Attosecond-Scale Probing of the Electron Motion in the H-Atom Groundstate

doi:10.4236/jmp.2012.312230

Paper Menu >>

Journal Menu >>

Journal of Modern Physics, 2012, 3, 1840-1841

http://dx.doi.org/10.4236/jmp.2012.312230 Published Online December 2012 (http://www.SciRP.org/journal/jmp)

Attosecond-Scale Probing of the Electro n Motion in the

H-Atom Groundstate

Gerald Rosen

Department of Physics, Drexel University, Philadelphia, USA

Email: [email protected], [email protected]

Received September 21, 2012; revised October 24, 2012; accepted November 2, 2012

ABSTRACT

Based on recent advances in attosecond strong-field spectroscopy and the current feasibility for trapping individual

groundstate H-atoms from a neon-gas matrix, an experiment to probe the groundstate motion of the electron in the

H-atom is proposed here.

Keywords: H-Atom Groundstate; Electron Motion

1. Introduction

Both the quasi-quantum-theoretic Bohr model for the

H-atom, with integer-quantized classical orbits for the

electron, and the Schrödinger wavefunction formulation,

with the pointlike electron residing in stationary-state

probability distributions around the proton, accurately

yield Rydberg’s spectra for the Lyman, the Balmer and

the higher-order series. Why both Bohr and Schrödinger

produce the experimental Rydberg physics stems from

the characteristic-caustic mathematical theory for linear

partial and associated ordinary differential equations [1].

However, the physical pictures of Bohr and Schrödinger

are strikingly different: the Bohr picture features integer-

quantized classical paths, while the Schrödinger formula-

tion has the pointlike electron simply filling station-

ary-state probability distributions, with observable elec-

tron motion precluded by the axioms of quantum theory.

Now in the Bohr model 1s groundstate, the electron

moves on a circular orbit of radius

at a velocity

.529 10cm







12 8

213.6eV0.511 MeV2.18910cmsec,c









with the virial theorem implying that the kinetic energy

of the electron is the negative of the total groundstate

binding energy, –13.6 eV. Hence the transit time for a

complete orbit is

2. Proposed Experiment

A proposed scheme for trapping individual cold H-atoms

from a solid neon matrix has been suggested recently,

along with quantitative ab initio quantum calculations

that demonstrate theoretical feasibility if the heating-rate

to the H-atoms can be properly limited [7]. The solid

neon matrix with magnetically captured paramagnetic

low-energy H-atoms is grown in a cell structured with a

cold sapphire substrate. The trapping technique depends

essentially on the energy transfer rate from the thermal

bath to the H-atoms, given in theory by the classical lin-

ear Boltzmann equation. While manifest assumptions are

involved in the proposed scheme, current experiments in

progress will determine if this trapping scheme for cold

H-atoms can be effected [8].

Let us assume that the trapping scheme for individual

cold H-atoms can indeed be effected. Then, if such iso-

lated H-atoms are subjected to strong



13 3

~10W cm





attosecond pulses at the Bohr groundstate frequency



 and wavelength





45.6 nmcct





45.6nm

BB , a sharply peaked reso-

nance ionization may be evident. The key thing here is

that B





from the Bohr model is precisely

one-half the wavelength 91.2 nm, the ionization wave-

length for groundstate H. Thus, since the concentration

of isolated H-atoms is anticipated to be greater than

2π1.52 10sec152tr





 

attosec, a magnitude in the range of recent attosecond

strong-field spectroscopy experiments [2-6]. Also re-

cently, it has been shown feasible to trap individual

groundstate H-atoms from a neon-gas matrix [7]. These

two remarkable recent technological advances suggest an

experiment to probe the groundstate motion of the elec-

tron in an isolated cold H-atom.

14 3

~10 cm

45.6nm

in the neon-gas matrix-trap, a sharply

peaked resonance associated with two ionizations of

H-atoms may appear as the ultraviolet laser is tuned

through B





. On the other hand, the H-atom

1s groundstate in the Schrödinger formulation does not

feature any motion-related significance to B45.6 nm





and the attosecond pulses should ionize H-atoms with a

G. ROSEN 1841

monotone increase in number of ionizations as the laser

wavelength decreases through B45.6nm



, without a

sharply peaked resonance. Hence, the observational re-

sult of the experiment would be of fundamental theoreti-

cal interest.

3. Acknowledgements

The author would like to thank an anonymous reviewer

for helpful suggestions.

REFERENCES

[1] G. Rosen, “Formulations of Classical and Quantum Dy-

namical Theory,” Academic Press, New York, 1969, pp.

22-61.

[2] F. Krauz and M. Ivanov, “Attosecond Physics,” Reviews

of Modern Physics, Vol. 81, No. 1, 2009, pp. 163-234.

doi:10.1103/RevModPhys.81.163

[3] G. Sansone, et al., “Electron Localization Following At-

tosecond Molecular Photoionization,” Nature, Vol. 465,

No. 7299, 2010, pp. 763-766. doi:10.1038/nature09084

[4] E. Golielmakis, et al., “Real-Time Observation of Va-

lence Electron Motion,” Nature, Vol. 466, No. 7307, 2010,

pp. 739-743. doi:10.1038/nature09212

[5] S. Haessler, et al., “Attosecond Imaging of Molecular

Electronic Wavepackets,” Nature Physics, Vol. 6, 2010,

pp. 200-206. doi:10.1038/nphys1511

[6] Y. Huismans, et al., “Time-Resolved Holography with

Photoelectrons,” Science, Vol. 331, No. 6013, 2011, pp.

61-64. doi:10.1126/science.1198450

[7] S. Bovino, et al., “Trapping Hydrogen Atoms from a

Neon-Gas Matrix: A Theoretical Simulation,” Journal of

Chemical Phys ics , Vol. 131, No. 5, 2009, Article ID: 054302.

doi:10.1063/1.3180822

[8] Anonymous Reviewer (2012).