Role of Pions in Nuclear Fusion ?

[Widdekind]

Nucleons are apparently immersed in a "pion cloud", of extended, delocalized, diffuse pions. And, pions apparently produce the Yukawa Potential, to mediate the Strong Nuclear Force. What role do pions play, in nuclear fusion processes ? Could you create some sort of "pion catalyzed fusion", along the lines of [math]p^{+} + p^{+} + \pi \rightarrow He^{2+}:\pi \rightarrow He^{2+} + \pi[/math] ? Could you "pre-treat" fusion fuels, by bombarding the protons in order to "stress" their gluon fields, thereby (electro- or neutrino-)producing quark/antiquark pairs (as gluon bonds break), which could "hadronize" into pions, and make the protons "pion rich" and "extra (Strong Force) sticky" ???

 

 

 

 

 

Anthony W. Thomas, Wolfram Weise. The Structure of the Nucleon:

 

At low energy, the nucleon an be viewed, as a system of three constituent quarks, surrounded by an interacting cloud of pions.

(pg. 192)

 

The role of the pion cloud of the nucleon is vital... The dominant long-range structure of the proton, is given by the virtual process [math] p \rightarrow n \pi^{+}[/math]; and, in a simple valence picture of the nucleon and the pion, this Fock component of the wave-function involves only [math]\bar{d}[/math] quarks, not [math]\bar{u}[/math].

(pg. 94)

 

Pions are also an important feature of nucleon structure itself. When probing the nucleon with long-wavelength, electro-weak fields, a substantial part of the response comes from the pion cloud, the "soft" surface of the nucleon.

(pg. 202)

 

The structure of a physical hadron will consist of a valence quark core "dressed" by a cloud of pions.

(pg. 236)

Edited July 30, 2010 by Widdekind

[Klaplunk]

Excuse me for asking but if you had to explain what a pion was using simple terms, what would it be? I'm not educated in this subject.

[Widdekind]

A pion is a Meson, a "middle-weight" combo of a quark & antiquark, whose mass-energy equivalent is ~140 MeV (~1/7^th of nucleon mass-energies). They flit between nucleons, in a nucleus, and bind them all together, thereby accounting for the Strong Force, to my understanding. Their Wave Functions are apparently more extended, distended, or delocalized, than those of the nucleons themselves, which are typically spread out over ~1 fm. Thus, the "pion cloud" has a "tail" which extends out well beyond the "surface" of the nucleons to which they are bound.

[swansont]

Note the phrase virtual process in your quote.

[Widdekind]

Note the phrase virtual process in your quote.

 

(Thanks for pointing that out.)

 

Virtual pions are "off-mass shell" ? Actual pions would not help bind nuclei together, for fusion effects ?

Edited August 1, 2010 by Widdekind

[swansont]

(Thanks for pointing that out.)

 

Virtual pions are "off-mass shell" ? Actual pions would not help bind nuclei together, for fusion effects ?

 

I don't know for sure, but I suspect not.

[Widdekind]

I found these references, seemingly suggesting, that nucleons "clique" together, inside nuclei, w/ pions apparently representing "thermal collisional" excitations (my words), which I would guess come from "stressing & stretching" the "glue" linking & locking quark-triplets together, inside nucleons:

 

In the nucleus, the scattering can happen on a nucleon cluster, and the scattered electron may acquire a larger momentum than on a free nucleon...

 

If one supplies energy to a normal nucleus, it heats up, and emits nucleons or small nuclei (mainly alpha clusters [math]\left( \alpha = He^{2+} \right)[/math]), just as a liquid droplet evaporates atoms or molecules. If, however, one confines the material, increasing the energy supplied leads [instead] to the excitation of internal degrees of freedom. In a molecular gas, these are rotational & vibrational excitations. In nuclei, nucleons can be excited into [math]\Delta(1232)[/math] [spin] resonances, or to still higher nucleon states. We have called the mish-mash of nucleons & pions, where are then created by decays, Hadronic Matter.

 

Bogdan Povh, Klaus Rith. Particles & Nuclei, pp. 93,321.

 

 

 

The Wave [Function] of an alpha particle, within a heavy radioactive nucleus, has a tiny [diffuse] "tail" that extends well outside the nucleus. Because of this remote bit of Wave [Function], the alpha particle has a certain probability of springing through the force barrier that would otherwise hold it within the nucleus, whereupon it flies away, to signal an alpha-decay event. This is the tunneling phenomenon... explained in the quantum world through the wave nature of matter, and the link between waves & probability.

