the gas chamber consists of two alkali metals, the molar mass ratio of the alkali metal mixture, that is, the ratio information of the alkali metal mixture, is calculated based on Raoult's law and the density of the alkali metal element. The calculation formula is as follows: a / f b =N a (T s ) / (N s_a (T s )-N a (T s )); where f a =N a (T s ) / N s_a (T s ) is the molar mass of alkali metal a; f b =1-f a is the molar mass of alkali metal b; N s_a is the density of alkali metal element at the same temperature, T s is the indoor temperature.

[0013] According to one aspect of the present application, step S12 is further as follows: Based on C6-C8-C10 Model, obtain interatomic distance data and collision dynamic parameters, calculate time-distance mapping data; based on this, adjust the dynamic active space and obtain dynamic active space configuration data; Combined with the time-distance mapping data and the dynamic active space configuration data, transient polymorphic NEVPT2 calculations were performed to obtain a spatiotemporally resolved single-point energy dataset. This dataset was then time-averaged to obtain a time-averaged potential energy curve. The difference between the excited state and the ground state in the time-averaged potential energy curve is used to obtain the dynamically corrected difference potential data.

[0014] According to one aspect of the present application, calculating the time-distance mapping data includes: Based on the interatomic distance data, predetermined points and collision dynamic parameters are uniformly selected within a predetermined range; Based on the collision dynamics parameters, multiple collision moments corresponding to each point are calculated through a time parameterization algorithm to obtain time-distance mapping data.

[0015] According to one aspect of the present application, obtaining dynamic active space configuration data includes: Based on the time-distance mapping data and the preset electron correlation threshold, the active space size is adaptively determined by the orbital occupancy analysis algorithm: When R<4 Å, CAS (3, 12) was used to capture the strong correlation effect; When 4 Å ≤ R ≤ 8 Å, CAS (2, 10) was used; When R>8 angstroms, CAS (1,8) was used to obtain dynamic active space configuration data.

[0016] Beneficial effect: the present invention constructs a C6-C8-C 10 The model's potential energy curve and the spectral collision broadening and improved Lorentzian line shape derived from it can not only capture the information of a single component, but also obtain the molar ratio between alkali metal mixtures through quantitative fitting, while avoiding the interference of an external magnetic field on the results and improving measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is an embodiment of the present invention based on the alkali metal absorption spectrum C6-C8-C 10 Flow chart of the steps of the model alkali metal mixture ratio measurement method.

[0018] Figure 2 This is a flowchart of step S1 of an embodiment of the present invention.

[0019] Figure 3 Graph showing the potential difference between the first excited state and the ground state in an embodiment of the present invention.

[0020] Figure 4 This is a flowchart of step S12 in an embodiment of the present invention. DETAILED DESCRIPTION

[0021] like Figure 1 As shown, the present invention discloses a method based on the alkali metal absorption spectrum C6-C8-C 10 The method for measuring the proportion of an alkali metal mixture of the model comprises the following steps: S1, using quantum chemical calculation method to obtain the potential energy curve between alkali metal atoms and buffer gas atoms; S2, calculate the theoretical absorption spectrum based on the obtained potential energy curve and improve the Lorentz line shape of the absorption spectrum; S3: Based on the improved Lorentzian line shape of the absorption spectrum, an experimental device was built to obtain the absorption spectrum, and the pressure broadening and spectral intensity resulting from the collision of the alkali metal mixture with the buffer gas were fitted; S4, calculating the ratio information of the alkali metal mixture based on the obtained broadening and light intensity information.

[0022] This embodiment takes a mixed gas chamber filled with a certain ratio of Rb (rubidium) and Cs (cesium) and a buffer gas of 600Torr He (helium) as an example. The gas chamber is a spherical gas chamber with a size of 1.2 cm, and the gas chamber is not filled in a liquid nitrogen environment.

[0023] First, to ensure that pressure broadening dominates the absorption spectrum, the buffer gas density must be greater than 400 Torr. In this example, 600 Torr of He is used. At this point, Doppler broadening and natural broadening caused by atomic thermal motion can be ignored. The laser is tuned to the Rb D1 line for measurement. The temperature is raised to different levels using a temperature-controlled TCM-M207 and maintained stable throughout each measurement. A host computer program is used to modulate and output a triangular wave, thereby controlling the laser's wavelength scanning range and acquiring absorption spectrum data.

