Wave function collapse, also known as orbital collapse, refers to a phenomenon in which the energy level of an atom decreases and the radius of an electron's orbit decreases sharply as the effective potential experienced by electrons outside the core changes. Wave function collapse largely affects the properties of atoms or ions. GoeppertM first pointed out in 1941 that the properties of neutral rare earth elements are largely dependent on the collapse properties of the f-electron wave function of this group of elements.
Wavelet function collapse. For many years afterwards, theoretical and experimental research on the effect of wave function collapse on the properties of atoms or ions has been a topic of general interest.
In the past few decades, a great deal of work has been done on theoretical and experimental research on the effect of 4f wave function collapse on the atomic or ion / absorption spectra of lanthanides (especially 2 = 5470). The Dong research group based on the relativistic multi-configuration Dirac-Fock method on the 4 / wave function collapse and 4f wave function collapse of the Xe atom isonuclear and isoelectronic series ions on its 44 / radiation transition properties and HFR self-consistency The field method has also made relevant theoretical studies on the collapse of Ca-like 3d wave function and the effect of 3d wave function on the transition properties of Ca-like radiation. At present, the study of the atom / ion collapse of the actinides 5 / wave function and the effect of 5 / wave function collapse on the absorption spectrum is also attracting interest, especially for the nuclear series ions such as the actinide Th and U elements 5 / Excited experimental research has had a lot of research results. For example, Carroll et al. Observed the XUV spectrum of U ions in different ionization states in plasma generated by lasers in 1984 and found that the spectrum is mainly generated by 5 / transition around a wavelength of 10 nm and is based on Har-tree -The calculation of Fock and Dirac-Fock methods identifies the 5 / transition spectra of UVI and UXV. In 1986, Carroll et al. Again observed the XUV spectra of different ionized Th ions in the plasma generated by the laser, and found that many of them belong to ThXI and ThXI-5, 6/5 / and W1.6 / ―5, 5 /, 6 household transition lines. Ka-mpen et al. Studied the light absorption process of the U atom in 2000 and found that the light absorption spectrum of the U atom shell is mainly generated by the 5 / excitation transition of the discrete excitation region. For actinides, the collapse of the 5 / wave function strongly affects the interaction between the 5 / wave function and the higher fir (> 6) wave function and the 5, ― (n> 5) transition energy and oscillator strength, so It is necessary to conduct systematic theoretical research on the 5 / wave function collapse.
In this paper, the HFR and LS-dependent HFR self-consistent field methods that consider the electronic correlation effect and configuration interaction are used to collapse the 4 / wave function and 4 ° -44 / radiation transition of the Xe atom isonuclear and isoelectronic series of ions. Based on the research of properties, the 5 /, 6 / electron radial wave functions of Rn and other electron series ions are calculated systematically, the collapse law of 5 / wave function and the changing characteristics of n / wave function are analyzed, and the Rn and other electron series ions are further discussed. (5 2 Theoretical method 2.1 Calculation of radial wave function and its orbital radius For a detailed description of the HFR theoretical method that considers electron correlation effects and configuration interactions, please refer to here for brief introduction.
In the HFR theoretical method, the calculation of the configured average radial wave function can be obtained by solving the following self-consistent iterative HFR equation (1): where, is the HF potential, which can be expressed as (2), and p represents the spherical average of electrons The number density represents the probability density of the electron f, and has + = + 0―. In all the above integrals, r represents the smaller and larger of r and r2, respectively.
Radial wave functions of different spectral terms can be obtained by solving the Hartree-Fock equation of LS-de-pendent. Different from equation (1), the following direct and commutation terms are further added to the potential: if once found In order to calculate the radial wave function for a long time O), the following formula can be used to further calculate the average orbital radius, 2.3 Calculation of the probability of radiative transition and the strength of the oscillator The probability is that it is an electric dipole transition matrix element, which can be expressed as> respectively representing the excited initial state i and the final state / atomic state wave function, which can be linearly combined by configuring the wave function.
