Relativistic corrections to the Zeeman effect in diatomic molecules

Basic molecular g-factors for the ²Π ground states of OH, SH, NO, NS, and ClO have been determined by a weighted nonlinear least squares fit including zero-field as well as Zeeman data. The combined g-factor $\text{g}{}_{\mathrm{l}}\text{+}\text{1}\text{2}\text{g}{}_{\mathrm{s}}$ accounts for the dominant contribution to the Zeeman effect of the paramagnetic ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ substate. Theoretical values of $\text{g}{}_{\mathrm{l}}\text{+}\text{1}\text{2}\text{g}{}_{\mathrm{s}}$ have been computed by considering the relativistic corrections arising from the reduction of the Breit equation to the second Pauli limit, and a contribution due to the motion of the nuclear center of mass is also included. The relativistic corrections have been computed by use of known LCAO molecular wavefunctions. Furthermore the free electron quantum electrodynamic correction ($\text{α}\text{2}\text{Π}$) to g_s is used as an ad hoc value for an electron bound to a diatomic molecule. A systematic difference is found between theoretical and fitted values of $\text{g}{}_{\mathrm{l}}\text{+}\text{1}\text{2}\text{g}{}_{\mathrm{s}}$. The difference increases linearly with the parameter $\text{Y = |}\text{A}\text{B}\text{|}$ for the molecules OH, SH, and NO. The maximum difference is encountered for NO and is about 20% of the free electron quantum electrodynamic correction. With further increase in Y (NS and ClO) the agreement seems to improve again.     

Relativistic correction for the Zeeman effect in a hydrogen-like atom

Based on an algebraic system of equations whose eigenvalues in the semirelativistic approximation determine the magnetic splitting of energy levels of two coupled Dirac particles with charges ±e and different masses, the splitting in extremely weak and weak magnetic fields is determined. In addition, a system of equations for charged particles with anomalous magnetic moments is given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 3–13, December, 2006.     

Relativistic Zeeman effect in positronium,n=2

Approximate relativistic center-of-mass variables are employed for the calculation of the relativistic corrections to the Zeeman structure of then=2 energy level of positronium.     

Chemical shift of Zeeman masses in polar semiconductors

We discuss the problem of determining effective masses from the Zeeman splitting of 2p-levels in shallow impurities. In polar semiconductors we find the Zeeman mass to depend upon the chemical nature of the impurity (chemical shift), which can usually be described by a central-cell potential. In spite of its short range, it can influence even 2p-levels, if, due to electron-phonon interaction, 1s-one-phonon states are admixed to 2_p-zero-phonon states.     

Evaluation of second-order Zeeman frequency shift in NTSC-F2

Caesium atomic fountain clock is a primary frequency standard, which realizes the duration of second. Its performance is mostly dominated by the frequency accuracy, and the C-field induced second-order Zeeman frequency shift is the major effect, which limits the accuracy improvement. By applying a high-precision current supply and high-performance magnetic shieldings, the C-field stability has been improved significantly. In order to achieve a uniform C-field, this paper proposes a doubly wound C-field solenoid, which compensates the radial magnetic field along the atomic flight region generated by the lead-out single wire and improves the accuracy evaluation of second-order Zeeman frequency shift. Based on the stable and uniform C-field, we launch the selected atoms to different heights and record the magnetically sensitive Ramsey transition|F = 3, mF=-1 → |F = 4, mF=-1 central frequency, obtaining this frequency shift as 131.03×10~(-15) and constructing the C-field profile(σ = 0.15 n T). Meanwhile, during normal operation, we lock NTSC-F2 to the central frequency of the magnetically sensitive Ramsey transition |F = 3, mF=-1 → |F = 4, mF=-1 fringe for ten consecutive days and record this frequency fluctuation in time domain. The first evaluation of second-order Zeeman frequency shift uncertainty is 0.10×10~(-15). The total deviation of the frequency fluctuation on the clock transition induced by the C-field instability is less than 2.6×10~(-17). Compared with NTSC-F1, NTSC-F2, there appears a significant improvement.     

Gravitational analog of the Zeeman effect

An equation is obtained for calculating the spin-gravitational interaction analogous to the Zeeman effect.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 30–33, September, 1973.     

The Zeeman effect revisited

We announce three new rigorous results for the quantum mechanical hydrogen atom in constant magnetic field: (i) Borel summability of the small field perturbation series, (ii) detailed large field asymptotics, and (iii) non-degeneracy of the ground state Ω₀ and a proof that it has $\text{L}{}_{\mathrm{z}}\text{Ω}{}_0\text{= 0}$ for all values of the field.     

The vibrational Zeeman effect

The theory of the vibrational Zeeman effect in symmetric top molecules is presented. It is shown that vibrational g factors may be related to rotational g factors and estimates are made of their magnitude for a number of molecules; these calculations indicate that vibrational Zeeman effects should be observable in symmetric top molecules in degenerate vibrational states. In addition, the novel features of the theory for linear molecules are discussed.     

