Point-like Nucleus Research Articles

Continuum solutions of the Klein-Gordon equation

We construct explicit solutions of the Klein-Gordon equation for continuum states. The role of the energy in the single-particle Klein-Gordon theory is elucidated. Special emphasis is laid on the determination of resonance states in the continuum for overcritical potentials. As examples for long-range interactions we depict solutions for the Coulomb potential of a point-like nucleus as well as an extended nucleus. The square-well potential and the exponential potential are treated to exemplify peculiarities of short-range interactions. We also derive continuum solutions for a scalar interaction of square-well type. Finally we discuss the behaviour of a spin-0 particle in an external homogeneous magnetic field.

Implication of the virial theorem on the atomic physics of the nuclearite.

Within the Thomas-Fermi model we have computed, for several values of the nuclear radius, the total energies of the atomic physics of the nuclearite. The transition between the pointlike nucleus and the extended nucleus asymptotic regimes is discussed. By using the virial theorem it is found that the thickness of the ''electron skin'' (s) of large nuclearites grows as s = 0.23 x 10/sup -2/Z/sup 1/3/a/sub 0/, as a function of Z.

Determination via classical mechanics of the maximum number of electrons in an atomic bound state.

Let \ensuremath{\psi} be any normalizable energy eigenfunction for N electrons in an atom having Z protons in a fixed pointlike nucleus. Recently, it has been shown with use of quantum mechanics [Phys. Rev. Lett. 53, 907 (1984)] that, for the state \ensuremath{\psi}, N+1 with F no larger than 4. Evidence was presented that F=F(N)\ensuremath{\rightarrow}2 as N\ensuremath{\rightarrow}\ensuremath{\infty}. In this paper we show that the same result holds in classical mechanics for a bound system.

Maximum Number of Electrons in an Atomic Bound State

Let $\ensuremath{\psi}$ be any normalizable energy eigenfunction for $N$ electrons in an atom having $Z$ protons in a fixed pointlike nucleus. It is shown that, for the state $\ensuremath{\psi}$, $N$ and $Z$ are rigorously related by $N<FZ+1$ with $F=4$. This is independent of any statistics. Evidence is presented that the result can be improved in the sense that $F=F(N)\ensuremath{\rightarrow}2$ for $N\ensuremath{\rightarrow}\ensuremath{\infty}$. A comparison is made with a recent result of Lieb.

Velocity dispersions in galaxies. The nucleus of M31.

view Abstract Citations (52) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Velocity dispersions in galaxies. III. The nucleus of M31. Morton, D. C. ; Thuan, T. X. Abstract A stigmatic spectrum covering 116" through the pointlike nucleus of M31 was obtained with the Princeton integrating television system at the coude' spectrograph of the Hale telescope. The spectrum covered the range 4918 to 5302 A at a resolution of 0.66 A or 39 km s ' with the slit in the E-W direction about 38 from the major axis of the nucleus. The seeing disk had a diameter of about 4" at half the peak light. Comparison of our spectrum with standard G8 III, K0 III, and K3 III stars broadened for various velocity dispersions gives a line-of-sight dispersion at the center of M31 of a = 120 I 30 km s-' with no detectable change out to 113". The spectral lines appear to have a rotational tilt of 20 km s ' (arc sec) -1 out to 13" where the velocities reach +62 and -44 km s-' and then return close to zero. If the nucleus of M3 1 can be considered a dynamical entity, application of the virial theorem, including the effect of rotation, gives a mass of (1.8 1 0.8) x 108 M0 and a ratio of mass to visual light of 13 M0/Ly0. Subject headings: galactic nuclei - galaxies, motions in Publication: The Astrophysical Journal Pub Date: March 1973 DOI: 10.1086/152000 Bibcode: 1973ApJ...180..705M full text sources ADS | data products SIMBAD (4) NED (1) Related Materials (4) Part 1: 1972ApJ...174..489M Part 2: 1973ApJ...179...55M Part 4: 1977ApJ...212...13M Part 5: 1976ApJ...205...63M