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In nuclear physics
Nuclear physics

Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei.The most commonly known applications of nuclear physics are nuclear power and nuclear weapons, but the research field is also the basis for a far wider range of applications, including in the medical sector , in materials engineering...
, a magic number is a number of nucleon
Nucleon

In physics, a nucleon is a collective name for two baryons: the neutron and the proton. They are constituents of the atomic nucleus and until the 1960s were thought to be elementary particles....
s (either proton
Proton

The proton is a subatomic particle with an electric charge of +1 elementary charge. It is found in the nucleus of each atom but is also stable by itself and has a second identity as the hydrogen ion, H+....
s or neutron
Neutron

The neutron is a subatomic particle with no net electric charge and a mass slightly larger than that of a proton.Neutrons are usually found in atomic nucleus....
s) such that they are arranged into complete shells
Shell model

In nuclear physics, the nuclear shell model is a nuclear model the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels....
 within the atomic nucleus
Atomic nucleus

The nucleus of an atom is the very dense region, consisting of nucleons , at the center of an atom. Although the size of the nucleus varies considerably according to the mass of the atom, the size of the entire atom is comparatively constant....
. The seven known magic numbers as of 2007 are
2
2 (number)

2 is a number, numeral, and glyph. It is the natural number following 1 and preceding 3 ....
, 8
8 (number)

8 is the natural number, following 7 and preceding 9 . The SI prefix for 10008 is yotta , and for its reciprocal yocto . It is the root of two other numbers: eighteen and eighty ....
, 20
20 (number)

20 is the natural number following 19 and preceding 21 . A group of twenty units may also be referred to as a score....
, 28
28 (number)

28 is the natural number following 27 and preceding 29 ....
, 50
50 (number)

This article discusses the number fifty. For the year 50 CE, see 50. For other uses of 50, see 50 50 is the integer following 49 and preceding 51 ....
, 82
82 (number)

82 is the natural number following 81 and preceding 83 ....
, 126
126 (number)

126 is the natural number following 125 and preceding one hundred twenty-seven....
.


Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy
Binding energy

Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system has a lower potential energy than its constituent parts; this is what keeps the system together....
 per nucleon
Nucleon

In physics, a nucleon is a collective name for two baryons: the neutron and the proton. They are constituents of the atomic nucleus and until the 1960s were thought to be elementary particles....
 than one would expect based upon predictions such as the semi-empirical mass formula
Semi-empirical mass formula

In nuclear physics, the semi-empirical mass formula , sometimes also called Weizs?cker's formula, is a formula used to approximate the mass and various other properties of an atomic nucleus....
 and are hence more stable against nuclear decay.

The unusual stability of isotope
Isotope

Isotopes are any of the different types of atoms of the same chemical element, each having a different atomic mass . Isotopes of an element have atomic nucleus with the same number of protons but different numbers of neutron....
s having magic numbers means that transuranium element
Transuranium element

In chemistry, transuranium elements are the chemical elements with atomic numbers greater than 92 . None of these elements are stable; they Radioactive decay into other elements....
s can be created with extremely large nuclei and yet not be subject to the extremely rapid radioactive decay
Radioactive decay

Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide....
 normally associated with high atomic number
Atomic number

In chemistry and physics, the atomic number is the number of protons found in the atomic nucleus of an atom. It is conventionally represented by the symbol Z....
s (as of 2007, the longest-lived, known isotope among all of the elements between 110 and 120
Island of stability

The island of stability is a term from nuclear physics that describes the possibility of chemical elements with particularly stable "Magic number " of protons and neutrons....
 lasts only 12 min., next 22 sec.).






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In nuclear physics
Nuclear physics

Nuclear physics is the field of physics that studies the building blocks and interactions of atomic nuclei.The most commonly known applications of nuclear physics are nuclear power and nuclear weapons, but the research field is also the basis for a far wider range of applications, including in the medical sector , in materials engineering...
, a magic number is a number of nucleon
Nucleon

In physics, a nucleon is a collective name for two baryons: the neutron and the proton. They are constituents of the atomic nucleus and until the 1960s were thought to be elementary particles....
s (either proton
Proton

The proton is a subatomic particle with an electric charge of +1 elementary charge. It is found in the nucleus of each atom but is also stable by itself and has a second identity as the hydrogen ion, H+....
s or neutron
Neutron

The neutron is a subatomic particle with no net electric charge and a mass slightly larger than that of a proton.Neutrons are usually found in atomic nucleus....
s) such that they are arranged into complete shells
Shell model

