Deuteron

Deuteron (d)
properties
electric charge	1  e (+1.602 10 −19  C )
Dimensions	2.013 553 212 745 (40)  u 3.343 583 7724 (10) · 10 −27  kg 3670.482 967 88 (13)  m e
Resting energy	1875,612 942 57 (57)  MeV
magnetic moment	4.330 735 094 (11) 10 −27  J  /  T 0.857 438 2338 (22)  μ N
g factor	0.857 438 2338 (22)
Spin parity	1 +
Isospin	0 (z component 0)
average lifespan	stable

As deuteron (from ancient Greek δεύτερον deuteron , "the Second") which is the nucleus of deuterium ( "heavy hydrogen"), respectively. Its symbol is d or also ² H ⁺ . It consists of a proton and a neutron .

Deuterons play a role in nuclear fusion reactions in stars . They occur as an intermediate product in the proton-proton reaction :

${\displaystyle \mathrm {p+p\rightarrow d+e^{+}+\nu _{e}+0{,}42\,MeV} }$

Two protons fuse to form a deuteron. A positron , an electron neutrino and energy are released.

Deuterons will also be needed as fuel for future fusion reactors .

A common name for the cations of the hydrogen isotopes (proton, deuteron and triton ) is hydron .

Nuclear physical properties

The binding energy of the deuteron is 2.225  MeV . This is relatively little at a potential depth of the nuclear force of around 50 MeV and is due to the fact that the binding energy increases when the two nucleons move together, but on the other hand the kinetic energy of the nucleons increases according to the uncertainty relation.

Wave function in spatial space

Since the deuteron is the simplest bound nucleon system, it is often used to analyze the nucleon-nucleon interaction . Its nuclear spin J can be determined from hyperfine structure observations to be 1, and its parity P is positive. These are the quantum numbers that are expected for a ³ S ₁ state ( orbital angular momentum L  = 0; total spin S  = 1; total angular momentum J  = 1). Such a state would be spherically symmetric, the electric quadrupole moment would then have to be zero and the magnetic dipole moment the sum of the moments of the proton and neutron . ${\textstyle \mu _{\mathrm {p} }+\mu _{\mathrm {n} }=2{,}793\mu _{\mathrm {N} }-1{,}913\mu _{\mathrm {N} }=0{,}880\mu _{\mathrm {N} }}$

In fact, however, the electric quadrupole moment differs from zero with, and the magnetic moment is also slightly different with. It follows that there is an admixture of the ³ D ₁ -state ( L  = 2), the only other state with the same quantum numbers J ^P are. Mathematically it results ${\displaystyle Q=0{,}282\,\,\mathrm {fm} ^{2}}$ ${\textstyle 0,857\,\mu _{\mathrm {N} }}$

${\displaystyle |\psi _{\mathrm {d} }\rangle =0{,}98\cdot |^{3}\mathrm {S} _{1}\rangle +0{,}2\cdot |^{3}\mathrm {D} _{1}\rangle ={\sqrt {p_{\mathrm {S} }}}\cdot |^{3}\mathrm {S} _{1}\rangle +{\sqrt {p_{\mathrm {D} }}}\cdot |^{3}\mathrm {D} _{1}\rangle .}$

This means that the D-wave state is entered with a probability of 4%. Such a mixed state is only possible because the nuclear force is not a pure central force , but has a tensor component . The positive value of the electric quadrupole moment corresponds to a prolate , i.e. elongated ellipsoid of revolution . ${\displaystyle p_{\mathrm {D} }}$

Spin

Only the spin- triplet state is stable in the deuteron . The singlet state (antiparallel spins of the nucleons) is not bound due to the spin dependence of the nuclear force. The nuclear force is weaker with antiparallel spins; Diproton and Dineutron , in which the Pauli principle excludes the parallel position, are accordingly not bound. The deuteron is also so weakly bound that no excited bound states exist.

Isospin

In the isospin space the deuteron is in a singlet state. If it were in a triplet state, the diproton and dineutron would be part of the triplet; but these are not bound.

Total wave function

The total wave function is the product of the wave functions in spatial space, spin space and isospin space and, since it is a matter of fermions, it must be antisymmetric when the nucleons are swapped. The space portion is symmetrical (mainly L = 0), because due to the short range of the nuclear force, the nucleons have to move as close together as possible for a bond state. Isospin has a singlet (antisymmetric), spin a triplet (symmetric).

Nuclear reactions with deuterons

The average binding energy of a nucleon in an atomic nucleus is about 8 MeV. The mentioned binding energy of the deuteron is relatively small in comparison. This explains why with deuterons, which in a particle accelerator to a kinetic energy of z. B. some MeV , can easily trigger nuclear reactions of types (d, n) and (d, p) (stripping reactions ) as well as (d, np) (deuterons “break up”). Various neutron sources are based on this , for example the planned high-intensity IFMIF source .

The reaction

${\displaystyle {}^{3}\mathrm {H} +{}^{2}\mathrm {H} \,\rightarrow \,{}^{4}\mathrm {He} +{}\mathrm {n} +17,6\,\mathrm {MeV} }$

in the form of a thermonuclear process acts in some nuclear weapons as a source of neutrons and energy and is intended to provide useful energy in a controlled manner in future fusion reactors .

literature

• Theo Mayer-Kuckuk : Nuclear Physics. An introduction . Teubner, Stuttgart, Leipzig, Wiesbaden, ISBN 3-519-13223-0 .
• Bogdan Povh et al .: Particles and Cores . Springer, Berlin Heidelberg 2006, ISBN 978-3-540-36685-0 .

Individual evidence

1. ↑ The information on the particle properties (info box) is, unless otherwise stated, taken from the publication of the CODATA Task Group on Fundamental Constants : CODATA Recommended Values. (No longer available online.) National Institute of Standards and Technology, archived from the original on March 3, 2014 ; accessed on July 4, 2019 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. The figures in brackets indicate the uncertainty in the last digits of the value. This uncertainty is given as the estimated standard deviation of the given numerical value from the actual value.  
2. ↑ Klaus Bethge , Gertrud Walter, Bernhard Wiedemann: Nuclear physics: An introduction . Springer, 2007, ISBN 978-3-540-74566-2 , pp.  282 .
3. ^ Robert Harr: Isospin Symmetry. Elementary Particle Physics Lecture Notes, Wayne State University 2003 ( hep.physics.wayne.edu ).