The Mechanism of Nuclear Fission

The potential energy associated with any arbitrary deformation of the nuclear form may be plotted as a function of the parameters which specify the deformation, thus giving a contour surface which is represented schematically in the left-hand portion of the figure.<br /> The pass or saddle point corresponds to the critical deformation of unstable equilibrium. To the extent to which we may use classical terms, the course of the fission process may be symboiized by a ball lying in the hollow at the origin of coordinates (spherical form) which receives an impulse (neutron capture) which sets it to executing a complicated Lissajous figure of oscillation about equilibrium. If its energy is sufficient, it will in the course of time happen to move in the proper direction to pass over the saddle point (after which fission will occur), unless it loses its energy (radiation or neutron re-emission). At the right is a cross section taken through the fission barrier, illustrating the calculation in the text of the probability per unit time of fission occurring.

Niels Bohr and John Archibald Wheeler
On the basis of the liquid drop model of atomic nuclei, an account is given of the mechanism of nuclear fission. In particular, conclusions are drawn regarding the variation from nucleus to nucleus of the critical energy required for fission, and regarding the dependence of fission cross section fo’r a given nucleus on energy of the exciting agency. A detailed discussion of the observations is presented on the basis of the theoretical considerations. Theory and experiment fit together in a reasonable way to give a satisfactory picture of nuclear fission.
Read more at https://journals.aps.org/pr/pdf/10.1103/PhysRev.56.426
Phys. Rev. 56, 426 – Published 1 September 1939

Nonconservation of Energy and Loss of Determinism

I. Infinitely Many Balls
David Atkinson, Porter Johnson
An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This result holds in particular when the total mass of all the balls is finite, and even when the spatial extent and temporal duration of the process are also finite. Further, the process is shown to be indeterministic: there is an arbitrary parameter in the general solution that corresponds to the injection of an arbitrary amount of energy (classically), or energy-momentum (relativistically), into the system at the point of accumulation of the locations of the balls. Specific examples are given that illustrate these counter-intuitive results, including one in which all the balls move with the same velocity after every collision has taken place.
Read more at https://arxiv.org/pdf/1908.10458.pdf

II: Colliding with an Open Set
An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy non-conservation and (creatio ex nihilo) no longer occur. A numerical analysis of finite systems of colliding balls is given, and the asymptotic behavior that corresponds to the potentially infinite system is inferred.
Read more at https://arxiv.org/pdf/1908.09865.pdf

The aromatic Universe

The rich molecular structures of polycyclic aromatic hydrocarbons — essentially planar flakes of fused benzene rings — and their fullerene cousins are revealed through their vibrational and electronic spectra.

In this artistic impression, large polycyclic aromatic hydrocarbon (PAH) molecules exposed to the strong radiation field of a star first lose all their peripheral hydrogen atoms (white atoms, top right) and are transformed into small graphene flakes whose fragile, dangling carbon rings at the corners break off. That degradation is then followed by the loss of carbon atoms. The loss creates pentagons (red) in the dehydrogenated PAH molecule, which bends the structure out of the plane and culminates in the formation of a C60 fullerene

A. Candian, J. Zhen, A.G.G.M. Tielens
Over the past 20 years, ground- and space-based observations have revealed that the universe is filled with molecules. Astronomers have identified nearly 200 types of molecules in the interstellar medium (ISM) of our galaxy and in the atmospheres of planets; for the full list, see http://www.astrochymist.org. Molecules are abundant and pervasive, and they control the temperature of interstellar gas. Not surprisingly, they directly influence such key macroscopic processes as star formation and the evolution of galaxies.
read more at https://arxiv.org/ftp/arxiv/papers/1908/1908.05918.pdf

Quantum Poker

a pedagogical tool to learn quantum computing that is fun to play

bloch sphere

The state of a qubit can be represented geometrically as any state on the so-called Bloch sphere

