Investigation of the impact parameter method for electron-atom collisions

In this thesis we develop and investigate the use of a semi-classical impact parameter method for treating the excitation of atoms by electron impact. Our particular interest is forbidden, non-exchange transitions. Chapter 1 contains a brief description of the method along with reasons for considering such a method. Previous work employing the same general ideas is reviewed, as are other theoretical calculations and experimental results of direct relevance to this thesis. The paper of Seaton (1962) which applies the impact parameter method to optically allowed transitions is reviewed in some detail as our treatment of the subject is based largely on this work. In Chapter 2 we derive expressions for the transition probabilities and introduce the idea of the averaged probabilities. Cross section formulae are given which are applicable to dipole and quadrupole transitions and which include a strong coupling form. The formulae are generalized to apply to an incident point particle of arbitrary mass and charge. Chapter 3 contains formulae for the averaged probabilities for arbitrary interaction potentials and these are applied to the case where the potential is a sum of spherical tensor operators. Expressions for cross sections, applicable to arbitrary transitions induced by electron or proton impact, are given and the explicit form evaluated for the case of hydrogen. In Chapter 4 are presented results of calculations of cross sections for certain forbidden transitions in hydrogen and helium, both for electron and proton impact. We examine the validity of the approximations made and discuss the choice of the cut-off. Chapter 5 contains an evaluation of the method as well as suggestions for improving it and for further applications. The derivation of certain results used in the thesis is presented in the appendices.<p

Differential Cross Sections and Cross-Section Ratios for the Electron-Impact Excitation of the Neon 2p⁵3s Configuration

Electron-impact differential cross-section measurements for the excitation of the 2p53s configuration of Ne are reported. The Ne cross sections are obtained using experimental differential cross sections for the electron-impact excitation of the n = 2 levels of atomic hydrogen [Khakoo et al., Phys. Rev. A 61, 012701-1 (1999)], and existing experimental helium differential cross-section measurements, as calibration standards. These calibration measurements were made using the method of gas mixtures (Ne and H followed by Ne and He), in which the gas beam profiles of the mixed gases are found to be the same within our experimental errors. We also present results from calculations of these differential cross sections using the R-matrix and unitarized first-order many-body theory, the distorted-wave Born approximation, and relativistic distorted-wave methods. Comparison with available experimental differential cross sections and differential cross-section ratios is also presented

Viscosity cross sections for the heavy noble gases

We have calculated viscosity cross sections for argon, krypton and xenon from zero to 1 keV using the phase shifts from our previous publication [R.P. McEachran, A.D. Stauffer, Eur. Phys. J. D 68, 153 (2014)] which presented total elastic and momentum transfer cross sections for these gases. As previously, we present simple analytic fits to our results to aid in modelling plasmas containing these atoms. By using the current results and those in reference [R.P. McEachran, A.D. Stauffer, Eur. Phys. J. D 68, 153 (2014)] the first two ‘partial cross sections’ used in the general moment method of solving the Boltzmann equation can be obtained. The agreement of our viscosity cross sections with experimentally derived results indicates the overall reliability of our calculations

A method to obtain static potentials for electron-molecule scattering

We present a method for calculating the static potential of an arbitrary molecule which is represented by the well-known Gaussian wavefunctions. This potential is given in analytic form which, in additions to elementary functions, contains the error function for which simple and accurate methods for its evaluation exist. As an example we have used this potential, along with polarization-correlation and exchange potentials, to calculate the differential cross sections for the scattering of electrons from the water molecule in the energy range 30–100 eV. Comparison with previous calculations and experimental measurements show that this method produces accurate results for the differential scattering cross sections

Collisional-radiative model for non-Maxwellian inductively coupled argon plasmas using detailed fine-structure relativistic distorted-wave cross sections

Our recently developed collisional-radiative model which included fine-structure cross sections calculated with a fully relativistic distorted-wave method [R.K. Gangwar, L. Sharma, R. Srivastava, A.D. Stauffer, J. Appl. Phys. 111, 053307 (2012)] has been extended to study non-Maxwellian inductively coupled argon plasmas. We have added more processes to our earlier collisional-radiative model by further incorporating relativistic distorted-wave electron impact cross sections from the 3p54sJ = 0, 2 metastable states, (1s3, 1s5 in Paschen’s notation) to the 3p55p (3pi) excited states. The population of various excited levels at different pressures in the range of 1–25 mTorr for an inductively coupled argon plasma have been calculated and compared with the recent optical absorption spectroscopy measurements as well as emission model results of Boffard et al. [Plasma Sources Sci. Technol. 19, 065001 (2010)]. We have also calculated the intensities of two emission lines, 420.1 nm (3p9 → 1s5) and 419.8 nm (3p5 → 1s4) and compared with measured intensities reported by Boffard et al. [J. Phys. D 45, 045201 (2012)]. Our results are in good agreement with the measurements

