One remark on the inverse scattering problem for the perturbed Stark operator on the semiaxis

In the present paper, it is indicated that the proof of the main lemma is not valid, which relates to the inverse scattering problem for the perturbed Stark operator on the semiaxis. A correct proof of the mentioned lemma is given.

Eigenvalues asymptotics for Stark operators

We give the eigenvalues asymptotics for the Stark operator of the form −Δ+F x, F > 0 on L2([0, d]). This is given in the case when F is small enough or sufficiently large. We impose various boundary conditions. The proof is based on the asymptotics of the specialized Airy functions.

An inverse problem of scattering theory for the perturbed Stark operator on the semiaxis

In the present paper, we consider the inverse problem for the perturbed Stark operator. We obtain necessary and sufficient conditions on the set of values, which could serve as scattering data for the considered operator, and we prove their sufficiency.

The hyperfine structure Stark effect - III. The 2 P ½ level of aluminium

The quadratic Stark effect in the hyperfine structure of the 2 P ½ ground level of aluminium has been investigated by the method of atomic beams. A frequency shift caused by the application of an electric field has been interpreted in terms of an effective Stark operator, and the associated tensor polarizability α ten ( J = ½, F = 3) has a measured value of (8.13±0.72) × 10 –4 a 3 0 . The case of J = ½ is a special one in that the theoretical value of α ten ( J = ½, F = 3) vanishes in the absence of hyperfine structure effects. The inclusion of the hyperfine structure operator in a calculation of the tensor polarizability has led to a small theoretical value in agreement with experiment.

The hyperfine structure Stark effect II. The ground levels of samarium, europium and aluminium

The quadratic Stark effect in the hyperfine structure of the ground levels of samarium, europium and aluminium has been investigated by the method of atomic beams. Frequency shifts caused by the application of an electric field have been interpreted, to second order in perturbation theory, in terms of an effective Stark operator with which is associated a parameter called the tensor polarizability, α ten. . In the LS coupling approximation the results for five lines in samarium give a value α ten. ( 7 F ; J ═ 6) ═ – 3·64 ± 0·17 a 0 3 . Measurements on one line in europium give, for the ground level, α ten. ( J ═ 7 / 2 ) ═ 0·0141 ± 0·0007 a 0 3 . In the IJ coupling and LS coupling approximations the theory of the Stark effect in hyperfine structure has been tested and confirmed, but on the more stringent assumption that the central-field approximation is also valid, an attempt to evaluate a parameter α ten. (4 f ) common to both samarium and europium has only limited success. This result leads to the expected conclusion that in the rare earths the central-field model breaks down. Measurements on one line in aluminium give α ten. ( J ═ 3/2) ═ α ten. (3 p ) ═ – 8·15 ± 0·40 a 0 3 . In the course of this work new values of the hyperfine structure interaction constants and of the g -factor have been found for the 3 p 2 P 3/2 level of 27 Al. These results are A ═ + 94·27767 ± 0·00010 Mc/s, B ═ + 18·91526 ± 0·00070 Mc/s, gj ═ 1·33474 ± 0·00005.