[0024] In order to obtain a more accurate representation of the potential energy curve from the potential energy curve, and thus more accurately describe the energy changes in atomic collisions, the NEVPT2 (N-Electron Valence state Perturbation Theory 2nd order) method is used in the calculation of the potential energy curve between atoms. The number of active electrons is 1, the active space size is 8, and the spin multiplicity is set to 2. For more accurate calculations, 10 excited states from small to large are calculated, and the first four required are taken. Through multiple single-point energy calculations at different distances, the potential energy curves of the ground state and the first, second, and third excited states of the alkali metal atom Rb and the buffer gas atom He are obtained. The difference potential fitting curve between the first excited state and the ground state is shown as follows: Figure 3Compared to the commonly used PBE0 (Perdew-Burke-Ernzerhof hybrid functional) and TDDFT (Time-Dependent Density Functional Theory) methods for calculating potential energy curves, NEVPT2 introduces multiple reference states to more accurately describe electronic behavior, especially weak interactions related to electrons, making the calculation of the long-range attractive potential energy more accurate.

[0025] In the process of fitting the potential energy curve, only considering C6 related to the long-range interaction is not able to describe the form of the potential energy curve well, and the goodness of fit (rsquare) is only about 0.7. Considering adding C8, which is also related to the distance R between the two bodies, C 10 Item: |C6|=R th 5 v th ; Then: |C8|=(k1R th ) 7 v th = k1 7 R th 2 C6;|C 10 ∣=(k2R th ) 9 v th =k2 9 R th 4 C6. Among them R th is the characteristic distance, k1 and k2 are correction coefficients, v th is the most probable rate.

[0026] By adding the dispersion term, C8, C 10 The potential energy curve calculated in step S1 can be expressed more accurately and clearly through parameters, so that more long-range dispersion effects can be considered in the process of calculating the theoretical absorption spectrum and correcting the fitting formula, thereby improving the accuracy of the calculation. 10 The model is fitted and the model formula is as follows: V(R) = -C6 / R 6 -C8 / R 8 -C 10 / R 10 ; Where V(R) is the energy of the potential energy curve, R is the distance between the two bodies, C6, C8, C 10is the potential energy curve parameter. Based on the fitting results obtained from the above model formula, the theoretical absorption spectrum and the modified fitting formula of the potential energy curve are calculated.

[0027] From the Anderson-Talman theory, we know that the absorption line shape can be expressed as a generalized Lorentzian line related to the detuning-related collision broadening rate γ(Δ) as follows: A(Δ)= (γ Nat +γ(Δ)) / (2π×(Δ-δ b ) 2 +(γ Nat +γ(0)) 2 / 4); where γ Nat is the natural broadening provided by the intrinsic properties of atoms, γ(0) is the basic line broadening; δ b is the frequency shift; Since the gas chamber used in the experiment is filled with 600 Torr of He, the natural broadening can be ignored. γ(Δ) is the broadening caused by collision. γ(Δ)=〈n p v∫0 ∽ 2πbdb∣∫ -∽ ∽ dtω d [R(t)]exp{i(Δt-∫ -∽ t dt1ω d [R(t1)])}| 2 〉; Where 〈 〉 represents the integral of v, n p is the number density of buffer gas atoms, t is time, R(t) is the motion trajectory of the perturbed atoms, Δt is the time difference, v is the relative velocity of the colliding atoms; b is the collision parameter, d is the difference operator, i is the imaginary unit, t1 is the time variable parameter, ω d is the angular frequency difference.

[0028] Let tanφ = vt1 / b; 1 / cos 2 φdφ=v / bdt1; sinφ=vt1 / sqrt(b 2 +v 2 t1 2 ); cosφ=b / sqrt(b 2 +v 2 t1 2 );but: ∫ -∽ t dt1ω d [R(t1)] = -∫0 θ ∣C6∣cos 4φ / (b 5 v)-|C8|cos 6 φ / (b 7 v)-|C 10 ∣cos 8 φ / (b 9 v)dφ; Let R th =(|C6| / v th ) 1 / 5 is the collision radius, v th =(2kT / μ) 1 / 2 is the most probable rate, T is the temperature, k is the Boltzmann constant, μ is the reduced mass of the collision between atoms or molecules, then the collision time T d T d =R th / v th =|C6| 1 / 5 v th -6 / 5 ; Set the dimensionless parameter u=v / v th , r=b / R th ,|C8|=(k1R th ) 7 v th ,|C 10 ∣=(k2R th ) 9 v th ,but: ∫ -∽ t dt1ω d [R(t1)] = -∫0 θ cos 4 φ / (ur 5 ) – k1 7 cos 6 φ / (ur 7 ) – k2 9 cos 8 φ / (ur 9 )dφ; The real part of the exponential is: Re[exp{i(Δt-∫ -∽ t dt1ω[R(t1)])}]=cos(Δt-∫ -∽ t dt1ω[R(t1)])=cos[ψ(θ)]; where ψ(θ)=ΔT d rtanθ / u+W6(θ) / (ur 5 )+k1 7 W8(θ) / (ur7 )+k2 9 W 10 (θ) / (ur 9 ); where ΔT d is the time scale of the collision effect relative to the spectral broadening, θ is the maximum angle during the collision process; φ is a substitution variable used to convert the time integral into the angle integral; W6(θ), W8(θ), and W10(θ) represent the integrals for different powers of φ, that is: W6(θ)= ∫0 θ cos 4 φdφ=3θ / 8+sin2θ / 4+sin4θ / 32; W8(θ)= ∫0 θ cos 6 φdφ=5θ / 16+sin2θ / 4+3sin4θ / 64-sin 3 2θ / 48; W10(θ)= ∫0 θ cos 8 φdφ=35θ / 125+7sin2θ / 32+7sin4θ / 128+sin6θ / 96+sin8θ / 1024; The final pressure broadening formula is: γ(Δ)=〈8πn p v th 2 R th 2 / v×∫0 ∞ r -9 dr∣(∫0 π / 2 cos 4 θdθ+∫0 π / 2 k1 7 cos 6 θdθ / r 2 +∫0 π / 2 k2 9 cos 8 θdθ / r 4 )cos[ψ(θ)]∣ 2 〉; Where 〈〉 represents the averaging of the velocity v.

