Explicit formulae are derived relating the energies and the ionisation potentials of an arbitrary neutral two-particle system in a magnetic field B to the energies and the ionisation potentials of a hydrogen atom of infinite nuclear mass in a magnetic field (me/μ)2B.
References (5)
J.E. Avron et al.
Ann. Phys.
(1978)
R.F. O'Connell
Phys. Lett.
(1979)
There are more references available in the full text version of this article.
Paschen-series spectral lines have been calculated for H atoms in the presence of strong magnetic fields. Wavelengths and transition probabilities are presented for 54 electric dipole transitions as a function of magnetic field strengths ranging from 0.001 a.u. to 1 a.u. The effect of the finite proton mass is taken into account. The present calculations involve five symmetries , , and , and the 6 lowest electronic states for each symmetry, and thus a total of 26 magnetized atomic states are contained if excluding the 4 atomic states relevant to Lyman-series and Balmer-series spectral lines. The obtained results are compared with the available theoretical data. Our detailed atomic data, energy level differences between the initial and final states and dipole strengths under the infinite proton mass, for the selected Paschen-series spectral lines are compared to those from the other theoretical methods, and excellent agreement is shown.
Recent observations of hundreds of hydrogen-rich magnetic white dwarf stars with magnetic fields up to 105 T (103 MG) have called for more comprehensive and accurate databases for wavelengths and oscillator strengths of the H atom in strong magnetic fields for all states evolving from the field-free levels with principal quantum numbers . We present a code to calculate the energy eigenvalues and wave functions of such states which is capable of covering the entire regime of field strengths T to T. We achieve this high flexibility by using a two-dimensional finite element expansion of the wave functions in terms of -splines in the directions parallel and perpendicular to the magnetic field, instead of using asymptotically valid basis expansions in terms of spherical harmonics or Landau orbitals. We have paid special attention to the automation of the program such that the data points for the magnetic field strengths at which the energy of a given state are calculated can be selected automatically. Furthermore, an elaborate method for varying the basis parameters is applied to ensure that the results reach a pre-selected precision, which also can be adjusted freely. Energies and wave functions are stored in a convenient format for further analysis, e.g. for the calculation of transition energies and oscillator strengths. The code has been tested to work for 300 states with an accuracy of better than 10−6 Rydberg across several symmetry subspaces over the entire regime of magnetic field strengths.
The hydrogen problem in the presence of a magnetic field of arbitrary strength shall be solved for all states up to a principal quantum number of . We obtain the full energy vs. field strength function within a certain precision.
Solution method:
We expand the wave functions in a 2d -spline basis, vary the corresponding energy functional for the -spline coefficients and solve the resulting generalised eigenvalue problem. The -spline basis parameters are adapted iteratively to ensure the overall precision of our results.
Restrictions:
Non-relativistic Hamiltonian, non-moving atom.
Unusual features:
Automated analysis of the states at magnetic field strengths from to .
Running time:
Seconds to minutes per single result; hours to days for a full analysis.
2009, Physica A: Statistical Mechanics and its Applications
The scaling properties of various composite information-theoretic measures (Shannon and Rényi entropy sums, Fisher and Onicescu information products, Tsallis entropy ratio, Fisher–Shannon product and shape complexity) are studied in position and momentum spaces for the non-relativistic hydrogenic atoms in the presence of parallel magnetic and electric fields. Such measures are found to be invariant at the fixed values of the scaling parameters given by and . Numerical results which support the validity of the scaling properties are shown by choosing the representative example of the position space shape complexity. Physical significance of the resulting scaling behavior is discussed.
The hydrogen atom in crossed electric and magnetic fields is studied in an approximate but purely quantal way, with exact treatment of gauge invariance and centre-of-mass motion. Under some conditions, a triaxial harmonic motion appears where the electron average location is strongly delocalized with respect to the proton.