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"In condensed matter physics, a Cooper pair or BCS pair is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper.[1] Cooper showed that an arbitrarily small attraction between electrons in a metal can cause a paired state of electrons to have a lower energy than the Fermi energy, which implies that the pair is bound. In conventional superconductors, this attraction is due to the electron–phonon interaction. The Cooper pair state is responsible for superconductivity, as described in the BCS theory developed by John Bardeen, Leon Cooper, and John Schrieffer for which they shared the 1972 Nobel Prize.[2]
Although Cooper pairing is a quantum effect, the reason for the pairing can be seen from a simplified classical explanation.[2][3] An electron in a metal normally behaves as a free particle. The electron is repelled from other electrons due to their negative charge, but it also attracts the positive ions that make up the rigid lattice of the metal. This attraction distorts the ion lattice, moving the ions slightly toward the electron, increasing the positive charge density of the lattice in the vicinity. This positive charge can attract other electrons. At long distances, this attraction between electrons due to the displaced ions can overcome the electrons' repulsion due to their negative charge, and cause them to pair up. The rigorous quantum mechanical explanation shows that the effect is due to electron–phonon interactions, with the phonon being the collective motion of the positively-charged lattice.[4]
The energy of the pairing interaction is quite weak, of the order of 10−3 eV, and thermal energy can easily break the pairs. So only at low temperatures, in metal and other substrates, are a significant number of the electrons in Cooper pairs.
The electrons in a pair are not necessarily close together; because the interaction is long range, paired electrons may still be many hundreds of nanometers apart. This distance is usually greater than the average interelectron distance so that many Cooper pairs can occupy the same space.[5] Electrons have spin-1⁄2, so they are fermions, but the total spin of a Cooper pair is integer (0 or 1) so it is a composite boson. This means the wave functions are symmetric under particle interchange. Therefore, unlike electrons, multiple Cooper pairs are allowed to be in the same quantum state, which is responsible for the phenomena of superconductivity.
The BCS theory is also applicable to other fermion systems, such as helium-3. Indeed, Cooper pairing is responsible for the superfluidity of helium-3 at low temperatures. It has also been recently demonstrated that a Cooper pair can comprise two bosons.[6] Here, the pairing is supported by entanglement in an optical lattice."
I wonder if Muons can form into cooper-pairs. Wouldn't that be interesting? What i mean by this, is what would happen if Krypton79 was used as the active gas in a Cathode Ray tube, where the "hot" electrode is made of YBCO 2-layer material. When the Krypton decays from 79 to 78, it releases positrons, which decay into kaon's and pions, which decay into muons and EM radiation. If a Cooper-pair state is present at the exposed layer of the YBCO, and the field is compressed with a solenoid at 1Mhz or greater, could the Muons bind to the electrons and force Muonium to form where the mass of the muon will contribute to the bose-einstein condensation of the electrons within the YBCO material. Increasing the mass of the field, in theory, should increase any anomalous phenomena
Although Cooper pairing is a quantum effect, the reason for the pairing can be seen from a simplified classical explanation.[2][3] An electron in a metal normally behaves as a free particle. The electron is repelled from other electrons due to their negative charge, but it also attracts the positive ions that make up the rigid lattice of the metal. This attraction distorts the ion lattice, moving the ions slightly toward the electron, increasing the positive charge density of the lattice in the vicinity. This positive charge can attract other electrons. At long distances, this attraction between electrons due to the displaced ions can overcome the electrons' repulsion due to their negative charge, and cause them to pair up. The rigorous quantum mechanical explanation shows that the effect is due to electron–phonon interactions, with the phonon being the collective motion of the positively-charged lattice.[4]
The energy of the pairing interaction is quite weak, of the order of 10−3 eV, and thermal energy can easily break the pairs. So only at low temperatures, in metal and other substrates, are a significant number of the electrons in Cooper pairs.
The electrons in a pair are not necessarily close together; because the interaction is long range, paired electrons may still be many hundreds of nanometers apart. This distance is usually greater than the average interelectron distance so that many Cooper pairs can occupy the same space.[5] Electrons have spin-1⁄2, so they are fermions, but the total spin of a Cooper pair is integer (0 or 1) so it is a composite boson. This means the wave functions are symmetric under particle interchange. Therefore, unlike electrons, multiple Cooper pairs are allowed to be in the same quantum state, which is responsible for the phenomena of superconductivity.
The BCS theory is also applicable to other fermion systems, such as helium-3. Indeed, Cooper pairing is responsible for the superfluidity of helium-3 at low temperatures. It has also been recently demonstrated that a Cooper pair can comprise two bosons.[6] Here, the pairing is supported by entanglement in an optical lattice."
I wonder if Muons can form into cooper-pairs. Wouldn't that be interesting? What i mean by this, is what would happen if Krypton79 was used as the active gas in a Cathode Ray tube, where the "hot" electrode is made of YBCO 2-layer material. When the Krypton decays from 79 to 78, it releases positrons, which decay into kaon's and pions, which decay into muons and EM radiation. If a Cooper-pair state is present at the exposed layer of the YBCO, and the field is compressed with a solenoid at 1Mhz or greater, could the Muons bind to the electrons and force Muonium to form where the mass of the muon will contribute to the bose-einstein condensation of the electrons within the YBCO material. Increasing the mass of the field, in theory, should increase any anomalous phenomena