3. Results and discussion Xuan Wanxuan Miao You broke the rod to explain the 5 / wave function collapse law, this paper systematically calculated the 5 / electron radial wave function of Rn and other electron series ions. (A) The excitation configuration of Rn and other electron series ions (Rn-Pu8 +) 5,5 / 6/6, and the 5 / electron radial wave function under the average configuration are shown. It can be seen from the figure that the 5 / wave function suddenly shrinks between Fr + and Ra2 + ions, and the average radius of its orbit decreases from 7.791au of Fr + ion to 2.061au of Ra2 + ion (as shown in Table 1, ttO, The difference is about 6a.u., and the 5 / orbital radius of Ac3 + ions is about the same as that of Ra2 + ion. 46a.u In addition, it can also be seen that as the atomic number Z further increases, 5 / wave The shrinkage of the function becomes slow, and the difference between the 5 / orbital radius of adjacent ions becomes smaller and smaller. This shows that the collapse of the 5 / wave function of Rn and other electron series ions occurs between Fr + and Ra2 + ions, starting from Ra2 + ions. The averaged 5 / wave function collapses from the outer potential well into the inner potential well. (B), (c), (d) show the excitation configuration of Rn and other electron series ions 5, 5/6/6 / 5 / Wave function in sp, 3!), 1; 5 spectral terms. It can be seen that the collapse of the 5 / wave function in different spectral terms is different. The collapse in the 3P and 3D spectral terms is similar to the collapse in the average configuration. The collapse occurs in Fr + and Ra2 + ions. The 5f wave function in the 1P spectral term is gradually contracted, and there is no sudden collapse. This is called the partial collapse of the 5 / wave function. This shows that the 5 / wave function collapse table 1 Rn and other electronic series ions Under the configuration average and spectral term dependence approximation, 5 / orbit average radius (unit: au) 5, 5/6526 of electron series ions such as Rn, the excitation configuration is in the configuration average and 3P, 3D, 5 in the spectral phase / Wave function U) 5 / wave function under configuration average; (b) 5f wave function in 3 cadaver spectrum phase; (c) 5f wave function in 3D spectrum phase; (d) 5f wave in if spectrum phase The function Fig, 15 / -wavefunctionsoftheconfigurations has a strong dependence on spectral terms.
To further illustrate the partial collapse of the 5 / wave function, the wave functions of the Rn atom and Fr +, Ra2 + and Ac3 + ion 5 "5 / 6s26 excitation configurations under the configuration average and in the 3D and 3iVM general terms were compared respectively. It can be seen from the figure that for the Rn atom, the 5 / wave function is completely coincident with the configuration average and in the 313, 3 corpse, and 1 family spectrum terms. This is because for the Rn atom, the 5 / wave function is completely in The outer well of the effective barrier has little interference from the inner well. When the number of nuclear charges increases by 1, ie to Fr + ions, the inner well begins to deepen as the number of nuclear charges increases and affects the 5 / wave function, configuration The average value and the 5 / wave function in the 3D and 3P spectral terms have increased significantly in the peak of the inner well, and the 5 / wave functions in different spectral terms no longer coincide. When the number of nuclear charges continues to increase by 1, to the Ra2 + ion, the internal The deepening of the trap is sufficient to support the 5 / wave function of the bound state. The 5 / wave function is completely collapsed into the inner trap in the configuration average and 3D and 3P spectral terms, but at this time the 5 / wave function in the 1P spectral term is somewhat Contraction, but still in the outer well, the influence of the inner well on it is still very small, which causes a partial collapse of the 5 / wave function, at this time the 5 / wave function The separation is the largest in the spectral terms and in the spectral terms and in the configuration average. After that, as the number of nuclear charges continues to increase, the 5 / wave function in the 1P spectral term continues to shrink, and the The separation in the spectral terms and the configuration average begins to decrease until the 5 / wave function in the 1P spectral term completely collapses and completely coincides with the 3D and 3P spectral terms and the configuration average.
