Quantum Chromodynamical Explanation of the Strong Nuclear Force




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Volume PHY, Number 3903 P H Y S I C A L R E V I E W L E T T E R S 14 November 2003


Quantum Chromodynamical Explanation of the Strong Nuclear Force


Jakub Cieniak, #2587463

Physics Department, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario, Canada K1N 6N5

(Received 14 November 2003)


The Strong Nuclear Force was proposed to explain the unintuitive attraction between protons and neutrons within an atomic nucleus, despite the relatively immense repulsion of the electromagnetic force overshadowing the attraction between the particles due to gravitation. It is responsible for binding quarks, the building blocks of sub-atomic particles like protons and neutrons, via a process governed by Quantum Chromodynamics involving the exchange of colour-charged particles called gluons. Particles constituting bound pairs of quarks, called mesons, are exchanged between the sub-atomic particles at short distances to hold protons and neutrons together within the nucleus. These processes will be explained in this paper in detail and different theories on the origin of the force will be examined, including an explanation using the Gravitational Field Theory proposing that the Strong Nuclear Force is nothing more than the Force of Gravity. The properties of quarks and gluons will also be examined to aid in the explanation of the interactions between them that create the Strong Nuclear Force.


PACS number(s): 12.38.Mh, 24.85.+p, 12.39.Ki, 13.60.Hb



T
Figure 1. The Fundamental Particles
he reason atoms heavier than Hydrogen exist, despite the relatively large repulsive Coulomb force between protons at such close proximity as within the nucleus of an atom, is a residual effect of the Strong Nuclear Force, or Strong Interaction [1] between the fundamental building blocks of protons, neutrons and other hadrons: quarks. Quarks, at present, are considered the fundamental particles in physics along with leptons (electrons, muons, taus, neutrinos and their respective anti-particles) (see Figure 1) as it cannot be determined of what, if anything, these particles are composed. Leptons, however, lack colour-charge and hence do not participate in Strong Interaction, which is defined by the exchange of colour-charge carriers called gluons as explained by the Theory of Quantum Chromodynamics (QCD) [2]. QCD explains the interactions necessary to keep particles, like nucleons within an atom, from breaking apart into their constituents, the quarks, and provides an explanation for the ability of protons to overcome the repulsive forces between them when part of an atomic nucleus.

There are six different types, or flavours, of quarks as shown in Figure 1 and some of their properties are described in Table I. Quarks will combine [1]: in pairs (e.g. gluons, pions, kaons) to form bosonic hadrons, or mesons (see Table II); in triplets (e.g. protons, neutrons) to form Fermionic hadrons, or baryons (see Table III); and even quintets (e.g. the recently discovered Θ+ baryon [3]). (Bosons are carrier particles of interactions with integer units of quantum angular momentum, or spin, and Fermions have odd half units of spin and obey the Pauli Exclusion Principle.) These combinations are governed by a property of the quarks called the colour-charge.

A
Table I. The Different Flavours of Quarks [1]

Flavour

Mass (Gev/c2)

Electronic Charge

up (u)

0.004

+2/3

down (d)

0.008

-1/3

strange (s)

0.15

-1/3

charm (c)

1.5

+2/3

bottom (b)

4.7

-1/3

top (t)

176

+2/3




Table II. Some Bosonic Hadrons (Mesons) [1]

Name

Quark Content

Electronic Charge

Mass (GeV/c2)

Spin

pion, π+

ud-

+1

0.140

0

kaon, K+

su-

-1

0.494

0

rho, ρ+

ud-

+1

0.770

1

eta-c, ηc

cc-

0

2.979

0





Table III. Some Fermionic Hadrons (Baryons) [1]

Name

Quark Content

Electronic Charge

Mass (GeV/c2)

Spin

proton, p

uud

+1

0.938

1/2

neutron, n

udd

0

0.940

1/2

lambda, Λ

uds

0

1.116

1/2

omega, Ω-

sss

-1

1.672

3/2



quark can possess one of three colours, for example red, green and blue. Antiquarks possess the corresponding anti-colours. (These colours are merely a means of describing a characteristic of the quarks and are in no way related to any visual aspect of the quarks.) Similar to electric charge, like colours repel and unlike colours attract; a quark of a certain colour will feel an especially strong attraction to an antiquark of the corresponding anti-colour. Observable particles can only exist if their net colour is neutral: a combination of a colour with its anti-colour (creating a meson); or a combination of each of the three colours or each of the three anti-colours (creating a baryon). Within a baryon or meson (each a subset of particles called hadrons), interactions between quarks [2] occur by exchanging particles called gluons carrying one colour charge and one anti-colour charge. As per QCD, the net change in colour-charge for such an interaction must be zero; that is, colour-charge is conserved. For example, a green quark interacts with a blue quark within a baryon by emitting a gluon carrying green and anti-blue colour-charges; this leaves the formerly green quark with a blue colour-charge and converts the blue quark into a green one. The net colour-charge is conserved as the process results in one green and one blue quark, just as before the interaction. In a meson composed of a red quark and an anti-red antiquark, for example, the red quark can turn into a green quark by emitting a gluon carrying red and anti-green colour-charges that the anti-red antiquark will absorb turning it into an anti-green antiquark. Again, colour-charge is conserved as a colour-neutral meson is obtained. The flavour of a quark is one characteristic that can never be changed by an exchange of gluons between two quarks.