 

K.W.Ford. The Quantum World, pg. 203.

 

 

 

At normal nuclear densities, each nucleon occupies a volume of about 6 fm³, whereas the actual volume of a nucleon itself is only about a tenth of this [0.6 fm³]. If one, then, were to compress a cold nucleus (T=0) to ten times its usual density, the individual nucleons would overlap, and cease to exist as individual particles.

 

Bogdan Povh, Klaus Rith. Particles & Nuclei, pg. 321.

 

 

 

Virtual mesons surround ("clothe") the Dirac ("bare") nucleon... Nucleons are composed primarily of three quarks, the proton has the composition (uud), the neutron (udd), where u stands of an up quark, and d for a down quark. Nucleons contain not just one point particle and a meson cloud; three point particles reside there. The interaction among the quarks is transmitted by gluons; the force is weak at short distances ([math]\leq 0.1 fm[/math]) and strong at large ones ([math]\geq 0.5 fm[/math])... The [virtual] mesons are an effective means of describing "large" distance hadronic structure. Pions are the lightest mesons, thus they account for the outermost part of the structure, and are, therefore, the most important ones to consider in addition to the quarks... A number of "bag" models have been constructed; some of the more successful ones include a pion cloud in addition to the quarks, to explain the structure of the nucleon. In such a picture, a photon interacts not only with the core (bare proton or [three] quarks), but also with the surrounding meson cloud. Since the pions do not leave the nucleon, and have to return, they can only go about half the pion Compton Wavelength. The radius of the nucleons, consequently, is expected to be about [math]\hbar / 2 m_{\pi} c[/math], or about 0.7 fm. In this model, which can account for the static properties of both the proton & neutron, the quarks and the pion cloud contribute to the magnetic moment.

 

Ernest M. Henley, Alejandro Garcia. Subatomic Physics, pp. 153-154.

 

 

We describe the proton as three constituent, or valence, quarks ([math]u_v u_v d_v[/math]), accompanied by many quark-antiquark pairs ([math]u_s u_s, d_s d_s, s_s s_s[/math], and so on). These are known as "sea" quarks. If we picture them as being radiated by the valence quarks, then, as a first approximation, we may assume that the three lightest flavor quarks (u,d,s) occur in the "sea", with roughly the same frequency & momentum distribution, and neglect the heavier flavor quark pairs ([math]c_s c_s[/math], and so on).

 

Francis Halzen, Alan D. Martin. Quarks and Leptons, 198.

 

 

 

Complicated processes are going on inside [nucleons] -- valence quarks emitting virtual gluons, gluons producing quark-antiquark pairs, [and these] 'sea' quarks recombining, and so on... all this frenzied activity conserves [electric] charge.

 

J.D.Griffiths. Introduction to Elementary Particles, pg. 320.

 

EDIT: These last two sources seemingly suggest, that pions represent a radial, quasi-periodic, "breather mode", expansion of core [constituent / valence / structural] quarks:

 

[math](d u u) \rightarrow (d u) u[/math]

[

up quark

in

proton

gets "quantum kick" (of some sort)...]

[math]\rightarrow (d u) + g + u[/math]

[

up quark

"puffs out" radially, stretching

gluon

bonds, which thusly "ooze more glue"]

[math]\rightarrow (d u) + (d \bar{d}) + u[/math]

[

up quark

"swells" further still, stretching

gluon

bonds until they break, "ripping" into

quark-antiquark

pairs]

[math]\rightarrow ((d u) + d) + (\bar{d} u)[/math]

[

up quark

's expansion "stalls out", as it

Hadronizes

with the

antidown antiquark

, whilst

down quark

, left behind at smaller radii,

Hadronizes

with "spectator"

structural quarks

, to form a

neutron

]

[math]\rightarrow (d u) + (d \bar{d}) + u[/math]

[

up quark

begins being brought back inwards, in "infall"...]

[math]\rightarrow (d u) + g + u[/math]

[

up quark

continues "deflating",

quark-antiquark

recombine into

gluon

bond]

[math]\rightarrow (d u) u[/math]

[quasi-stable

proton

has reformed]

This "Cepheid Variable pulsating breather mode" model, of virtual pion production in protons, seems consistent w/ claims, that the proton spends ~80% of its time being "bare", and ~20% of its time "dissociated" into neutron + pion [looking for the book every which where].