In nuclear physics, the nuclear shell model is a nuclear model the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels....
 within the atomic nucleus
Atomic nucleus

The nucleus of an atom is the very dense region, consisting of nucleons , at the center of an atom. Although the size of the nucleus varies considerably according to the mass of the atom, the size of the entire atom is comparatively constant....
. The seven known magic numbers as of 2007 are
2
2 (number)

2 is a number, numeral, and glyph. It is the natural number following 1 and preceding 3 ....
, 8
8 (number)

8 is the natural number, following 7 and preceding 9 . The SI prefix for 10008 is yotta , and for its reciprocal yocto . It is the root of two other numbers: eighteen and eighty ....
, 20
20 (number)

20 is the natural number following 19 and preceding 21 . A group of twenty units may also be referred to as a score....
, 28
28 (number)

28 is the natural number following 27 and preceding 29 ....
, 50
50 (number)

This article discusses the number fifty. For the year 50 CE, see 50. For other uses of 50, see 50 50 is the integer following 49 and preceding 51 ....
, 82
82 (number)

82 is the natural number following 81 and preceding 83 ....
, 126
126 (number)

126 is the natural number following 125 and preceding one hundred twenty-seven....
.


Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy
Binding energy

Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system has a lower potential energy than its constituent parts; this is what keeps the system together....
 per nucleon
Nucleon

In physics, a nucleon is a collective name for two baryons: the neutron and the proton. They are constituents of the atomic nucleus and until the 1960s were thought to be elementary particles....
 than one would expect based upon predictions such as the semi-empirical mass formula
Semi-empirical mass formula

In nuclear physics, the semi-empirical mass formula , sometimes also called Weizs?cker's formula, is a formula used to approximate the mass and various other properties of an atomic nucleus....
 and are hence more stable against nuclear decay.

The unusual stability of isotope
Isotope

Isotopes are any of the different types of atoms of the same chemical element, each having a different atomic mass . Isotopes of an element have atomic nucleus with the same number of protons but different numbers of neutron....
s having magic numbers means that transuranium element
Transuranium element

In chemistry, transuranium elements are the chemical elements with atomic numbers greater than 92 . None of these elements are stable; they Radioactive decay into other elements....
s can be created with extremely large nuclei and yet not be subject to the extremely rapid radioactive decay
Radioactive decay

Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide....
 normally associated with high atomic number
Atomic number

In chemistry and physics, the atomic number is the number of protons found in the atomic nucleus of an atom. It is conventionally represented by the symbol Z....
s (as of 2007, the longest-lived, known isotope among all of the elements between 110 and 120
Island of stability

The island of stability is a term from nuclear physics that describes the possibility of chemical elements with particularly stable "Magic number " of protons and neutrons....
 lasts only 12 min., next 22 sec.). Large isotopes with magic numbers of nucleons are said to exist in an island of stability
Island of stability

The island of stability is a term from nuclear physics that describes the possibility of chemical elements with particularly stable "Magic number " of protons and neutrons....
. 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.

Double magic

Nuclei which have both neutron number and proton (atomic
Atomic number

In chemistry and physics, the atomic number is the number of protons found in the atomic nucleus of an atom. It is conventionally represented by the symbol Z....
) 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
Helium-4

Helium-4 is a non-radioactive and light isotope of helium. It is by far the most abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on earth....
 (4He), oxygen-16 (16O), calcium-40 (40Ca), calcium-48
Calcium-48

Calcium-48 is a rare isotopes of calcium containing 20 protons and 28 neutrons. It makes up 0.187% of natural calcium by mole fraction. Although it is unusually neutron-rich for such a light nucleus, the only radioactive decay pathway open to it is the extremely rare process of double beta decay....
 (48Ca), nickel
Nickel

Nickel is a chemical element, with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge....
-48 (48Ni) and lead
Lead

Lead is a main-group Chemical element with symbol Pb and atomic number 82. Lead is a soft, malleable poor metal, also considered to be one of the heavy metal ....
-208 (208Pb). tin
Tin

Tin is a chemical element with the symbol Sn and atomic number 50. Tin is obtained chiefly from the mineral cassiterite, where it occurs as an oxide, SnO2....
-100 (100Sn) & tin
Tin

Tin is a chemical element with the symbol Sn and atomic number 50. Tin is obtained chiefly from the mineral cassiterite, where it occurs as an oxide, SnO2....
-132 (132Sn) are doubly-magic isotopes of tin
Isotopes of tin

Tin is the element with the greatest number of stable isotopes , which is probably related to the fact that 50 is a "Magic number " of protons....
 that are unstable; however they represent endpoints beyond which stability drops off rapidly. It is no accident that helium-4
Helium-4

Helium-4 is a non-radioactive and light isotope of helium. It is by far the most abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on earth....
 (4He) is among the most abundant (and stable) nuclei in the universe and that 208Pb is the heaviest stable nuclide.