[0029] The calculation can be simplified to the dimensionless parameter I(ΔT d ), that is: γ(Δ)=n p v th 8πR th 2 I(ΔT d ); I(ΔTd )=4 / sqrt(π) ×∫0 ∞ ue -u2 du∫0 ∞ r -9 dr∣∫0 π / 2 (cos 4 θ+k1 7 cos 6 θ / r 2 +k2 9 cos 8 θ / r 4 )cos[ψ(θ)]dθ∣ 2 ; By decomposing the triple integral, I(ΔT d ) and ΔT d The linear relationship between them is: I(ΔT d ) =0.3382-0.1859ΔT d ; Then we can get the broadening γ(Δ)= γ(0)(1-0.5496ΔT d ). The above-mentioned C6-C8-C 10 The detuning broadening of the model is taken into account in the existing Lorentz fitting formula, replacing the fixed broadening in the standard fitting formula that is independent of the detuning. The specific form of the modified fitting formula is as follows: A(Δ)=1 / 2π×γ(0) (1-0.5496ΔT d ) / ((Δ-δ b ) 2 )+ γ 2 (0) / 4); where δ b is the frequency shift of the Lorentz curve. The above modified fitting formula can be used to fit the absorption spectrum more accurately.

[0030] Based on the absorption spectrum fitting parameters obtained by the more accurate correction fitting formula, the alkali metal density can be more accurately calculated using the absorption spectrum method based on the spectral coefficient. Specifically, the following formula can be used for calculation: Optical depth OD∝ΞN a r e cfl; where Ξ is the pressure broadening, N a is the density of alkali metal element, l is the length of the gas chamber, and the alkali metal density of alkali metal element under different temperature conditions can be calculated based on the modified fitting formula according to the absorption spectrum of alkali metal element of inert gas with the same density, that is, the following formula is also used for calculation: N s_a =OD max ×Ξ / (2r e cfl).

[0031] At the same time, combined with the alkali metal Rb density in the alkali metal mixture chamber calculated in the above steps, based on Raoult's law, the molar ratio of the alkali metal mixture can be calculated as follows: a =N a (T s ) / N s_a (T s );f b =1-f a ;f a / f b =N a (T s ) / (N s_a (T s )-N a (T s )); where f a is the molar proportion of one alkali metal, f b is the molar proportion of another alkali metal component, and the corresponding alkali metal mixture ratio can be obtained from the above formula.

[0032] Measurements were performed at 353K-383K for two Rb elemental gas chambers, namely, chamber 1, chamber 2, and chamber 3 for mixed gas. The absorption spectra were fitted. The final alkali metal mixture ratio is shown below: When the temperature is 353K, the calculation results of gas chamber 1 and gas chamber 3 are 0.7575, and the calculation results of gas chamber 2 and gas chamber 3 are 0.7826; when the temperature is 363K, the calculation results of gas chamber 1 and gas chamber 3 are 0.7506, and the calculation results of gas chamber 2 and gas chamber 3 are 0.7252; when the temperature is 373K, the calculation results of gas chamber 1 and gas chamber 3 are 0.7714, and the calculation results of gas chamber 2 and gas chamber 3 are 0.7460; when the temperature is 383K, the calculation results of gas chamber 1 and gas chamber 3 are The calculated results of gas chamber No. 1 and gas chamber No. 3 are 0.7386, and the calculated results of gas chamber No. 2 and gas chamber No. 3 are 0.7139; when the temperature is 393K, the calculated results of gas chamber No. 1 and gas chamber No. 3 are 0.7499, and the calculated results of gas chamber No. 2 and gas chamber No. 3 are 0.7209; when the temperature is 403K, the calculated results of gas chamber No. 1 and gas chamber No. 3 are 0.7314, and the calculated results of gas chamber No. 2 and gas chamber No. 3 are 0.7308; the average calculated results of gas chamber No. 1 and gas chamber No. 3 are 0.7499, and the average calculated results of gas chamber No. 2 and gas chamber No. 3 are 0.7365.

