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Electron capture (K-electron capture, also K-capture, or L-electron capture, L-capture) is a process in which the proton-rich nucleus of an electrically neutral atom absorbs an inner atomic electron, usually from the K or L electron shells. This process thereby changes a nuclear proton to a neutron and simultaneously causes the emission of an electron neutrino. Proton + Electron → Neutron + Electron Neutrino or when written as a nuclear reaction equation, ^{0}{-1}e + ^{1}{1}p -> ^{1}{0}n + ^{0}{0} ν Since this single emitted neutrino carries the entire decay energy, it has this single characteristic energy. Similarly, the momentum of the neutrino emission causes the daughter atom to recoil with a single characteristic momentum. The resulting daughter nuclide, if it is in an excited state, then transitions to its ground state. Usually, a gamma ray is emitted during this transition, but nuclear de-excitation may also take place by internal conversion. Following capture of an inner electron from the atom, an outer electron replaces the electron that was captured and one or more characteristic X-ray photons is emitted in this process. Electron capture sometimes also results in the Auger effect, where an electron is ejected from the atom's electron shell due to interactions between the atom's electrons in the process of seeking a lower energy electron state. Following electron capture, the atomic number is reduced by one, the neutron number is increased by one, and there is no change in mass number. Simple electron capture by itself results in a neutral atom, since the loss of the electron in the electron shell is balanced by a loss of positive nuclear charge. However, a positive atomic ion may result from further Auger electron emission. Electron capture is an example of weak interaction, one of the four fundamental forces. Electron capture is the primary decay mode for isotopes with a relative superabundance of protons in the nucleus, but with insufficient energy difference between the isotope and its prospective daughter (the isobar with one less positive charge) for the nuclide to decay by emitting a positron.
[2]Paolo Prandoni, [3]LCAV, EPFL
In this notebook we will explore various ways to implement a system
that changes the voice of a speaker. Typical applications for these
techniques, strictly sorted by plausibility, include international spy
missions and prank telephone calls, and devices such as the one
displayed here can be easily bought on the web... or in a novelty shop.
No description has been provided for t [2]Paolo Prandoni, [3]LCAV, EPFL
The concept of "basis" for a vector space is one of the most profound
and fruitful ideas in linear algebra. Basis vectors are the "building
blocks" that all other vectors are built from; by "disassembling" a
vector into a linear combination of basis elements we are able to "look
inside" the vector and highlight many of its relevant features.
A vector space has an infinite number o