This book contains information on atomic, molecular and optical physics. Topics covered include: muon-catalyzed fusion and cooperative effects in atomic physics.

Advances in Atomic, Molecular, and Optical Physics

The field of experimental positronium physics has advanced significantly in the last few decades, with new areas of research driven by the development of techniques for trapping and manipulating positrons using Surko-type buffer gas traps. Large numbers of positrons (typically ≥106) accumulated in such a device may be ejected all at once, so as to generate an intense pulse. Standard bunching techniques can produce pulses with ns (mm) temporal (spatial) beam profiles. These pulses can be converted into a dilute Ps gas in vacuum with densities on the order of 107 cm−3 which can be probed by standard ns pulsed laser systems. This allows for the efficient production of excited Ps states, including long-lived Rydberg states, which in turn facilitates numerous experimental programs, such as precision optical and microwave spectroscopy of Ps, the application of Stark deceleration methods to guide, decelerate and focus Rydberg Ps beams, and studies of the interactions of such beams with other atomic and molecular species. These methods are also applicable to antihydrogen production and spectroscopic studies of energy levels and resonances in positronium ions and molecules. A summary of recent progress in this area will be given, with the objective of providing an overview of the field as it currently exists, and a brief discussion of some future directions.

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Experimental progress in positronium laser physics

The book is devoted to the applications of p-adic length scale hypothesis and dark matter hierarchy. 


p-Adic length scale hypothesis states that primes p≈ 2k, k integer, in particular prime, define preferred p-adic length scales. Physical arguments supporting this hypothesis are based on the generalization of Hawking's area law for blackhole entropy so that it applies in case of elementary particles. A deeper number theory based justification for this hypothesis is based on the generalization of the number concept fusing real number fields and p-adic number fields among common rationals or numbers in their non-trivial algebraic extensions. This approach also justifies the notion of multi-p-fractality and allows to understand scaling law in terms of simultaneous p≈ 2k- and 2-fractality. In TGD framework the levels of dark matter hierarchy are labeled by the values of dynamical quantized Planck constant. The justification for the hypothesis provided by quantum classical correspondence and the fact the sizes of space-time sheets identifiable as quantum coherence regions can be arbitrarily large. The weak form of electric-magnetic duality is the newest building brick of the vision and leads to a detailed view about electro-weak screening and color confinement and predicts new physics below weak scales. The weak form of electric-magnetic duality allows to identify Higgs bosons and to understand how they provide the longitudinal polarizations of gauge bosons. The most natural option is that photon eats the remaining Higgs scalar and receives a small mass. This true for all bosons regarded as massless and allows to have exact Yangian symmetry requiring the vanishing of IR divergences. Higgs potential and vacuum expectation of Higgs are not needed in the model. Twistors emerge naturally in TGD framework and several proposal for twistorialization of TGD is discussed in two chapters devoted to the topic. Twistorial approach combined with zero energy ontology, bosonic emergence, and the properties of the Chern-Simons Dirac operator leads to the conjecture that all particles -also string like objects- can be regarded as bound states of massless particles identifiable as wormhole throats. Also virtual particles would consist of massles wormhole throats but bound state property is not assumed anymore and the energies of wormhole throats can have opposite signs so that space-like momentum exchanges become possible. This implies extremely strong constraints on loop momenta and manifest finiteness of loop integrals. 


The first part of the book is about the description of elementary particle massivation in terms of p-adic thermodynamics and Higgsy contribution affecting the vacuum conformal weight. In the first chapter the view about quantum TGD from particle physics perspective is discussed and the remaining chapters are devoted to the detailed calculation of masses of elementary particles and hadrons, and to various new physics suggested or predicted by the resulting scenario. 

Second part of the book is devoted to the application of p-adic length scale hypothesis above elementary particle length scales. The so called leptohadron physics, originally developed on basis of experimental anomalies, is discussed as a particular instance of an infinite fractal hierarchy of copies of standard model physics, predicted by TGD and consistent with what is known about ordinary elementary particle physics. TGD based view about nuclear physics involves light exotic quarks as a essential element, and dark nuclear physics could have implications also at the level of condensed matter physics and biology. TGD based view about high Tc superconductors involves also in an essential manner dark matter and is summarized in the closing chapter.