Franz G. Fuchs, Vemund Falch, Christian Johnsen
Quantum computers are on the verge of becoming a commercially available reality. They represent a paradigm change to the classical computing paradigm, and the learning curve is considerably long. The creation of games is a way to ease the transition for novices. We present a game similar to the poker variant Texas hold ’em with the intention to serve as an engaging pedagogical tool to learn the basics rules of quantum computing. The difference to the classical variant is that the community cards are replaced by a quantum register that is “randomly” initialized, and the cards for each player are replaced by quantum gates, randomly drawn from a set of available gates. Each player can create a quantum circuit with their cards, with the aim to maximize the number of 1’s that are measured in the computational basis. The basic concepts of superposition, entanglement and quantum gates are employed. We provide a proof-of-concept implementation using Qiskit. A comparison of the results using a simulator and IBM machines is conducted, showing that error rates on contemporary quantum computers are still very high. Improvements on the error rates and error mitigation techniques are necessary, even for simple circuits, for the success of noisy intermediate scale quantum computers.

read more at https://arxiv.org/pdf/1908.00044.pdf

The “Terrascope”

On the Possibility of Using the Earth as an Atmospheric Lens

terrascope

Illustration of a detector of diameter W utilizing the terrascope. Two rays of different impact parameters, but the same wavelength, lens through the atmosphere and strike the detector. The ring formed by those two rays enables a calculation of the amplification. In this setup, the detector is precisely on-axis

David Kipping
Distant starlight passing through the Earth’s atmosphere is refracted by an angle of just over one degree near the surface. This focuses light onto a focal line starting at an inner (and chromatic)boundary out to infinity – offering an opportunity for pronounced lensing. It is shown here that the focal line commences at ∼85% of the Earth-Moon separation, and thus placing an orbiting detector between here and one Hill radius could exploit this refractive lens. Analytic estimates are derived for a source directly behind the Earth (i.e. on-axis) showing that starlight is lensed into a thin circular ring of thickness W H∆/R, yielding an amplification of 8H∆/W, where H∆ is the Earth’s refractive scale height, R is its geopotential radius and W is the detector diameter. These estimates are verified through numerical ray-tracing experiments from optical to 30 µm light with standard atmospheric models. The numerical experiments are extended to include extinction from both a clear atmosphere and one with clouds. It is found that a detector at one Hill radius is least affected by extinction since lensed rays travel no deeper than 13.7 km, within the statosphere and above most clouds. Including extinction, a 1 metre Hill radius “terrascope” is calculated to produce an amplification of ∼45, 000 for a lensing timescale of ∼20 hours. In practice, the amplification is likely halved in order to avoid daylight scattering i.e. 22, 500 (∆mag=10.9) for W =1 m, or equivalent to a 150 m optical/infrared telescope.

Read more at https://arxiv.org/pdf/1908.00490.pdf

Using Earth to See Across the Universe: The Terrascope with Dr. David Kipping:

Read also: “The Terrascope – Using Earth As A Lens

Estimating the Moon to Earth radius ratio with a smartphone, a telescope and an eclipse


Hugo Caerols, Felipe A. Asenjo
On January 20th, 2019, a total lunar eclipse was possible to be observed in Santiago, Chile. Using a smartphone attached to a telescope, photographs of the phenomenon were taken. With Earth’s shadow on those images, and using textbook geometry, a simple open-source software and analytical procedures, we were allowed to calculate the ratio between the radii of the Moon and the Earth. The results are in very good agreement with the correct value for such ratio. This shows the strength of the smartphone technology to get powerful astronomical results in a very simple way and in a very short amount of time.
Read more at https://arxiv.org/pdf/1907.08339.pdf

Weighing the Sun with five photographs


Hugo Caerols, Felipe A. Asenjo
With only five photographs of the Sun at different dates we show that the mass of Sun can be calculated by using a telescope, a camera, and the third Kepler’s law. With the photographs we are able to calculate the distance from Sun to Earth at different dates along four months. These distances allow us to obtain the correct elliptical orbit of Earth, proving the first Kepler’s law. The analysis of the data extracted from photographs is performed by using an analitical optimization approach that allow us to find the parameters of the elliptical orbit. Also, it is shown that the five data points fit an ellipse using an geometrical scheme. The obtained parameters are in very good agreement with the ones for Earth’s orbit, allowing us to foresee the future positions of Earth along its trajectory. The parameters for the orbit are used to calculate the Sun’s mass by applying the third Kepler’s law. This method gives a result wich is in excellent agreement with the correct value for the Sun’s mass. Thus, in a span of time of four months, any student is capable to calculate the mass of the sun with only five photographs, a telescope and a camera.
Read more https://arxiv.org/pdf/1906.12272.pdf