[0033] like Figure 2 As shown, according to one aspect of the present application, step S1 is further: S11. When the buffer gas is He, when the alkali metal atoms in the ground state or excited state collide with the buffer gas atoms in the gas chamber, the commonly used model for the interaction between the atoms is the LJ potential energy curve model. In this case, when using the original model, it was found that its fitting effect was not good and it could only reflect the general trend of the potential energy curve. Therefore, in this application, the original C6 model was extended to C6-C8-C 10 In the model, in addition to the most important dipole-dipole interaction, the attraction term also takes into account the dipole-quadrupole interaction and the quadrupole-quadrupole interaction. Its basic form is as follows: V(R) = -C6 / R 6 -C8 / R 8 -C 10 / R 10 Although only the absorption term is considered in the potential energy curve, the term representing repulsion is also fitted. The actual fitting formula is: V(R) = -C6 / R 6 -C8 / R 8 -C 10 / R 10 +C 12 / R 12 .

[0034] S12, in order to calculate the potential energy curve of the collision between Rb atoms and He atoms, different quantum chemical calculation methods are compared and analyzed. Since what needs to be calculated is a weak interaction system, more weak interactions need to be considered. In this embodiment, the NEVPT2 method is selected, and a rigid scanning method is adopted, that is, the scanning distance is determined. After the scanning step length, the single point energy of different positions is calculated respectively. In the actual calculation, the number of points calculated and the step length of the calculation can be adjusted according to the needs of the actual calculation. For example, when the curve changes greatly, more points can be calculated to better describe the trend and details of the potential energy curve. When the curve changes less, the number of calculation points can be reduced to improve the calculation efficiency and reduce the use of computing resources. In this example, alkali metal atoms and buffer gas atoms are evenly taken in the range of 2-12 angstroms, and the single point energy of the ground state, the first to the third excited state of each point is calculated respectively, so as to obtain the potential energy curve of the ground state and the excited state.

[0035] S13. After the potential energy curve is obtained by calculation, the potential energy curves of the first excited state to the third excited state are respectively subtracted from the ground state potential energy curve to obtain a difference potential, which can be used to calculate the theoretical absorption spectrum and correct the alkali metal absorption spectrum fitting formula.

[0036] According to one aspect of the present application, when using NEVPT2 to calculate the potential energy curve, the settings for the CASSCF module are that the number of active electrons is 1, the size of the active space is 8, and the spin multiplicity is 2. Generally speaking, calculating 5 more states than the required excited states will make the calculated results more stable and accurate. In this example, a total of 10 excited states with energy from small to large are calculated, and the first four calculation results are taken.

[0037] like Figure 4 As shown, in another embodiment, step S12 may also be: S121, collision time series parameter setting, read atomic distance data {R1, R2, ..., R 50} (50 points uniformly in the range of 2-12 angstroms) and collision dynamics parameters {collision velocity v, characteristic time τcol}, multiple collision moments corresponding to each distance point are calculated by the time parameterization algorithm t= (R - R0) / v, and the time-distance mapping data {(R1, t 1i ), (R2, t 2i ), ..., (R 50 , t 50i )}, where each R j Corresponding to 5 different moments.

[0038] S122, dynamic active space adaptive adjustment, based on time-distance mapping data {(R j , t ji )} and the preset electron correlation threshold εcorr = 10⁻ 6 The size of the active space is adaptively determined by the orbital occupancy number analysis algorithm: CAS (3, 12) is used to capture the strong correlation effect when R < 4 angstroms, CAS (2, 10) is used when 4 angstroms ≤ R ≤ 8 angstroms, and CAS (1, 8) is used when R > 8 angstroms to obtain the dynamic active space configuration data {CAS (ne, no) ji} corresponds to each (R j , t ji )point.

[0039] S123, transient polymorphic NEVPT2 calculation, combined with time-distance mapping data {(R j , t ji )} and dynamic active space configuration {CAS(ne,no) ji}, perform NEVPT2 single point energy calculation at each time and space point: first perform dynamic CASSCF calculation to obtain the reference state |Ψref(R j , t ji )〉, and then calculate the electron correlation correction E by second-order perturbation theory (2) = Σ k〈Ψref| H*|Ψ k 〉 2 / (E0-E k ), calculate the ground state, the first to the third excited state, and obtain the time-space resolved single point energy data set {Eground(R j , t ji ), E1(R j , t ji ), E2(R j , t ji ), E3(R j , t ji )}. Where H* is the total energy operator of the system, E0 is the zero-order energy of the system, and E k is the energy of the system in different excited states.

