[arXiv:physics/0605038]: According to Dirac’s theory of the positron, an electromagnetic field tends to create pairs of particles which leads to a change of Maxwell’s equations in the vacuum. These changes are calculated in the special case that no real electrons or positrons are present and the field varies little over a Compton wavelength. The resulting effective Lagrangian of the field reads: $\cal{L} = \frac{\displaystyle 1}{\displaystyle 2} (\cal{E}^2 - \cal{B}^2) + \frac{\displaystyle e^2}{\displaystyle h c}\int_0^\infty e^{-\eta} \frac{\displaystyle d \eta}{\displaystyle\eta^3}\left\{ i \eta^2 (\cal{EB})\cdot \frac{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB})}\right) + conj.}{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB}})\right) - conj. } + \vert\cal{E}\vert^2 + \frac{\displaystyle\eta^2}{\displaystyle 3} (\cal{B}^2 - \cal{E}^2)\right\}$. $\cal{E}$, $\cal{B}$ field strengths. $\vert\cal{E}_k\vert = \frac{\displaystyle m^2 c^3}{\displaystyle e\hbar} = \frac{\displaystyle 1}{\displaystyle 137} \frac{\displaystyle e}{\displaystyle(e^2/m c^2)^2}$ critical field strengths. The expansion terms in small fields (compared to $\cal{E}$) describe light-light scattering. The simplest term is already known from perturbation theory. For large fields, the equations derived here differ strongly from Maxwell’s equations. Our equations will be compared to those proposed by Born. Original German abstract [Z.Phys. 98(1936)714]: Aus der Diracschen Theorie des Positrons folgt, da jedes elektromagnetische Feld zur Paarerzeugung neigt, eine Abanderung der Maxwellschen Gleichungen des Vakuums. Diese Abanderungen werden fur den speziellen Fall berechnet, in dem keine wirklichen Elektronen und Positronen vorhanden sind, und in dem sich das Feld auf Strecken der Compton-Wellenlange nur wenig andert. Es ergibt sich fur das Feld eine Lagrange-Funktion: $\cal{L} = \frac{\displaystyle 1}{\displaystyle 2} (\cal{E}^2 - \cal{B}^2) + \frac{\displaystyle e^2}{\displaystyle h c}\int_0^\infty e^{-\eta} \frac{\displaystyle d \eta}{\displaystyle\eta^3}\left\{ i \eta^2 (\cal{EB})\cdot \frac{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB}})\right) + konj}{\displaystyle\cos\left(\frac{\displaystyle\eta}{\displaystyle\vert\cal{E}_k\vert}\sqrt{\cal{E}^2 - \cal{B}^2 + 2i (\cal{EB})}\right) - konj } + \vert\cal{E}\vert^2 + \frac{\displaystyle\eta^2}{\displaystyle 3} (\cal{B}^2 - \cal{E}^2)\right\}$. ($\cal{E}$, $\cal{B}$ Kraft auf das Elektron. $\vert\cal{E}_k\vert = \frac{\displaystyle m^2 c^3}{\displaystyle e\hbar} = \frac{\displaystyle 1}{\displaystyle ,,137``} \frac{\displaystyle e}{\displaystyle (e^2/m c^2)^2}$ „Kritische Feldstarke“.) Ihre Entwicklungsglieder fur (gegen $\vert\cal{E}_k\vert$) kleine Felder beschreiben Prozesse der Streuung von Licht an Licht, deren einfachstes bereits aus einer Storungsrechnung bekannt ist. Fur grose Felder sind die hier abgeleiteten Feldgleichungen von den Maxwellschen sehr verschieden. Sie werden mit den von Born vorgeschlagenen verglichen.

Consequences of Dirac's theory of positrons

A theory of highly condensed matter

Aus der Diracschen Theorie des Positrons folgt, da jedes elektromagnetische Feld zur Paarerzeugung neigt, eine Abanderung der Maxwellschen Gleichungen des Vakuums. Diese Abanderungen werden fur den speziellen Fall berechnet, in dem keine wirklichen Elektronen und Positronen vorhanden sind, und in dem sich das Feld auf Strecken der Compton-Wellenlange nur wenig andert.