 

 

EDIT to EDIT: According to I.S.Hughes' Elementary Particles (3rd. ed.), p.51, " part of the time the proton exists as a neutron plus a [math]\pi^{+} meson[/math], [math]p \rightleftharpoons n + \pi^{+}[/math] ", which orbits the central nucleon in an L=1 p-state. Given that gluons have S=1, the emission of a gluon, by a quark (S=1/2), Conservation of Angular Momentum must imply that the quark spin-flips; and, that, when the gluon bond breaks, the resulting quark-antiquark pair produced must be "born" spin-parallel:

 

[math]p^{+} = (d \downarrow u \uparrow u \uparrow) \rightarrow (d \downarrow u \uparrow) \; u \uparrow[/math]

[math]\rightarrow (d \downarrow u \uparrow) + g \uparrow + \; u \downarrow[/math]

[math]\rightarrow (d \downarrow u \uparrow) + (d \uparrow \bar{d} \uparrow) + u \downarrow[/math]

[math]\rightarrow \left( (d \downarrow u \uparrow) + d \uparrow \right) + (\bar{d} \uparrow u \downarrow)[/math]

[math]\rightarrow \left( d \downarrow u \uparrow d \downarrow \right) + \pi^{+}_{l=1}[/math]

[the spin-up

down quark

, from the torn tendon of

glue

,

Hadronizes

with

spectator quarks

in the core, but must spin-flip to spin-down, to align with its new-found fellow

down quark

. That spin-flip can account for the "

Angular Momentum

boost" (L=0 to L=1) given to the newly

Hadronized

pion

.]

[math]= n + \pi^{+}_p[/math]

[math]\rightarrow \left( (d \downarrow u \uparrow) + d \uparrow \right) + (\bar{d} \uparrow u \downarrow)[/math]

[math]\rightarrow (d \downarrow u \uparrow) + (d \uparrow \bar{d} \uparrow) + u \downarrow[/math]

[math]\rightarrow (d \downarrow u \uparrow) + g \uparrow + \; u \downarrow[/math]

[math]\rightarrow (d \downarrow u \uparrow u \uparrow) = p^{+}[/math]

In-so-far as any kind of crude comparison can be construed, between the L=1 p-state pion, and the corresponding Hydrogenic Wave Function (L=1, m=1 [?]), then the Wave Function of the "spun up" pion perhaps takes on a toroidal, donut-like shape, rotating around the neutron at the center. According to Hughes (ibid.), this simple model predicts that protons spend a time-fraction x=0.7 in the "bare" proton state, and the rest of the time in the "dressed" neutron + pion state. Repeating the process for neutrons ([math]n \leftrightharpoons p + \pi^{-}[/math]), yields a bare-state fraction x=0.76. If meaningful, this might imply, that the lighter, and more electrostatically repulsive, up quarks, in protons, are more likely to "poof out", into the "pion breather" mode, than the lighter & less repulsive down quarks, in neutrons.

 

Note that the "splitting" of gluons into quark-antiquark pairs seems superficially similar to the "splitting" of photons into electron-positron pairs.

Edited August 4, 2010 by Widdekind

[Widdekind]

D.Griffiths (Intro. Elem. Part. (2nd ed.), pg. 131) describes Deuteron production:

 

[math]p \; + \; p \rightarrow d \; + \; \pi^{+}[/math]

 

[math]p \; + \; n \rightarrow d \; + \; \pi^{0}[/math]

 

[math]n \; + \; n \rightarrow d \; + \; \pi^{-}[/math]

I.S.Hughes (Elem. Part. (3rd. ed.), pg. 51) describes Pion production, from fleeting nucleon dissociations:

 

[math]p \rightleftharpoons n \; + \; \pi^{+}[/math]

 

[math] n \rightleftharpoons p \; + \; pi^{-}[/math]

Are these processes related ?