[0040] S124, Dynamic potential energy surface construction and time averaging, based on the spatiotemporal resolution of single point energy dataset {En(R j , t ji )}, through the time averaging algorithm〈En(R)〉t = (1 / Nt)Σ i En(R,t i ) to obtain the time-averaged potential energy curve {〈Eground(R)〉t, 〈E1(R)〉t, 〈E2(R)〉t, 〈E3(R)〉t}, and simultaneously calculate the dynamic fluctuation correction term ΔEn(R) = sqrt[(1 / Nt)Σ i (En(R,t i ) - 〈En(R)〉t) 2 ], and obtain the dynamically corrected potential energy data {〈En(R)〉t, ΔEn(R)}.

[0041] S125, excited state difference potential extraction, the excited state energy in the dynamic correction potential data is subtracted from the ground state energy: ΔV1(R) = 〈E1(R)〉t - 〈Eground(R)〉t, ΔV2(R) = 〈E2(R)〉t - 〈Eground(R)〉t, ΔV3(R) = 〈E3(R)〉t - 〈Eground(R)〉t, and the dynamic uncertainty σΔVn(R) = sqrt[ΔE1 2 (R) + ΔEground 2 (R)], and the dynamically corrected potential difference data {ΔV1(R), ΔV2(R), ΔV3(R), σΔVn(R)} are obtained for subsequent theoretical spectrum calculations.

[0042] The traditional NEVPT2 method is based on a static wave function with a fixed geometric configuration, which simplifies the inherently dynamic process of atomic collisions into a static snapshot. It ignores the continuous evolution of the electronic structure along the collision trajectory, fails to capture the temporal variation of the electron correlation effect, and loses the quantum coherence and memory effects during the collision process. This embodiment introduces a time-dependent wave function |Ψ(R, t)〉 to achieve real-time calculation of the evolution of the electronic structure along the collision trajectory. n}Corresponding to each interatomic distance R, a complete time-space resolved quantum chemical description is established.

[0043] During alkali metal-helium atom collisions, the electron correlation strength changes rapidly with the interatomic distance R: in the long-range region (R>8 A*), the electron correlation is weak, mainly due to dispersion interaction; in the medium-range region (4-8 A*), the electron clouds begin to overlap; in the short-range region (R<4 A*), the electron correlation is strong, with significant overlap and exchange. This embodiment uses a dynamic active space strategy, CAS (ne(R, t), no(R, t)), which adaptively adjusts based on the real-time electron correlation strength: when R < 4 A*, CAS (3, 12) captures strong correlation effects; when 4 A* ≤ R ≤ 8 A*, CAS (2, 10) handles moderate correlations; when R > 8 A*, CAS (1, 8) describes weak correlations, achieving an optimal balance between correlation processing accuracy and computational cost. Where A* is angstroms.

[0044] In the short-range strong interaction region, the transient correlation effects produced by electron cloud overlap have the following characteristics: rapid redistribution of electron density; transient polarization and antipolarization effects; nonlinear changes in electron exchange-correlation energy; sudden enhancement of many-body correlation effects; and the inability of static NEVPT2 to describe the time scale and intensity changes of these transient effects.

[0045] Correction of E by instantaneous correlation (2) (R, t) and the correlation memory function Mcorr(t, τ), accurately capturing: the time dependence of instantaneous electron correlation energy; the influence of historical correlation effects on the current state; and the coupling of multi-timescale correlation processes.

[0046] In this embodiment, V(R,t) = -C6(t) / R 6 - C8(t) / R 8 - C 10 (t) / R 10 + ΔV_dynamic(R, t).

[0047] According to one aspect of the present application, step S2 is further: S21. Since the Lorentz linewidth in the gas chamber used in this embodiment is much larger than the Gaussian linewidth, the broadening line shape of the absorption spectrum can be simplified to the Lorentz lineshape. Taking into account the collision broadening between the alkali metal atoms and the buffer gas atoms, the line shape of the absorption spectrum is expressed as follows: I(Δ)= γ / ((Δ-δ b ) 2 )+ γ 2 (0) / 4); Where γ is the line width, γ=γ N +γ b , δ b is the frequency shift of the Lorentz curve, ω is the laser frequency, ω0 is the resonance frequency, and Δ=ω-ω0.

[0048] S22. In the formula, the broadening caused by collision detuning is taken into account, which can be used to correct the asymmetry shown by the spectral line shape. The specific expression is as follows: γ=γ N +γ(Δ); S23. According to the Anderson-Talman collision model, at time t, the motion trajectory of the disturbed atom can be expressed as: R(t)=sqrt(b 2 +v 2 t 2 ), where b is the impact parameter and v is the velocity of the perturbed atoms. The broadening is calculated based on the above results as follows: γ(Δ)=n p v th 8πR th 2 I(ΔT d ); where v th =sqrt(2kT / μ) is the most probable rate, and C6 in the potential energy curve parameter is expressed as |C6|=R th 5 v th , then C8, C 10 They are: |C8|=(k1R th ) 7 v th ,|C 10 ∣=(k2R th ) 9 v th ; and T d =R th / v th =|C6| 1 / 5 v th -6 / 5 , represents the characteristic collision duration; where I(ΔT d) is a dimensionless parameter related to the line shape derived from the collision broadening rate.

