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In nuclear physics, a magic number is a number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus. The seven known magic numbers as of 2007 are Image File history File links Mergefrom. ... The term magic number can refer to: Magic number - in sports, a number used to indicate how close a front-running team is to clinching a season title; Magic number - in computer programming, a special constant used for some specific purpose; Magic number - in nuclear physics, a number of nucleons... This box:      Nuclear physics is the branch of physics concerned with the nucleus of the atom. ... In physics a nucleon is a collective name for two baryons: the neutron and the proton. ... For other uses, see Proton (disambiguation). ... This article or section does not adequately cite its references or sources. ... In nuclear physics, the nuclear shell model is a model of the atomic nucleus. ... The nucleus of an atom is the very small dense region, of positive charge, in its centre consisting of nucleons (protons and neutrons). ... Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ...

2, 8, 20, 28, 50, 82, 126. (sequence A018226 in OEIS)

Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per nucleon than one would expect based upon predictions such as the semi-empirical mass formula and are hence more stable against nuclear decay. For other uses of 2, see 2 (disambiguation). ... Look up eight in Wiktionary, the free dictionary. ... 20 (twenty) is the natural number following 19 and preceding 21. ... 28 (twenty-eight) is the natural number following 27 and preceding 29. ... 50 (fifty) is the number following 49 and preceding 51. ... 82 is the natural number following 81 and preceding 83. ... 126 is the natural number following 125 and preceding 127. ... The On-Line Encyclopedia of Integer Sequences (OEIS) is an extensive searchable database of integer sequences, freely available on the Web. ... Binding energy is the energy required to disassemble a whole into separate parts. ... In physics a nucleon is a collective name for two baryons: the neutron and the proton. ... In nuclear physics, the semi-empirical mass formula (SEMF), sometimes also called Weizsäckers formula, is a formula used to approximate the mass and various other properties of an atomic nucleus. ...

The unusual stability of isotopes having magic numbers means that transuranium elements can be created with extremely large nuclei and yet not be subject to the extremely rapid radioactive decay normally associated with high atomic numbers (as of 2007, the longest-lived, known isotope among all of the elements between 110 and 120 lasts only 12 min., next 22 sec.). Large isotopes with magic numbers of nucleons are said to exist in an island of stability. Unlike the magic numbers 2-126, which are realized in spherical nuclei, theoretical calculations predict that nuclei in the island of stability are deformed. Before this was realized, higher magic numbers, such as 184, were predicted based on simple calculations that assumed spherical shapes. It is now believed that the sequence of spherical magic numbers cannot be extended in this way. For other uses, see Isotope (disambiguation). ... This article needs additional references or sources to facilitate its verification. ... Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. ... See also: List of elements by atomic number In chemistry and physics, the atomic number (also known as the proton number) is the number of protons found in the nucleus of an atom. ... 3-dimensional rendering of the theoretical Island of Stability. ... 3-dimensional rendering of the theoretical Island of Stability. ...

Double magic

Nuclei which have both neutron number and proton (atomic) number equal to one of the magic numbers are called "double magic", and are especially stable against decay. Examples of double magic isotopes include helium-4 (⁴He), oxygen-16 (¹⁶O), calcium-40 (⁴⁰Ca), calcium-48 (⁴⁸Ca), nickel-48 (⁴⁸Ni), nickel-56 (⁵⁶Ni), tin-100 (¹⁰⁰Sn), tin-132 (¹³²Sn) and lead-208 (²⁰⁸Pb). It is no accident that for instance helium-4 (⁴He), or Fe-56 (⁵⁶Fe) are among the most abundant (and stable) nuclei in the universe^[1] and that ²⁰⁸Pb is the heaviest stable nuclide. See also: List of elements by atomic number In chemistry and physics, the atomic number (also known as the proton number) is the number of protons found in the nucleus of an atom. ... Helium-4 is a non-radioactive and light isotope of helium. ... General Name, Symbol, Number oxygen, O, 8 Chemical series Nonmetals, chalcogens Group, Period, Block 16, 2, p Appearance transparent (gas) very pale blue (liquid) Atomic mass 15. ... Calcium (Ca) Standard atomic mass: 40. ... Calcium 48 is a rare isotope of calcium. ... For other uses, see Nickel (disambiguation). ... For other uses, see Nickel (disambiguation). ... This article is about the metallic chemical element. ... This article is about the metallic chemical element. ... General Name, Symbol, Number lead, Pb, 82 Chemical series Post-transition metals or poor metals Group, Period, Block 14, 6, p Appearance bluish gray Standard atomic weight 207. ... Helium-4 is a non-radioactive and light isotope of helium. ...

