First-order Stark effect

The shift in the energy of a quantum-mechanical system caused by an applied electric field is called the Stark effecLThc first-order (or linear) Stark effect is given by... 

Fig. 6.1 Charge distribution for H, for parabolic eigenstates n = 8, m = 0, nt — / = —7 to 7. The dipole moments that give rise to the first order Stark effect are conspicuous (from...

When a) l/n3, the field required for ionization is E = 1/9n4, and as a> approaches l/n3 it falls to E=0.04n. These observations can be explained qualitatively in the following way. At low n, so that a> 1/n3, the microwave field induces transitions between the Stark states of the same n and m by means of the second order Stark effect. With only a first order Stark shift a state always has the same dipole moment and wavefunction, as indicated by the constant slope dW/d of the energy level curve. Thus when the field reverses, — — , the Rydberg electron s orbit does not change. With a second order Stark shift as well, the slope dW/d is not the same at E and —E, and as a result the dipole moment and wavefunction are not the same. If the field is reversed suddenly a single Stark state in the field E is projected onto several Stark states of the same n and m when E — - E. Since all the Stark states of the same n make transitions among themselves they ionize once the field is adequate to ionize one of them, the red one, at E = 1/9n4 for m n. 

Rotational constants obtained for both the ground and the three first excited vibrational states allowed one to derive the equilibrium molecular structures of GeF2 (re = 1.7321 A, 6>e = 97.1480211) and GeCl2 (re = 2.169452 A, <9e = 99.8825°285). From measurements of the Stark effect the dipole moment of GeF2 has been determined to be 2.61 Debye283. The harmonic and anharmonic force constants up to the third order have been obtained for both molecules and reported too283,285. 

Owing to the special form of the eigenwave functions for t] f=0, and in accordance with the absence of first-order Zeeman effect, it may be shown that the magnetic dipolar contribution to nitrogen resonance line width is very small33,34). Lines are consequently narrow for many of the compounds studied, a very convenient feature when weak effects, like the Stark effect, are to be studied35). 

The first successful electric resonance experiment was reported by Hughes [48] who studied the CsF molecule, an appropriate beam being produced from a hot oven. He used both A and B electric dipole fields, separated by a homogeneous electric C field combined with a radio frequency electric field at right angles to the static field. In order to understand both the deflection and state selection in the dipole fields, as well as the electric resonance spectrum, we first consider the details of the Stark effect. 

Now for CsF in its X ground state the value of A is zero the second 3-j symbol in (8.278) is then non-zero only if 1 + J + J is even, so that. / =. / I is a requirement. In other words, there can be no first-order Stark effect in this case. Equation (8.278) tells us that each rotational level J is mixed by the electric field with the adjacent rotational levels. / 1, and the Stark behaviour may therefore be represented by the following 3x3 truncated matrix. 

In the "nonrigid symmetric-top rotors" (such as NH ), the second-order Stark effect is observed under normal circumstances. Indeed, field strengths of the order of 1 600 000 [V/m] are required to bring the interaction into the first-order regime in this case [18]. In contrast, very weak interactions suffice to make the mixed-parity states and appropriate for the description of optically active systems. Parity-violating neutral currents have been proposed as the interaction missing from the molecular Hamiltonian [Eq.(1)] that is responsible for the existence of enantiomers [14,19]. At present, this hypothesis is still awaiting experimental verification. 

Legon, A. C. and Willoughby, L. C., First-order Stark effect and electric dipole moment of HjP"HC N by pulsed-nozzle Fourier-transform microwave spectroscopy, Chem. Phys. Lett. 111,566-570(1984). 

Bagus et al. [119] have proposed that the largest contribution to the field-induced band shift of carbon monoxide is due to a Stark effect, represented by a first-order perturbation of the energy. A first-order Stark effect has been also proposed by Lambert [170, 171], who has derived an expression based on the effect of the potential upon the dipole moment. The theoretical treatment proposed by Lambert is based on a perturbation of the electric field on the potential energy function, which is written as a double Taylor expansion [171] ... 

This condition combined with the restriction (15) makes our term 3A 3F/2/ze completely equivalent to Epstein s expression of the first order Stark effect, leading to exactly the same energy levels. 

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