[0049] When |ΔT d When ∣<1, γ(Δ) can be written as γ(Δ)= γ(0) (1+p1ΔT d Since the buffer gas He in the gas cell to be measured is 600 Torr, the natural broadening of the Lorentzian line shape can be ignored in this case, and only the pressure broadening caused by collision can be considered.

[0050] From the above formula, the absorption spectrum fitting correction line shape near resonance is as follows: I(Δ)=γ(0) (1+p1ΔT d ) / ((Δ-δ b ) 2 + γ 2 (0) / 4).

[0051] According to one aspect of the present application, step S23 is further as follows: S231, Dynamic C6-C8-C 10 Potential energy model fitting: read the dynamic correction potential difference data {ΔV1(R), ΔV2(R), ΔV3(R), σΔVn(R)}, and establish the improved potential energy model V(R) = -C6 / R 6 - C8 / R 8 - C 10 / R 10 + f_dynamic(R), where f_dynamic(R) is the dynamic correction function, which is obtained by weighted least squares fitting algorithm w(R) = 1 / σΔVn 2 (R) Parameter optimization is performed to obtain the dynamic correction potential energy parameter {C6 eff , C8 eff , C 10 eff , α_dynamic} and its parameter uncertainty matrix Σparam.

[0052] S232, Temperature dependent collision parameter calculation: Based on the dynamic correction potential energy parameter {C6 eff , C8 eff , C 10 eff} and the input experimental temperature data T, the characteristic parameters are calculated by the improved Anderson-Talman theory: collision radius R_th = (|C6 eff | / v_th) 1 / 5, the most probable rate v_th = sqrt(2kT / μ), the characteristic collision time T_d = R_th / v_th, and the dynamic correction factor f_corr = 1 + α_dynamic(kT / |C6 eff |) 1 / 3 , and obtain the temperature-corrected collision parameter {R_th eff (T), T_d eff (T), f_corr(T)}.

[0053] S233, Theoretical calculation of dynamic broadening rate: Combined with the temperature correction collision parameter {R_th eff (T), T_d eff (T)} and the buffer gas density n_p, by the improved collision integral γ(Δ) = n_p v_th 8πR_th 2 I_dynamic(ΔT_d eff ) calculates the pressure broadening rate, where I_dynamic includes a time-dependent correction: I_dynamic(x) = I_static(x) × [1+ β_dynamic x 2 ],β_dynamic is used to calculate the potential energy and obtain the theoretical broadening parameter {γ0 theory (T), p1 theory (T)}.

[0054] S234, Detuned broadening line type construction: The theoretical broadening parameter {γ0 theory (T), p1 theory (T)} is substituted into the detuning correction formula γ(Δ) = γ0 theory [1 + p1 theory ΔT_d eff ], constructing the improved Lorentz line shape I(Δ) = γ(Δ) / [(Δ-δ_b) 2 + γ 2 (Δ) / 4], where δ_b is the frequency shift parameter, and the dynamic correction spectrum fitting function I_theory is obtained. TD (Δ, T) is used for fitting the experimental data in step S3.

[0055] Using dynamic uncertainty σΔVn(R) as the weight function w(R) = 1 / σΔVn 2(R), achieves differentiated precision control in different distance regions. Compared with the traditional equal-weighted fitting, the fitting accuracy of the key short-range region is improved by 2-3 orders of magnitude. The dynamic correction term α_dynamic directly reflects the intensity of the time-dependent effect and provides a quantitative indicator for the physical understanding of the collision process. Through the dynamic correction factor f_corr = 1 + α_dynamic(kT / |C6 eff |) 1 / 3 , a quantitative relationship between quantum dynamic effect and temperature was established. Improved collision integral I_dynamic(x) = I_static(x) × [1 + β_dynamicx 2 ], where β_dynamic is directly derived from TD-NEVPT2 calculations, eliminating the empirical nature of traditional methods. The dynamic correction term β_dynamic x 2 This captures the nonlinear broadening effects associated with detuning, improving the accuracy of the calculations by 1-2 orders of magnitude in the large detuning region (|Δ| > 2γ0) compared to traditional linear approximations. Overall, this reduces the number of free parameters in subsequent experimental data fitting from the traditional 5-7 fitting parameters to 2-3, improving the stability and convergence speed of the fit.

[0056] According to one aspect of the present application, in the alkali metal mixture ratio detection method, the coefficient k1 between C8 and C6, C 10 The coefficient k2 between C6 and C8 is obtained by fitting the potential energy curve model calculated by quantum chemical method. 10 Potential energy curve model, perform theoretical calculation potential energy curve fitting corresponding to the D1 line of the Rb-He system, that is, the potential energy curve fitting of the first excited state, and obtain the potential energy curve parameters C6, C8, C 10 They are 3.40E-44, 4.39E-64, and 2.40E-82 respectively, corresponding to the calculated parameters k1=0.6662 and k2=0.8059.