P-Adic Length Scale Hypothesis and Dark Matter Hierarchy

Positron range impairs resolution in PET imaging, especially for high-energy emitters and for small-animal PET. De-blurring in image reconstruction is possible if the blurring distribution is known. Furthermore, the percentage of annihilation events within a given distance from the point of positron emission is relevant for assessing statistical noise. 
This paper aims to determine the positron range distribution relevant for blurring for seven medically relevant PET isotopes, $^{18}$F, $^{11}$C, $^{13}$N, $^{15}$O, $^{68}$Ga, $^{62}$Cu and $^{82}$Rb, and derive empirical formulas for the distributions. This paper focuses on allowed-decay isotopes. It is argued that blurring at the detection level should not be described by the positron range $r$, but instead the 2D projected distance $\delta$ (equal to the closest distance between decay and line of response). To determine these 2D distributions, results from a dedicated positron track-structure Monte Carlo code, Electron and POsitron TRANsport (EPOTRAN), were used. Materials other than water were studied with PENELOPE. 
The radial cumulative probability distribution G$_{2D}$($\delta$) and the radial probability density distribution $g_{2D}$($\delta$) were determined. G$_{2D}$($\delta$) could be approximated by the empirical function 1 - exp(-$A \delta^2$ - $B \delta$), where A = 0.0266 ($E_{mean}$)$^{-1.716}$ and B = 0.1119 ($E_{mean}$)$^{-1.934}$, with $E_{mean}$ being the mean positron energy in MeV and $\delta$ in mm. The radial density distribution $g_{2D}$($\delta$) could be approximated by differentiation of G$_{2D}$($\delta$). Distributions in other media were very similar to water. The positron range is important for improved resolution in PET imaging. Relevant distributions for the positron range have been derived for seven isotopes. Distributions for other allowed-decay isotopes may be estimated with the above formulas.

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Positron range in PET imaging: an alternative approach for assessing and correcting the blurring

Technical advances towards high resolution PET imaging try to overcome the inherent physical limitations to spatial resolution. Positrons travel in tissue until they annihilate into the two gamma photons detected. This range is the main detector-independent contribution to PET imaging blurring. To a large extent, it can be remedied during image reconstruction if accurate estimates of positron range are available. However, the existing estimates differ, and the comparison with the scarce experimental data available is not conclusive. In this work we present positron annihilation distributions obtained from Monte Carlo simulations with the PeneloPET simulation toolkit, for several common PET isotopes (18F, 11C, 13N, 15O, 68Ga and 82Rb) in different biological media (cortical bone, soft bone, skin, muscle striated, brain, water, adipose tissue and lung). We compare PeneloPET simulations against experimental data and other simulation results available in the literature. To this end the different positron range representations employed in the literature are related to each other by means of a new parameterization for positron range profiles. Our results are generally consistent with experiments and with most simulations previously reported with differences of less than 20% in the mean and maximum range values. From these results, we conclude that better experimental measurements are needed, especially to disentangle the effect of positronium formation in positron range. Finally, with the aid of PeneloPET, we confirm that scaling approaches can be used to obtain universal, material and isotope independent, positron range profiles, which would considerably simplify range correction.

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Positron range estimations with PeneloPET

Positronium (Ps), a hydrogen-like atom composed of an electron and its antimatter partner, the positron, is formed in considerable quantities whenever positrons interact with matter. It has unexpectedly been found to scatter from a wide variety of atoms and molecules in a way very similar to that of a bare electron moving at the same velocity, despite Ps being neutral and twice the mass.

https://science.sciencemag.org/content/sci/330/6005/789.full.pdf

Electron-like scattering of positronium.

The total cross sections of positronium (Ps) scattering from a carbon-dioxide molecule have been measured over the range (7--400) eV incident-Ps energy. For the first time in Ps collisions, a resonantlike structure is observed. For the present target, it occurs around 9.5 eV followed by a broader peak at $\ensuremath{\sim}60\text{ }\text{ }\mathrm{eV}$. Following Brawley et al. [Science 330, 789 (2010)] who have observed similarities between the total cross sections of positronium and of electrons incident upon a given target at the same velocity, a corresponding comparison is made for ${\mathrm{CO}}_{2}$. The comparison suggests that the former peak corresponds to the well-known $^{2}\ensuremath{\Pi}_{u}$ shape resonance which occurs for electrons at an incident velocity of 0.5 a.u. Further features are discussed and theoretical input is sought.

Resonant Scattering of Positronium in Collision with CO 2

Recent findings on the similarity between electron and positronium scattering at the same velocity [Brawley et al., Science 330, 789 (2010)] have guided us towards the realization of a detectable flux of positronium atoms at beam energies five times lower than previously obtained, enabling total cross sections to be measured in the energy range ∼(1-7)  eV for the first time. In collision with Ar and Xe, the total cross sections of positronium are found to be smallest at the lowest energy probed, approaching those of the Ramsauer-Townsend minima for electron projectiles. Additional structure has been observed in the case of positronium scattering at incident energies around 5 eV.

Positronium Production and Scattering below Its Breakup Threshold.

The first absolute experimental determinations of the differential cross sections for the formation of ground-state positronium are presented for He, Ar, H2, and CO2 near 0°. Results are compared with available theories. The ratio of the differential and integrated cross sections for the targets exposes the higher propensity for forward emission of positronium formed from He and H2.

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Absolute differential positronium-formation cross sections

Cross-sections are presented, both integrated and differential with respect to the longitudinal energy of the ejected positrons, for the fragmentation of Ps in collisions with Xe at 18 and 30 eV impact energy and compared with available theory. The shapes of the positron spectra are also compared with those measured in collisions with He at the same impact energy.

S. J. Brawley

Papers

Electron-like scattering of positronium.

Resonant Scattering of Positronium in Collision with CO 2

Positronium Production and Scattering below Its Breakup Threshold.

Absolute differential positronium-formation cross sections

Fragmentation of positronium in collision with xenon