Measurement of the diamagnetic Zeeman shift of potassium S and D Rydberg states

The diamagnetic Zeeman shifts of ²S and ²D Rydberg states of potassium were measured by Doppler-free two-photon absorption with fluorescence detection. Experimental results are found to agree excellently with theoretical values calculated using quantum defect method wavefunctions.     

Interaction theory: Relativistic hydrogen atom and the Lamb shift

The Dirac relativistic equation for the hydrogen atom as augmented by dual interaction terms is solved exactly and the eigenvalues for the bound states are determined. These areE _n =[1 + ²/ (n + s)²]^–1/2, withs ²=k ²– ²(1±)², where is a constant which is a measure of the strength of the dual interaction relative to the standard interaction ^µ A _µ . It is shown that the ratios of the experimental values for the Lamb shifts of various energy levels in hydrogen and singly ionized helium are correctly given by the theory. The origin of the anomalous magnetic moment and, in fact, the operator for the total magnetic moment is given.     

氦原子高激发态的塞曼效应

利用塞曼哈密顿的球张量形式以及塞曼哈密顿在耦合表象中的矩阵元公式,在考虑磁场二次项作用的基础上,研究了氦原子n3P(n=4,5)高激发态的塞曼效应,给出解析解,并绘出了塞曼能级分裂图.     

Relativistic description of single-particle resonances via phase shift analysis

Single-particle resonant states in spherical nuclei are studied by the real stabilization method in coordinate space within the framework of self-consistent relativistic mean field theory. Taking 122Zr as an example, the resonant parameters, including the energies and widths are extracted by fitting energy and phase shift. Good agreement with the previous calculations has been found. The details of single-particle resonant states are analysed.     

Relativistic description of single-particle resonances via phase shift analysis

Single-particle resonant states in spherical nuclei are studied by the real stabilization method in coordinate space within the framework of self-consistent relativistic mean field theory. Taking 122Zr as an example, the resonant parameters, including the energies and widths are extracted by fitting energy and phase shift. Good agreement with the previous calculations has been found. The details of single-particle resonant states are analysed.     

Relativistic Hall effect

We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin-Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices and mechanical flywheels and also discuss various fundamental aspects of this phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales, from elementary spinning particles, through classical light, to rotating black holes.     

Zeeman effect in the polarization spectroscopy of Na

The Doppler-free polarization spectrum of the D₁ line has been studied in fields of about 50 G and in zero field. Although the principal Zeeman resonances are resolved, the signals are confusing because of the very large number of cross-over resonances. Cross-over resonances also seriously distort well-resolved resonances in zero field. An interpretation is given, based on combining a first-order theory of optical pumping with the theory of Faraday rotation and dischroism.     

塞曼效应实验方法的改进

介绍一种利用CCD摄像头、图像处理软件Photoshop 6．0、电子表格处理软件Excel进行塞曼效应实验时图像采集和数据处理的方法．     

Determination of the isotope shift of115m Cd by a Zeeman scanning method

We have used an optical pumping-Zeeman scanning technique in order to determine the isotope shift in the 3,261 Å resonance line of 43-day, spin-11/2^115m Cd. A sample of ≈5×10¹² atoms was aligned in the¹ S ₀ diamagnetic ground state by optically pumping the sample with one selected Zeeman-scanned component of the³ P ₁?3,261 Å resonance line from a¹¹⁴Cd lamp. The alignment was detected through the modulation of the pumping beam at the nuclear resonance frequency. Thus by Zeeman scanning theF = 9/2 component of the³ P ₁ level and using previously determinedA- andB-values, we findδ5v(114–115m (9/2))= ?4,234(48) MHz and¹¹⁴Cd-^115mCd isotope shift = 87(48) MHz. We calculate a staggering parameterγ(^115mCd)=0.73(26), and a change in mean-square nuclear charge radiusδ〈r ²〉^114,115m =0.035(18)fm².     

Measurement of the quadratic Zeeman shift of Rb hyperfine sublevels using stimulated Raman transitions

We demonstrate a technique for directly measuring the quadratic Zeeman shift using stimulated Raman transitions. The quadratic Zeeman shift has been measured yielding Δν=1296.8±3.3 Hz/G² for magnetically insensitive sublevels (5S_1/2,F=2,m_F=0→5S_1/2,F=3,m_F=0) of ⁸⁵Rb by compensating the magnetic field and cancelling the ac Stark shift. We also measured the cancellation ratio of the differential ac Stark shift due to the imbalanced Raman beams by using two pairs of Raman beams (σ⁺, σ⁺) and it is 1:3.67 when the one-photon detuning is 1.5 GHz in the experiment.     

氦原子1snp组态的塞曼效应

利用塞曼哈密顿的球张量形式,采用将微扰理论与里兹变分方法相结合的方式,导出了氦原子1snp组态塞曼哈密顿矩阵元的一般形式,给出了氦原子1s3p组态塞曼效应之解,并绘出了不同磁场强度下氦原子1s3p组态的塞曼能级分裂图.