[0057] According to one aspect of the present application, step S3 is further: Based on the alkali metal absorption spectrum fitting correction line shape, the absorption spectrum fitting is performed to obtain the optical depth OD and broadening Ξ, which can be used to calculate the density of a certain alkali metal in the alkali metal mixture.

[0058] When acquiring absorption spectrum data, first place the gas chamber to be measured between the heating device and the heating plate made of boron nitride ceramics, connect the PT1000 resistor through the single-chip computer to acquire the temperature, and adjust the heating film current to control the temperature according to the acquired temperature. Turn on the laser and adjust the laser to the center wavelength of the D2 line. When the temperature stabilizes at around 90°C, use the LabView host computer program to output a triangular wave signal and modulate the laser output wavelength to achieve measurement of the entire absorption spectrum range. At the same time, use the host computer program to sample the light intensity signal, and compare the two to obtain the optical depth. After obtaining the optical depth of each sampling point, the absorption spectrum line of the gas chamber at 90°C can be obtained using wavelength or frequency as the independent variable. The optical depth calculation formula is as follows: OD=-ln(I o / I i ), where I o and I i are the transmitted light intensity and the incident light intensity respectively; the specific calculation formula of the alkali metal density based on the absorption spectrum is as follows: OD∝ΞN a r e cfl; where r e =2.82×10 -15 m is the classical electron radius, c=3×10 8 m is the speed of light, f is the oscillator strength, N a is the density of alkali metal A in the desired alkali metal mixture.

[0059] According to one aspect of the present application, step S4 is further: The molar mass ratio of Rb to Cs in the Rb-Cs gas chamber can be obtained by combining the density of the alkali metal element in the alkali metal mixture calculated in the above steps with the calculation results of the alkali metal element at different temperatures according to the following formula.

[0060] The molar mass ratio of the alkali metal mixture can be calculated based on Raoult's law. The molar mass ratio of the alkali metal Rb and the alkali metal Cs is calculated as follows: Rb =N Rb (T s ) / N s_Rb (T s );f Cs =1-f Rb ; f Rb / f Cs =N Rb (T s ) / (N s_Rb (T s )-N Rb (T s )).

[0061] The density of alkali metal elements can be calculated based on the measurement results of alkali metal element gas chamber under the same conditions, or by the saturated vapor pressure formula. s_Rb =10 21.866+A-B / T / T. For Rb, A in the above formula is 4.312 and B is 4040.

[0062] In summary, in the present invention, the absorption spectroscopy method has high selectivity and can detect low-concentration substances without introducing other external magnetic fields. Due to its non-invasive detection method, wide range of applications and relatively simple detection platform, it can easily realize real-time detection and analysis of alkali metal ratios. The present invention first calculates the potential energy curve based on the first principles and improves the Lorentz fitting model of the absorption spectrum; according to the optimized alkali metal absorption spectrum model, the relevant formula for calculating the density of alkali metals is derived, and the absorption spectrum intensity and broadening information obtained by the collision of alkali metal atoms with buffer gas are used to obtain the ratio of the alkali metal mixture. The present invention obtains the optical depth and pressure broadening in the absorption spectrum by fitting the absorption spectrum lines of the alkali metal mixture, thereby obtaining the ratio information of the alkali metal mixture; based on the corrected absorption spectrum fitting formula, the accuracy of obtaining spectral information can be improved, thereby optimizing the density calculation of different alkali metals in alkali metal elements and alkali metal mixtures, and further improving the accuracy of the calculation of the ratio of the alkali metal mixture.

Claims

1. Based on the absorption spectrum of alkali metals C6-C8-C 10 The method for measuring the proportion of alkali metal mixture of the model is characterized in that: include: S1, using quantum chemical calculation method to obtain the potential energy curve between alkali metal atoms and buffer gas atoms; S2, calculate the theoretical absorption spectrum based on the obtained potential energy curve and improve the Lorentz line shape of the absorption spectrum; S3: Based on the improved Lorentzian line shape of the absorption spectrum, an experimental device was built to obtain the absorption spectrum, and the pressure broadening and spectral intensity resulting from the collision of the alkali metal mixture with the buffer gas were fitted; S4, calculating the ratio information of the alkali metal mixture based on the obtained pressure broadening and spectral intensity.

2. The method according to claim 1, characterized in that Step S1 is further as follows: S11, when the buffer gas is He, when the alkali metal atoms in the ground state or excited state collide with the buffer gas atoms in the gas chamber, the interaction between the atoms is expressed by C6-C8-C 10 Model representation, its basic form is as follows: V(R)=-C6 / R 6 -C8 / R 8 -C 10 / R 10 ; R is the distance between the two bodies; C6, C8, C 10 is the potential energy curve parameter; S12, based on C6-C8-C 10 The NEVPT2 method is used to calculate the single point energy of the ground state and the first to third excited states of each point, and the potential energy curves of the ground state and excited state are obtained.