Viscosity cross sections for the heavy noble gases

We have calculated viscosity cross sections for argon, krypton and xenon from zero to 1 keV using the phase shifts from our previous publication [R.P. McEachran, A.D. Stauffer, Eur. Phys. J. D 68, 153 (2014)] which presented total elastic and momentum transfer cross sections for these gases. As previously, we present simple analytic fits to our results to aid in modelling plasmas containing these atoms. By using the current results and those in reference [R.P. McEachran, A.D. Stauffer, Eur. Phys. J. D 68, 153 (2014)] the first two ‘partial cross sections’ used in the general moment method of solving the Boltzmann equation can be obtained. The agreement of our viscosity cross sections with experimentally derived results indicates the overall reliability of our calculations

Introduction STATE OF THE CLIMATE IN 2022

Abstract —J. BLUNDEN, T. BOYER, AND E. BARTOW-GILLIES Earth’s global climate system is vast, complex, and intricately interrelated. Many areas are influenced by global-scale phenomena, including the “triple dip” La Niña conditions that prevailed in the eastern Pacific Ocean nearly continuously from mid-2020 through all of 2022; by regional phenomena such as the positive winter and summer North Atlantic Oscillation that impacted weather in parts the Northern Hemisphere and the negative Indian Ocean dipole that impacted weather in parts of the Southern Hemisphere; and by more localized systems such as high-pressure heat domes that caused extreme heat in different areas of the world. Underlying all these natural short-term variabilities are long-term climate trends due to continuous increases since the beginning of the Industrial Revolution in the atmospheric concentrations of Earth’s major greenhouse gases. In 2022, the annual global average carbon dioxide concentration in the atmosphere rose to 417.1±0.1 ppm, which is 50% greater than the pre-industrial level. Global mean tropospheric methane abundance was 165% higher than its pre-industrial level, and nitrous oxide was 24% higher. All three gases set new record-high atmospheric concentration levels in 2022. Sea-surface temperature patterns in the tropical Pacific characteristic of La Niña and attendant atmospheric patterns tend to mitigate atmospheric heat gain at the global scale, but the annual global surface temperature across land and oceans was still among the six highest in records dating as far back as the mid-1800s. It was the warmest La Niña year on record. Many areas observed record or near-record heat. Europe as a whole observed its second-warmest year on record, with sixteen individual countries observing record warmth at the national scale. Records were shattered across the continent during the summer months as heatwaves plagued the region. On 18 July, 104 stations in France broke their all-time records. One day later, England recorded a temperature of 40°C for the first time ever. China experienced its second-warmest year and warmest summer on record. In the Southern Hemisphere, the average temperature across New Zealand reached a record high for the second year in a row. While Australia’s annual temperature was slightly below the 1991–2020 average, Onslow Airport in Western Australia reached 50.7°C on 13 January, equaling Australia's highest temperature on record. While fewer in number and locations than record-high temperatures, record cold was also observed during the year. Southern Africa had its coldest August on record, with minimum temperatures as much as 5°C below normal over Angola, western Zambia, and northern Namibia. Cold outbreaks in the first half of December led to many record-low daily minimum temperature records in eastern Australia. The effects of rising temperatures and extreme heat were apparent across the Northern Hemisphere, where snow-cover extent by June 2022 was the third smallest in the 56-year record, and the seasonal duration of lake ice cover was the fourth shortest since 1980. More frequent and intense heatwaves contributed to the second-greatest average mass balance loss for Alpine glaciers around the world since the start of the record in 1970. Glaciers in the Swiss Alps lost a record 6% of their volume. In South America, the combination of drought and heat left many central Andean glaciers snow free by mid-summer in early 2022; glacial ice has a much lower albedo than snow, leading to accelerated heating of the glacier. Across the global cryosphere, permafrost temperatures continued to reach record highs at many high-latitude and mountain locations. In the high northern latitudes, the annual surface-air temperature across the Arctic was the fifth highest in the 123-year record. The seasonal Arctic minimum sea-ice extent, typically reached in September, was