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Positronium is a system consisting of an electron and its anti-particle, a positron, bound together into an exotic atom an onium. The system is unstable: the two particles annihilate each other to predominantly produce two or three gamma-rays, depending on the relative spin states; the orbit and energy levels of the two particles are similar to that of the hydrogen atom. However, because of the reduced mass, the frequencies of the spectral lines are less than half of the corresponding hydrogen lines; the mass of positronium is 1.022 MeV, twice the electron mass minus the binding energy of a few eV. The ground state of positronium, like that of hydrogen, has two possible configurations depending on the relative orientations of the spins of the electron and the positron; the singlet state, 1S0, with antiparallel spins is known as para-positronium. It has a mean lifetime of 0.125 ns and decays preferentially into two gamma rays with energy of 511 keV each. By detecting these photons the position at which the decay occurred can be determined.

This process is used in positron-emission tomography. Para-positronium can decay into any number of photons, but the probability decreases with the number: the branching ratio for decay into 4 photons is 1.439×10−6. Para-positronium lifetime in vacuum is t 0 = 2 ℏ m e c 2 α 5 = 0.1244 n s. The triplet state, 3S1, with parallel spins is known as ortho-positronium, it has a mean lifetime of 142.05±0.02 ns, the leading decay is three gammas. Other modes of decay are negligible. Ortho-positronium lifetime in vacuum can be calculated as: t 1 = 1 2 9 h 2 m e c 2 α 6 = 138.6 n s. However more accurate calculations with corrections to O yield a value of 7.040 μs−1 for the decay rate, corresponding to a lifetime of 142 ns. Positronium in the 2S state is metastable having a lifetime of 1100 ns against annihilation; the positronium created in such an excited state will cascade down to the ground state, where annihilation will occur more quickly. Measurements of these lifetimes and energy levels have been used in precision tests of quantum electrodynamics, confirming quantum electrodynamics predictions to high precision.

Annihilation can proceed via a number of channels, each producing gamma rays with total energy of 1022 keV 2 or 3, with up to 5 gamma ray photons recorded from a single annihilation. The annihilation into a neutrino–antineutrino pair is possible, but the probability is predicted to be negligible; the branching ratio for o-Ps decay for this channel is 6.2×10−18 and 9.5×10−21 in predictions based on the Standard Model, but it can be increased by non-standard neutrino properties, like high magnetic moment. The experimental upper limits on branching ratio for this decay are <4.3×10−7 for p-Ps and <4.2×10−7 for o-Ps. While precise calculation of positronium energy levels uses the Bethe–Salpeter equation or the Breit equation, the similarity between positronium and hydrogen allows a rough estimate. In this approximation, the energy levels are different because of a different effective mass, m*, in the energy equation: E n = − μ q e 4 8 h 2 ε 0 2 1 n 2, where: qe is the charge magnitude of the electron, h is Planck's constant, ε0 is the electric constant, μ is the reduced mass: μ = m e m p m e + m p = m e 2 2 m e = m e 2, where me and mp are the mass of the electron and the positron.

Thus, for positronium, its reduced mass only differs from the electron by a factor of 2. This causes the energy levels to roughly be half of what they are for the hydrogen atom. So the energy levels of positronium are given by E

Philip Goldson Highway

The Philip Goldson Highway in Belize joins Belize City through Orange Walk Town and Corozal Town with the Mexican border at the state of Quintana Roo. It is 95 miles long. Crude side-roads suitable only for over-land vehicles connect to such localities as Aguas Turbias, on the corner where Belize and Guatemala meet; the highway was commissioned in 1968 as the Northern Highway. In 1979, 30 miles of new highway brought the route much further to the west between Belize City and Orange Walk, much closer to Crooked Tree, to which a causeway and road was built in 1984. On 21 September 2012, Prime Minister Dean Barrow announced that it would be renamed the Philip Goldson Highway, named after a Belizean activist and politician; the highway passes the international airport named for Goldson. Transport in Belize

Sarah Byrd Askew

Sarah Byrd Askew was an American public librarian who pioneered the establishment of county libraries in the United States. A prominent librarian during the first half of the 20th century, she worked for the New Jersey Public Library Commission for 37 years. Sarah Byrd Askew was born on February 15, 1877, in Dayton, Alabama, to Thyrza and Samuel Horton Askew, she graduated from high school in Atlanta. After attending business school, she found employment as a stenographer for a brief time, but after working temporarily at Cleveland Public Library in Ohio while visiting her sister, decided to pursue librarianship, she attended the Pratt Institute's School of Information and Library Science in New York and graduated in 1904. The New Jersey Public Library Commission hired Askew on January 1, 1905, assigning her to travel among the state's libraries to introduce them to modern library practice and to set up a summer training program for New Jersey librarians, she was to be their "organizer and missionary" to "get libraries going," as there were only 66 libraries in the state at that time.