3. The method according to claim 2, characterized in that When using the NEVPT2 method to calculate the potential energy curve, the settings for the CASSCF module are: the number of active electrons is 1, the active space size is 8, the spin multiplicity is 2, and a total of 10 excited states with energy from small to large are calculated, and the first four calculation results are taken.

4. The method according to claim 2, characterized in that Step S2 is further as follows: Based on the potential energy curve and C6-C8-C 10 Model, perform potential energy curve fitting, and obtain potential energy curve parameters C6, C8, C 10 ; Based on this, the collision broadening is constructed through the Anderson-Talman collision model: γ(Δ)=n p v th 8πR th 2 I(ΔT d ); where v th =(2kT / μ) 1 / 2 The most probable rate is expressed as C6 in the potential energy curve parameter |C6|=R th 5 v th , then C8, C 10 They are: |C8|=(k1R th ) 7 v th ,|C 10 ∣=(k2R th ) 9 v th ; and T d =C6 1 / 5 v th -6 / 5 =R th / v th Indicates the characteristic collision duration; I(ΔT d ) is a dimensionless parameter related to the line shape derived from the collision broadening rate; when |ΔT d When ∣<1, γ(Δ) is written as γ(Δ)=γ(0)(1+p1ΔT d ); Based on this, the improved absorption spectrum Lorentz line shape is: I(Δ)=γ(0) (1+p1ΔT d ) / ((Δ-δ b ) 2 +γ 2 (0) / 4); where n p is the number density of buffer gas atoms, R th is the characteristic distance, k is the Boltzmann constant, T is the temperature, μ is the reduced mass of the collision between atoms or molecules, Δ is the deviation between the laser frequency and the resonance frequency, ΔT d is the time scale of the collision effect relative to the spectral broadening, γ(0) is the basic line broadening, p1 is the correction factor, and δ b is the frequency shift of the Lorentz curve, k1 and k2 are correction coefficients.

5. The method according to claim 4, characterized in that Correction factors k1 and k2 are based on C6-C8-C 10 Obtained by model fitting.

6. The method according to claim 1, characterized in that Step S3 further includes: Based on the improved Lorentzian line shape of the absorption spectrum, the optical depth OD and pressure broadening Ξ are obtained by fitting the absorption spectrum, and the density of the alkali metal element in the alkali metal mixture is calculated using the formula: N a =OD max ×Ξ / (2r e cfl); where r e is the classical electron radius, c is the speed of light, f is the oscillator strength, N a is the density of alkali metal a in the desired alkali metal mixture, l is the optical path length, OD max is the maximum optical depth, that is, the spectral light intensity.

7. The method according to claim 6, characterized in that Step S4 is further as follows: If the mixture in the gas chamber consists of two alkali metals, the molar mass ratio of the alkali metal mixture, that is, the ratio information of the alkali metal mixture, is calculated based on Raoult's law and the density of the alkali metal element. The calculation formula is as follows: a / f b =N a (T s ) / (N s_a (T s )-N a (T s )); where f a =N a (T s ) / N s_a (T s ) is the molar mass of alkali metal a; f b =1-f a is the molar mass of alkali metal b; N s_a is the density of alkali metal element at the same temperature, T s is the indoor temperature.

8. The method according to claim 2, characterized in that Step S12 is further as follows: Based on C6-C8-C 10 Model, obtain interatomic distance data and collision dynamic parameters, calculate time-distance mapping data; based on this, adjust the dynamic active space and obtain dynamic active space configuration data; Combining time-distance mapping data with dynamic active space configuration data to perform transient polymorphic NEVPT2 calculations, we obtain a spatiotemporally resolved single-point energy dataset. Perform time averaging processing on it to obtain the time average potential energy curve; The difference between the excited state and the ground state in the time-averaged potential energy curve is used to obtain the dynamically corrected difference potential data.

9. The method according to claim 8, characterized in that The calculated time-distance mapping data includes: Based on the interatomic distance data, predetermined points and collision dynamic parameters are uniformly selected within a predetermined range; Based on the collision dynamics parameters, multiple collision moments corresponding to each point are calculated through a time parameterization algorithm to obtain time-distance mapping data.

10. The method according to claim 8, characterized in that Obtaining dynamic active space configuration data includes: Based on the time-distance mapping data and the preset electron correlation threshold, the active space size is adaptively determined by the orbital occupancy analysis algorithm: When R<4 Å, CAS (3, 12) was used to capture the strong correlation effect; When 4 Å ≤ R ≤ 8 Å, CAS (2, 10) was used; When R>8 angstroms, CAS (1,8) was used to obtain dynamic active space configuration data.

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