3.2 Variation characteristics of n / (n> 6) wave function of Rn-like ions (a), (b) show the 5 /, 6 / wave functions of Rn atoms to Radon-like Th4 + ions under the configuration average. For comparison, the figure also shows the 4 /, 5 / wave function of H atoms and hydrogen-like He +, Li2 + ions and the 4 / wave function of Xe atoms. As we all know, when the / wave function is not collapsed, the outer well of the effective potential is subjected to the long-range Coulomb potential, which is a hydrogen-like potential. Therefore, the 4 / wave function of the Xe atom is similar to the 4f wave function of the H atom, which can be seen in (a). When a certain orbit / wave function collapses, it is no longer a hydrogen-like potential, but the more orbital / wave function still suffers from a hydrogen-like potential. For example, for Ba atom, after its 4 / wave function collapses, the 4 / wave function is no longer similar to that of hydrogen-like ions, but its 5 / wave function is similar to that of H atom. For the Rn atom, we also found that when its 4 / wave function collapses, the 5 / wave function is similar to the 5f wave function in the 5, 5/6/6 /> 6 excitation configuration of electron series ions such as Rn and Rn, etc. 5 / wave function of electron series ions under configuration average and 4 / wave function of hydrogen-like ions and Xe atoms; (b) Rn is equivalent to 4 / wave function of H atoms and uncollapsed Xe atoms. This can also be clearly seen in (a). In the same way, if the 5 / wave function collapses, the 5 / wave function is no longer similar to the hydrogen-like 4 / wave function, but then the 6 / wave function is still similar to the hydrogen-like 4 / wave function, that is, at this time The higher n / (n> 6) wave function is similar to the hydrogen-like ion (n-2) / wave function.
In addition, observations (a) and (b) show that the 5 /, 6 / wave function of Fr + ion is very different from the 5 /, 6 / wave function of other radon ions. The 5 /, 6 / wave function of Fr + ion There is a clear double-peak structure, which shows that Fr + ions are compared with Ra2 +, Ac3 + and Th4 + ions. Although the effective potential of the inner well is not deep enough to support the 5 / wave function of the bound state, the deepening of the inner well has already begun Affect the Fr + ion 5 / wave function. At this time, the 5 / wave function is in the stage of strong interaction between the eigenstates of the inner and outer wells, so from (a) Table 2 we can see that the Fr + ion 5 / wave function and The 4f wave function of hydrogen-like He + ions is very different.
3.3 Rn-like 5d-n / (5 images are the so-called resonance phenomena. For neutral atoms, the channel's potential resonance can lead to a giant resonance above the ionization threshold, so in the discrete excitation region, the / (66) energy level The interaction between the two is enhanced, resulting in the hybridization of the n / (; 2> 6) wave function and the relatively large t / ip (66) Rydberg sequence in the discrete excitation region, becoming a true bound state, with the atomic number The continued increase of Z only widens the energy separation between n / states, while the interaction between the fully collapsed 5 / and higher states disappears, resulting in a transition to the collapsed 5 / 1P energy level The intensity of the vibrator reaches the maximum.
Based on current calculations, we can further explain the effect of partial collapse of the wave function on the strength of the transition oscillator. Ra2 + -like ions (65 / transfer, finally when 5 / wave function is completely collapsed, the transition mainly occurs between 5-5 / 1P.
4 Conclusion This paper uses the HFR self-consistent field method to systematically calculate the 5 /, 6 / electron radial wave function and 5W ° of Rn and other electron series ions (6
This is a special vozol Alien 2 electronic cigarette product series. We sell Vozol Vape, vozol vape Pen, vozol vape 3000 Puffs, and other vozol vapes.
We are specialized electronic cigarette manufacturers from China, Vapes For Smoking, Vape Pen Kits suppliers/factory, wholesale high-quality
products of Modern E-Cigarette R & D and manufacturing, we have the perfect after-sales service and technical support. Look forward to
your cooperation!
vozol alien 2 vape kit,vozol alien 2 vape pen, vozol alien 2 e-cigarette, vozol alien 2 vape 600 puffs,vozol alien 2 disposable vape
Ningbo Autrends International Trade Co.,Ltd. , https://www.supervapebar.com