This interaction between quarks in a hadron is very similar to the interaction known as the Strong Nuclear Force, or what is called the Residual Strong Interaction. This force is responsible for keeping protons and neutrons together within an atomic nucleus; the minor difference between the two forces is the scale. The participants of the Strong Nuclear Force are the composite particles of quarks, the nucleons. The force between the nucleons is created by the exchange of particles carrying colour-charges, like the exchange of gluons between quarks. These particles are in fact the mesons, e.g. pions, kaons. If the nucleons are close enough that their boundaries actually overlap, the Strong Interaction can occur between quarks of different hadrons.

One major difference between the strong nuclear force and the other fundamental forces of nature is that the force between two interacting quarks increases with increasing separation distance between the quarks. Additional energy is needed to increase the force, and if the quarks are separated far enough, there is enough energy to create new quarks that will group with the separating ones, thereby creating more hadrons. This phenomenon, also known as confinement, is the reason for not being able to observe quarks directly, on their own, outside of a hadron. Conversely, when quarks are very close to each other, it is presumed that the force between them becomes non-existent, thereby making the quarks ‘free’ particles. This condition is known as asymptotic freedom. However, recent experiments at CERN [4] have brought about a notion of a quark-gluon plasma (QGP) phase consisting of quarks and gluons that are essentially ‘free’ particles not confined to the structure of a hadron. The plasma is formed from hot, dense nuclear matter that is subjected to relativistic collisions. Tests still need to be performed to analyze the new matter phase and confirm that it is indeed composed of these fundamental particles in the ‘free’ state.

H
Figure 2. Multi-Jet Hadronic Event [1] showing Three Distinct Localized Hadronic Jets
igh-energy hadronic collisions are also studied to examine particular effects of the confinement phenomenon of QCD called Multi-Jet Hadronic Events [1]. When hadrons collide with enough energy such that their confined quarks are forced to separate, the unconfined quarks can sometimes radiate one last gluon of high energy before new quarks and antiquarks are formed to create hadrons. This unconfined gluon will result in the production of a stream, or jet, of hadrons in order to decrease the energy of the unmatched quarks and antiquarks. This process can in fact result in multiple localized jets as can be seen in Figure 1. Many of these events can be examined to determine the average angle at which the jets occur with respect to the axes perpendicular to the axis of the collision of the hadrons. Specifically, experiments are being performed at CERN to study the collisions between gold nuclei, for example.

One property of the quarks that QCD cannot explain is their mass. There is a proposition that suggests a simple mechanism called the Higgs mechanism that accounts for the mass of the fundamental particles. The proposal involves the exchange of a particle called the Higgs boson as part of a new fundamental force, the Higgs force. This particle, however, has yet to be discovered.

A completely different explanation for the ability of protons to overcome the Coulombic force repelling them from each other within the nucleus of an atom is proposed by Kenneth F. Wright. Wright suggests [5] that it can be proven using quantum mechanics, Newton’s Law of Gravity and Einstein’s Theory of General Relativity that the strong nuclear force and the force of gravity are actually the same force. To summarize, Wright relates the energy of the force produced by an electric field of a proton with the energy of a photon and, using the equation for the energy of a photon, E = hc/λ, he associates a particular wavelength with the proton’s electric field. Wright likens the energy levels of the protons within an atomic nucleus with that of gamma- and X-rays as both are on the order of MeV. Since the wavelengths of gamma- and X-rays are on the order of 10-13 to 10-12 meters, 10 to 1000 times greater than the diameters of atomic nuclei, the nuclei are ‘invisible’ to the incoming rays. Wright claims that this same analysis can be related to the ‘wavelength’ of the electric fields of protons and that at such small distances as those within a nucleus, the electrostatic repulsion force becomes invisible to the protons. Consequently, the force of gravity takes over as the reigning force acting between the nucleons when within the boundary of the nucleus. One problem with this hypothesis is that the energy state of a proton confined to an atomic nucleus is unrelated to the potential energy created


by the electric field acting between two protons. Consequently, Wright associates a static energy value for the potential between the two interacting protons when, in fact, the energy is dependent on the distance between the protons and increases as they approach each other. Using Wright’s analogy, the ‘wavelength’ of the electrostatic force field would decrease proportionally as the two protons approached each other to within nuclear distances; hence, the electrostatic force would not vanish as he suggests.

Quantum chromodynamics has provided a sound theory that is gaining more and more supporting evidence from experiments. The recent developments in the Quark-Gluon Plasma matter phase still leave questions to be answered; fortunately, procedures are underway at laboratories like CERN that will hopefully shed some light on this new discovery.


[1] Theory: SLAC Virtual Visitor Center, www2.slac.standford.edu/vvc/theory.html and webpages therein; last accessed 13 November 2003.

[2] Encyclopedia: Strong nuclear force, www. nationmaster.com/encyclopedia/strong-nuclear-force; last accessed 2 October 2003.

[3] B. Schwarzschild, Four Experiments Give Evidence of an Exotic Baryon With Five Quarks, www.physicstoday.org/vol-56/iss-9/ p19.html; last accessed 2 October 2003.

[4] S. Hamieh, J. Letessier, and J. Rafelski, Phys. Rev. C 62, 064901 (2000).

[5] K. F. Wright, Nuclear Gravitation Field Theory, Chapter VIII: Nuclear Gravitation Field Theory Versus Accepted Strong Nuclear Force Overcoming Proton Electrostatic Repulsion, www.gravitywarp drive.com/NGFT_Chapter_8.htm; last accessed 13 November 2003.



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