Both calcium-48 (⁴⁸Ca) and nickel-48 (⁴⁸Ni) are double magic because calcium-48 has 20 protons and 28 neutrons while nickel-48 has 28 protons and 20 neutrons. Calcium-48 is very neutron-rich for such a light element, but is made stable by being double magic. Similarly, nickel-48, discovered in 1999, is the most proton-rich isotope known^[2]. Calcium 48 is a rare isotope of calcium. ... For other uses, see Nickel (disambiguation). ...

In December 2006 hassium-270 (²⁷⁰Hs) was discovered by an international team of scientists led by the Technical University of Munich having the unusually long half-life of 22 seconds. Hassium-270 evidently forms part of an island of stability, and may even be double magic^[3]. General Name, Symbol, Number hassium, Hs, 108 Chemical series transition metals Group, Period, Block 8, 7, d Appearance unknown, probably silvery white or metallic gray Atomic mass (269) g/mol Electron configuration perhaps [Rn] 5f14 6d6 7s2 (guess based on osmium) Electrons per shell 2, 8, 18, 32, 32, 14... Technische Universität München (TUM) (English: Technical University of Munich) is a German university, part of the Deutsche Forschungsgemeinschaft, a society of Germanys leading research universities in Munich. ... Half-Life For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value. ... 3-dimensional rendering of the theoretical Island of Stability. ...

Derivation

Magic numbers are typically obtained by empirical studies; however, if the form of the nuclear potential is known then the Schrödinger equation can be solved for the motion of nucleons and energy levels determined. Nuclear shells are said to occur when the separation between energy levels is significantly greater than the local mean separation. A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or consequences that are observable by the senses. ... This article is about the force sometimes called the residual strong force. ... This box:      For a non-technical introduction to the topic, please see Introduction to quantum mechanics. ...

In the shell model for the nucleus, magical numbers are the numbers of nucleons at which a shell is filled. For instance the magic number 8 occurs when 1s_1/2, 1p_3/2, 1p_1/2 energy levels are filled as there is a large energy gap between the 1p_1/2 and the next highest 1d_5/2 energy levels. The empirical values can be reproduced using the classical shell model with a strong spin-orbit interaction. In nuclear physics, the nuclear shell model is a model of the atomic nucleus. ... In nuclear physics, the nuclear shell model is a model of the atomic nucleus. ... Spin-orbit interaction, in quantum mechanics, is a shift in energy levels due to the potential energy of the spin magnetic moment of the electron in the magnetic field it feels as it moves through the electric field of the nucleus. ...

See also

• Island of stability
• Maria Göppert-Mayer
• Nuclear shell model
• Superatom
• Superdeformation
• Semi-empirical mass formula

3-dimensional rendering of the theoretical Island of Stability. ... Maria Goeppert Mayer: Physicist (Women in Science) ISBN 0791072479 Maria Goeppert-Mayer (June 28, 1906 – February 20, 1972) was born Maria Goeppert in Katowice, Silesia (then in Germany, now part of Poland). ... In nuclear physics, the nuclear shell model is a model of the atomic nucleus. ... Superatoms are clusters of atoms which seem to exhibit some of the properties of elemental atoms. ... In nuclear physics a superdeformed nucleus is a nucleus that is very far from spherical, forming an ellipsoid with axes in ratios of approximately 2:1:1. ... In nuclear physics, the semi-empirical mass formula (SEMF), sometimes also called Weizsäckers formula, is a formula used to approximate the mass and various other properties of an atomic nucleus. ...

References

Science News is an American weekly magazine devoted to short articles about new scientific and technical developments, typically gleaned from recent scientific and technical journals. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 272nd day of the year (273rd in leap years) in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 348th day of the year (349th in leap years) in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 359th day of the year (360th in leap years) in the Gregorian calendar. ...

External links

• Shell Model of Nucleus