Fowler-Nordheim Electron Cold Emission Formalism in Presence of Strong Magnetic Field

Formalisms for both non-relativistic as well as relativistic versions of field emission of electrons in presence of strong quantizing magnetic field, relevant for strongly magnetized neutron stars or magnetars are developed. In the non-relativistic scenario, where electrons obey Schr{$\ddot{\rm{o}}$}dinger equation, we have noticed that when Landau levels are populated for electrons in presence of strong quantizing magnetic field the transmission probability exactly vanishes unless the electrons are spin polarized in the opposite direction to the external magnetic field. On the other hand, the cold electron emission under the influence of strong electrostatic field at the poles is totally forbidden from the surface of those compact objects for which the surface magnetic field strength is $\gg 10^{15}$G (in the eventuality that they may exist). Whereas in the relativistic case, where the electrons obey Dirac equation, the presence of strong quantizing magnetic field completely forbids the emission of electrons from the surface of compact objects if $B >10^{13}$G.Comment: Nine pages including one figure. Some version will apprear in Monthly Notice of Royal Astronomical Society (MNRAS), 2012. arXiv admin note: substantial text overlap with arXiv:1006.519

The Study of Magnetically Deformed Atoms in the Outer Crust of Neutron Stars in Presence of Strong Quantizing Magnetic Field

We have studied the various properties of magnetically deformed atoms, replaced by deformed Wigner-Seitz cells, at the outer crust region of strongly magnetized neutron stars (magnetars) using a relativistic version of Thomas-Fermi model in cylindrical coordinates.Comment: 15 pages REVTEX file, 14 .eps figure

Can There be Quark Matter Core in a Strongly Magnetized Neutron Star?

The effect of strong quantizing magnetic field on the nucleation of quark matter droplets and on the chemical evolution of nascent quark phase at the core of a neutron star are investigated. The surface energy of quark phase diverges logarithmically. As a consequence there can not be a first order transition to quark phase. However, a metal-insulator type of second order transition is possible unless the field strength exceeds $10^{20}$G. The study of chemical evolution of newborn quark phase shows that in $\beta$-equilibrium the system becomes energetically unstable.Comment: RevTeX, 6 pages, 5 eps figures, for preprint request send mail to [email protected]

Anisotropic Nature of Work Function in Strong Quantizing Magnetic Field

Following an extremely interesting idea \cite{R1}, published long ago, the work function associated with the emission of ultra-relativistic electrons from magnetically deformed metallic crystal of astrophysical relevance is obtained using relativistic version of Thomas-Fermi type model. In the present scenario, surprisingly, the work function becomes anisotropic; the longitudinal part is an increasing function of magnetic field strength, whereas the transverse part diverges.Comment: Some verson has been accepted in Journal of Astrophysics and Astronomy, 11 pages with two.eps figure

A Relativistic Generalization of Fowler-Nordheim Cold Emission in Presence of Strong Magnetic Field

A relativistic version of cold emission of electrons in presence of strong magnetic field, relevant for strongly magnetized neutron stars is obtained. It is found that in this scenario, a scalar type potential barrier does not allow quantum tunneling through the surface. Whereas, in presence of a vector type surface barrier, the probability of electron emission is much larger compared to the original Fowler-Nordheim cold emission of electrons. It is found that the relativistic version in presence of strong magnetic field does not follow exponential decay.Comment: Seven pages REVTEX file, one.eps figure. Text is revise

Work Function of Strongly Magnetized Neutron Star Crustal Matter and the Associated Magneto-Sphere

Following an extremely interesting idea \cite{R1}, published long ago, the work function at the outer crust region of a strongly magnetized neutron star is obtained using relativistic version of Thomas-Fermi type model. In the present scenario, the work function becomes anisotropic; the longitudinal part is an increasing function of magnetic field strength, whereas the transverse part diverges. An approximate estimate of the electron density in the magnetosphere due to field emission and photo emission current, from the polar cap region are obtained.Comment: 4 pages REVTEX with three .eps figure

Chiral Symmetry Breaking in Presence of Strong Quantizing Magnetic Fields- A Nambu-Jona-Lasino Model with Semi-Classical Approximation

The breaking of chiral symmetry of light quarks at zero temperature in presence of strong quantizing magnetic field is studied using Nambu-Jona-Lasinio (NJL) model with Thomas-Fermi type semi-classical formalism. It is found that the dynamically generated light quark mass can never become zero if the Landau levels are populated and increases with the increase of magnetic field strength.Comment: Revtex file, Seven Pages, One .eps figure (included

A Theoretical Study of the Equation of States for Crustal Matter of Strongly Magnetized Neutron Stars

We have investigated some of the properties of dense sub-nuclear matter at the crustal region (both the outer crust and the inner crust region) of a magnetar. The relativistic version of Thomas-Fermi (TF) model is used in presence of strong quantizing magnetic field for the outer crust matter. The compressed matter in the outer crust, which is a crystal of metallic iron, is replaced by a regular array of spherically symmetric Wigner-Seitz (WS) cells. In the inner crust region, a mixture of iron and heavier neutron rich nuclei along with electrons and free neutrons has been considered. Conventional Harrison-Wheeler (HW) and Bethe-Baym-Pethick (BBP) equation of states are used for the nuclear mass formula. A lot of significant changes in the characteristic properties of dense crustal matter, both at the outer crust and the inner crust, have been observed.Comment: 20 pages, 11 .eps figures, to appear in EPJ

Thomas-Fermi Model in Rindler Space

In this article we have investigated the Thomas-Fermi model for the electron gas in Rindler space. We have found that if the uniform acceleration is along $+x$-direction, then there is $y-z$-symmetry in space. For the sake of mathematical simplicity, we have assumed two dimensional spatial structure ($x-y$) in Rindler space. It has been observed that in two dimensional spatial coordinates the electrons are distributed discontinuously but in a periodic manner in a number of rectangular strips like domain along $\pm y$-direction. Some of them are having void structure, with no electrons inside such rectangular strips, while some are filled with electrons. We call the later type domain as the normal zone. We have also given physical interpretation for such exotic type electron distribution in Rindler space.Comment: 9 pages with one embedded .eps figure. Some version will appear in Mod. Phys. Lett.

Magnetically Induced "Dry" Water Like Structure of Charged Fluid at the Core of a Magnetar

It is shown that charged fluid, e.g., electron gas or proton matter at the core of a magnetar exhibit super-fluid (frictionless) like property if the magnetic field strength is high enough to populate only the zeroth Landau levels.Comment: Four pages REVTEX FILE, One .eps file (included