the 11th-smallest in the 43-year record; however, the amount of multiyear ice—ice that survives at least one summer melt season—remaining in the Arctic continued to decline. Since 2012, the Arctic has been nearly devoid of ice more than four years old. In Antarctica, an unusually large amount of snow and ice fell over the continent in 2022 due to several landfalling atmospheric rivers, which contributed to the highest annual surface mass balance, 15% to 16% above the 1991–2020 normal, since the start of two reanalyses records dating to 1980. It was the second-warmest year on record for all five of the long-term staffed weather stations on the Antarctic Peninsula. In East Antarctica, a heatwave event led to a new all-time record-high temperature of −9.4°C—44°C above the March average—on 18 March at Dome C. This was followed by the collapse of the critically unstable Conger Ice Shelf. More than 100 daily low sea-ice extent and sea-ice area records were set in 2022, including two new all-time annual record lows in net sea-ice extent and area in February. Across the world’s oceans, global mean sea level was record high for the 11th consecutive year, reaching 101.2 mm above the 1993 average when satellite altimetry measurements began, an increase of 3.3±0.7 over 2021. Globally-averaged ocean heat content was also record high in 2022, while the global sea-surface temperature was the sixth highest on record, equal with 2018. Approximately 58% of the ocean surface experienced at least one marine heatwave in 2022. In the Bay of Plenty, New Zealand’s longest continuous marine heatwave was recorded. A total of 85 named tropical storms were observed during the Northern and Southern Hemisphere storm seasons, close to the 1991–2020 average of 87. There were three Category 5 tropical cyclones across the globe—two in the western North Pacific and one in the North Atlantic. This was the fewest Category 5 storms globally since 2017. Globally, the accumulated cyclone energy was the lowest since reliable records began in 1981. Regardless, some storms caused massive damage. In the North Atlantic, Hurricane Fiona became the most intense and most destructive tropical or post-tropical cyclone in Atlantic Canada’s history, while major Hurricane Ian killed more than 100 people and became the third costliest disaster in the United States, causing damage estimated at $113 billion U.S. dollars. In the South Indian Ocean, Tropical Cyclone Batsirai dropped 2044 mm of rain at Commerson Crater in Réunion. The storm also impacted Madagascar, where 121 fatalities were reported. As is typical, some areas around the world were notably dry in 2022 and some were notably wet. In August, record high areas of land across the globe (6.2%) were experiencing extreme drought. Overall, 29% of land experienced moderate or worse categories of drought during the year. The largest drought footprint in the contiguous United States since 2012 (63%) was observed in late October. The record-breaking megadrought of central Chile continued in its 13th consecutive year, and 80-year record-low river levels in northern Argentina and Paraguay disrupted fluvial transport. In China, the Yangtze River reached record-low values. Much of equatorial eastern Africa had five consecutive below-normal rainy seasons by the end of 2022, with some areas receiving record-low precipitation totals for the year. This ongoing 2.5-year drought is the most extensive and persistent drought event in decades, and led to crop failure, millions of livestock deaths, water scarcity, and inflated prices for staple food items. In South Asia, Pakistan received around three times its normal volume of monsoon precipitation in August, with some regions receiving up to eight times their expected monthly totals. Resulting floods affected over 30 million people, caused over 1700 fatalities, led to major crop and property losses, and was recorded as one of the world’s costliest natural disasters of all time. Near Rio de Janeiro, Brazil, Petrópolis received 530 mm in 24 hours on 15 February, about 2.5 times the monthly February average, leading to the worst disaster in the city since 1931 with over 230 fatalities. On 14–15 January, the Hunga Tonga-Hunga Ha'apai submarine volcano in the South Pacific erupted multiple times. The injection of water into the atmosphere was unprecedented in both magnitude—far exceeding any previous values in the 17-year satellite record—and altitude as it penetrated into the mesosphere. The amount of water injected into the stratosphere is estimated to be 146±5 Terragrams, or ∼10% of the total amount in the stratosphere. It may take several years for the water plume to dissipate, and it is currently unknown whether this eruption will have any long-term climate effect.</jats:p