With the exception of her time as a reference librarian at the New Jersey State Library in Trenton from 1909–15, Askew worked for the New Jersey Public Library Commission for the entirety of her career. There, she established a county library program, created as a regional approach to serve towns that could not support local libraries on their own, she oversaw the establishment of 12 county libraries herself. Askew worked to increase the effectiveness of public libraries. In 1906, she founded a summer school for the staff of small libraries to share knowledge and skills. Concerned with providing books to rural areas still without a local or county library, Askew began sending "traveling libraries" - shipments of around 300 books - to community buildings throughout the state, she began shipping specific collections to libraries in New York and Connecticut by 1913, an early example of interlibrary loan. In 1920, Askew designed one of the earliest bookmobiles in the U. S. A. driving her Ford Model T to carry materials to people who did not have access to a library.

During World War I, Askew organized a program to send books overseas to military camps and hospitals. She wrote and published scholarly articles and books, including The Place, the Man and the Book. Throughout her career, she was supported in her cause by the State Teachers' Association, the Federation of Women's Clubs and local grange groups, others. Askew served as president of the New Jersey Library Association, vice-president of the American Library Association, chairwoman of children's reading for the National Congress of Parents and Teachers, was a member of the Trenton Board of Education. In recognition of her accomplishments, the New Jersey College for Women at Rutgers University conferred an honorary doctorate of library science upon Askew in 1930; the campus library at William Paterson University was named in her honor for some time. Askew resided in Trenton, New Jersey. By 1942, there were 316 local libraries in the state of New Jersey. In 1951, Library Journal named Askew to its Library Hall of Fame.

The New Jersey Library Association awards an annual scholarship in Askew's honor. The Place, the Man, the Book available as a Google Book

Samantha Ellis

Samantha Ellis is a British playwright and writer. Her 2010 play Cling to Me Like Ivy was described by The Guardian newspaper as "genuinely rare beast, a popular comedy with heart and the stomach to make some difficult choices". Ellis was born in London to Iraqi-Jewish parents, she studied English at Cambridge. Ellis's play The Candy Jar was produced at the Edinburgh Fringe in 1996, she worked as a journalist, wrote a column on theatrical history for The Guardian newspaper. Her play Patching Havoc was produced at Theatre503 in 2003, her radio play Sugar and Snow, set in the Kurdish community in north London, was produced on BBC Radio 4 in 2006 and given a reading at the Hampstead Theatre. Her short play A Sudden Visitation of Calamity was produced at Menagerie Theatre in 2008. In 2010 her play The Thousand and Second Night was produced by LAMDA. In 2010 her play Cling To Me Like Ivy, published by Nick Hern Books, was produced by the Birmingham Repertory Theatre and went on tour. In 2012 she was a founder member of women's theatre company Agent 160.

Her book How to be a Heroine was published by Chatto & Windus in January 2014, her biography of Anne Brontë Take Courage: Anne Bronte and the Art of Life was published in January 2017. Samantha Ellis's doollee page Samantha Ellis's blog Agent 160

Borroway Rovers

Borroway Rovers F. C. is an association football club based in Co.. Tipperary; the club plays in the North Tipperary & District Division 1 having been promoted as champions from Division 2 in 2009/2010. The club's playing colours are red with white trim although they have used white and black trim and navy and white trim; the club's home ground is Loughtagalla Park and its main rival is Thurles Celtic, with whom they share the park. The Borroway Rovers F. C. was re-formed in 2002. Success eluded them in their first two seasons but they succeeded in assembling a good group of local lads; the club struck gold in the 2004/2005 season when they annexed their first trophy by winning the Second Division Shield Final. In the 2005/2006 season the club won the Fast Food Cup, beating Rearcross The following season saw them again reach The Fast Food Final but this time they were beaten by Ballymackey. In 2008/2009 Borroway were unlucky in the Division 2 League and missed out on promotion by a mere couple of points.

They contested the Cup Final for a record fourth year in a row. This time they won the Nora Kennedy Cup. Borroway Rovers took part in last seasons FAI Junior Cup and beat Borrisoleigh before advancing to meet South Tipp "big guns" Cahir, they lost this game 0-2. In March 2010 Borroway played in Division 1 the next season. Borroway Rovers won the Second Division Cup title against Cloughjordan'B' on a dramatic penalty shootout 3-2. Bernard Keane Eilish Treacy Owen Ryan Veronica Moore Cecilia Keane Bernard Keane Michael Callanan


Modautal is a municipality in the Darmstadt-Dieburg district, in Hesse, Germany. 5,050 inhabitants live in 11 districts on an area of 31 km2 with about 38.7% wood. The first historical chronicles date back to the 13th century; the municipality was formed in 1977 by putting together eleven districts during the so-called Gebietsreform. During the time of the Celts the area must have been inhabited since the so-called "Heuneburg" on a hill in Fischbachtal was a celtic castle where the people and their animals from the region could flee. To construct such a building, a lot of helping hands must have been living nearby. In the Middle Ages, the eleven villages of Modautal belonged to different knight's families: The family of Rodenstein, the family from Frankenstein, the one from Mosbach, the family of Wallbrunn as well as Stumpf von Asbach and Kalb von Reinheim just to name a few; the oldest available documents date back to 1651 and are the so-called "Haingerichtsbücher". During the revolution in 1848 and due to failure of crops, huge parts of the inhabitants of the villages emigrated to North America.

Website Modautal