 

[math]p \; + \; p \rightarrow p \; + \; (n + \pi{+}) \rightarrow d \; + \; \pi^{+}[/math]

 

[math]n \; + \; n \rightarrow n \; + \; (p + \pi^{-}) \rightarrow d \; + \; \pi^{-}[/math]

It is almost as if, one nucleon runs into the "sticky slime molasses", of the Meson Cloud, enveloping the other nucleon; and, that the Meson Cloud acts like an "aero-brake" on an incoming nucleon, slowing it & sticking it, into a fused state, with the original nucleon -- even as that Meson Cloud, absorbing the impact energy, is "kicked out", & "blown free & clear", of the new nucleus. Would head-on collider beams improve the performance of fusion engines ??? (It also seems, that all of the "jittering, jiggling, & jostling" going on in the nucleus, ought possibly to perturb [the central cores of] any bound electron Wave Functions.)

 

It seems as if you can conceive of three (3) different Ranges, of relevant forces, on nuclear sizes scales:

 

• Long-Range (Electro-Magnetism via Photons) -- extra-nuclear (r > 7 fm)
  
• Medium-Range (Strong Force via Pions) -- intra-nuclear, inter-nucleon (r > 1 fm)
  
• Short-Range (Color Force via Gluons) -- intra-nucleon (1 fm > r)
  

If Deuterons are spin-parallel combinations of protons & neutrons (S=1), would it help, for fusion, to "spin prepare" the fusion fuels, to make them "spin-aligned", and, thereby, expedite the fusion process ???

 

Edited August 9, 2010 by Widdekind

[Widdekind]

B.R.Martin's Nuclear & Particle Physics (pp. 14,17,95) lists other pionic nuclear reactions:

 

[elastic scattering]

[math]\pi^{-} + \; p \; \rightarrow \; \pi^{-} + \; p[/math]

 

[single

pion

charge exchange]

[math]\pi^{-} + \; p \; \rightarrow \; n [/math]

 

[charge exchange]

[math]\pi^{-} + \; p \; \rightarrow \; n \; + \; \pi^{0}[/math]

 

[inelastic scattering]

[math]\pi^{-} + \; p \; \rightarrow \; \pi^{-} + \; p \; + \; \pi^{-} + \; \pi ^{+}[/math]

 

 

Now, in nucleons, when gluon bonds break, "tearing" into a newly-formed quark-antiquark pair, down antiquarks appear up to 50% more often, than up antiquarks:

 

At large momentum fractions, the two [u & d quarks] make an equal but tiny contribution. But, for quarks & antiquarks having less than a fifth of a proton's momentum, down antiquarks outnumber up antiquarks. This is the first time [that] flavor asymmetry had been witnessed across the antiquark distribution, within the nucleon 'sea' ['sea' quarks].

 

Watson. The Quantum Quark, pp. 336,340.

Since the proton dissociation reaction ([math]p \rightarrow n + \pi^{+}[/math]) relies on the creation of a comparatively common down-antiquark, whereas the neutron dissociation reaction ([math]n \rightarrow p + \pi^{-}[/math]) relies upon the creation of a relatively rare up-antiquark, this could be construed as consistent, with the observation, that the former rate appears to be about 20% more frequent than the latter (p spend 30% of their time in the dissociated state, n spend only 25%) [see PPs].

 

Since (anti-)down quarks are actually more massive than (anti-)up quarks, perhaps the preference for production of the former flows from the fact, of the latter's larger electric charge -- which might make for more intense electro-magnetic attractions, between bond-broken [math]u \bar{u}[/math], vs. [math]d \bar{d}[/math], and which might make the former somewhat stronger, and less likely to unlink.

Edited August 12, 2010 by Widdekind

[Widdekind]

Are these processes related ?

 

[math]p \; + \; p \rightarrow p \; + \; (n + \pi{+}) \rightarrow d \; + \; \pi^{+}[/math]

 

[math]n \; + \; n \rightarrow n \; + \; (p + \pi^{-}) \rightarrow d \; + \; \pi^{-}[/math]

It is almost as if, one nucleon runs into the "sticky slime molasses", of the Meson Cloud, enveloping the other nucleon; and, that the Meson Cloud acts like an "aero-brake" on an incoming nucleon, slowing it & sticking it, into a fused state, with the original nucleon -- even as that Meson Cloud, absorbing the impact energy, is "kicked out", & "blown free & clear", of the new nucleus...

 

When very high energy projectiles collide with other nuclei, they sometimes apparently knock

pions

out... Some rather difficult experiments, involving beams of

electrons & photons

... can only be understood, if it is assumed, that there are

pions

within

nuclei

.

 

Ray Mackintosh, Jim Al-Khalili.

Nucleus: A Trip into the Heart of Matter

, 56.