Folgerungen aus der Diracschen Theorie des Positrons

Neutron Stars 1: Equation of State and Structure

accademiche [38]. Ada [45]. Adrian [45]. African [56]. Age [39, 49, 61]. Al [23]. Al-Rawi [23]. Aldous [68]. Alex [15]. Allure [46]. America [60, 66]. American [49, 69, 61, 52]. ancienne [25]. Andreas [28]. Angela [42]. Animals [16]. Ann [26]. Anna [19, 47]. Annotated [46]. Annotations [28]. Anti [37]. Anti-Copernican [37]. Antibiotic [64]. Anxiety [51]. Apocalyptic [61]. Archaeology [26]. Ark [36]. Artisan [32]. Asylum [48]. Atri [54]. Audra [65]. Australia [41]. Authorship [15]. Axelle [29].

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A Complete Bibliography of Publications in Isis, 2000{2009

Nuclear Reactions at High Energies

When a target is bombarded with high energy deuterons, a narrow beam of high energy neutrons is produced by a process in which the proton in the deuteron strikes the edge of the nucleus and is stripped off, while the neutron misses and continues on its way. The cross section for this stripping process is $\ensuremath{\sigma}=\frac{1}{2}\ensuremath{\pi}R{R}_{d}$, where $R$ is the nuclear radius and ${R}_{d}$ is the deuteron radius, or $\ensuremath{\sigma}=5{A}^{\frac{1}{3}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}$ ${\mathrm{cm}}^{2}$. The yield of neutrons from a \textonehalf{}-in. Be target (in which the energy loss for 190-Mev deuterons is 20 Mev) is nearly 2 percent. The neutrons come out with an energy spread around $\frac{1}{2}{E}_{d}$ having a half-width $\ensuremath{\Delta}{E}_{\frac{1}{2}}=1.5{({E}_{d}{\ensuremath{\epsilon}}_{d})}^{\frac{1}{2}}$. Here ${E}_{d}$ is the kinetic energy of the deuteron, ${\ensuremath{\epsilon}}_{d}$ its binding energy. For light nuclei the half-width of the neutron angular distribution is $\ensuremath{\Delta}{\ensuremath{\theta}}_{\frac{1}{2}}=1.6{(\frac{{\ensuremath{\epsilon}}_{d}}{{E}_{d}})}^{\frac{1}{2}}$. The half-width increases somewhat with atomic number, primarily because of the deflection of the deuteron by the Coulomb field as it approaches the nucleus, and, to a lesser extent, because of multiple scattering in the target. The increase in half-width from Be to U is about 25 percent. The calculated halfwidths and angular distributions agree well with the measurements of Helmholz, McMillan, and Sewell.An equal number of high energy protons are produced by stripping processes in which it is the neutron that hits the nucleus.

The Production of High Energy Neutrons by Stripping

The experiments of Cook, McMillan, Peterson , and Sewell on the cross sections of nuclei for neutrons of about 90 Mev indicate that the nuclei are partially transparent to high energy neutrons. It is shown that the results can be explained quite satisfactorily using a nuclear radius R=1.37Ai X 10-" cm, a potential energy for the neutron in the nucleus of 31 Mev, and a mean free path for the neutron in nuclear matter of 4.5X 10-" cm. This mean free path agrees with that estimated from the high energy n-p cross section , but the results are not sensitive to the choice of mean free path.

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The Scattering of High Energy Neutrons by Nuclei

A number of experiments relating more or less directly to meson scattering and absorption are discussed and compared. Because of the variety of experiments interrelated by such considerations, it is seen that any model to describe meson scattering and absorption will have to meet a corresponding number of conditions. In particular, the absorption experiments of Panofsky and his collaborators permit one to put a lower limit on the absorption cross section for complex nuclei which seems appreciably larger than the expected scattering cross section.

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The Interaction of π-Mesons with Nuclear Matter

Expressions, accurate to the first order in ${e}^{2}$, are obtained for the charge and current densities which, according to positron theory, are induced in vacuum by an electromagnetic field. Because the corresponding correction terms in the Maxwell field equations involve integral operators, it does not seem possible to treat the modified field equations by Hamiltonian methods.

R. Serber

Papers

Nuclear Reactions at High Energies

The Production of High Energy Neutrons by Stripping

The Scattering of High Energy Neutrons by Nuclei

The Interaction of π-Mesons with Nuclear Matter

Linear Modifications in the Maxwell Field Equations