Both calcium-48
Calcium-48

Calcium-48 is a rare isotopes of calcium containing 20 protons and 28 neutrons. It makes up 0.187% of natural calcium by mole fraction. Although it is unusually neutron-rich for such a light nucleus, the only radioactive decay pathway open to it is the extremely rare process of double beta decay....
 (48Ca) and nickel
Nickel

Nickel is a chemical element, with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge....
-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.

In December 2006 hassium
Hassium

Hassium is a synthetic element in the periodic table that has the symbol Hs and atomic number 108. Hassium oxidizes similarly to osmium above it, to a hassium tetroxide with a lower Volatility than osmium tetroxide....
-270 (270Hs) was discovered by an international team of scientists led by the Technical University of Munich
Technical University of Munich

Technische Universit?t M?nchen is a research university with campuses in Munich, Garching, and Weihenstephan.TUM is among the highest acclaimed universities in Germany, producing several Nobel Laureates including Gerhard Ertl who in 2007 received the Nobel Prize in Chemistry....
 having the unusually long half-life
Half-life

The half-life of a quantity whose value decreases with time is the interval required for the quantity to decay to half of its initial value. The concept originated in describing how long it takes atoms to undergo radioactive decay but also applies in a wide variety of other situations....
 of 22 seconds. Hassium-270 evidently forms part of an island of stability
Island of stability

The island of stability is a term from nuclear physics that describes the possibility of chemical elements with particularly stable "Magic number " of protons and neutrons....
, and may even be double magic.

Derivation

Magic numbers are typically obtained by empirical
Empirical

The word empirical denotes information gained by means of observation, experience, or experiment, as opposed to theory. 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 Logical consequence that are observable by the senses....
 studies; however, if the form of the nuclear potential
Nuclear force

The nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into Atomic nucleus. To a large extent, this force can be understood in terms of the exchange of virtual light mesons, such as the pions....
 is known then the Schrödinger equation
Schrödinger equation

In physics, especially quantum mechanics, the Schr?dinger equation is an equation that describes how the quantum state of a physical system changes in time....
 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.

In the shell model
Shell model

In nuclear physics, the nuclear shell model is a nuclear model the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels....
 for the nucleus, magical numbers are the numbers of nucleons at which a shell is filled. For instance the magic number 8 occurs when 1s1/2, 1p3/2, 1p1/2 energy levels are filled as there is a large energy gap between the 1p1/2 and the next highest 1d5/2 energy levels. The empirical values can be reproduced using the classical shell model
Shell model

In nuclear physics, the nuclear shell model is a nuclear model the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels....
 with a strong spin-orbit interaction
Spin-orbit interaction

In quantum physics, the spin-orbit interaction is any interaction of a particle's spin with its motion. The first and best known example of this is that spin-orbit interaction causes shifts in an electron's energy level , due to electromagnetic interaction between the electron's spin and the nucleus's electric field, through which it moves...
.

See also

  • Island of stability
    Island of stability

    The island of stability is a term from nuclear physics that describes the possibility of chemical elements with particularly stable "Magic number " of protons and neutrons....
  • Maria Göppert-Mayer
  • Nuclear shell model
    Shell model

    In nuclear physics, the nuclear shell model is a nuclear model the atomic nucleus which uses the Pauli exclusion principle to describe the structure of the nucleus in terms of energy levels....
  • Superatom
    Superatom

    Superatoms are cluster chemistry of atoms that seem to exhibit some of the properties of elemental atoms.Sodium atoms, when cooled from vapor, naturally condense into clusters, more so into clusters of 2, 8, 20, 40, 58 or 82 atoms , than into the other numbers....
  • Superdeformation
    Superdeformation

    In nuclear physics a superdeformed Atomic nucleus is a nucleus that is very far from sphere, forming an ellipsoid with axes in ratios of approximately 2:1:1....
  • Semi-empirical mass formula
    Semi-empirical mass formula

    In nuclear physics, the semi-empirical mass formula , sometimes also called Weizs?cker's formula, is a formula used to approximate the mass and various other properties of an atomic nucleus....


External links

  • OEIS : A018226 Magic numbers: atoms with one of these numbers of protons or neutrons in their nuclei are considered to be stable.