Nuclear binding energy [Archive]

Jimi

Dec15-04, 12:35 PM

Zigoteau

Dec19-04, 07:17 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hi, Jimi,\n\n> I\'ve read about the Casimir effect and was wondering if it plays a\n> part in the confinement of protons and/or quarks in an atomic nucleus\n> as they are extremely close to each other. Could anyone run a\n> calculation to estimate the force of this effect if any?\n\nYou\'re not the only one who\'s had this idea. Ninham and Bostrom have\nproposed it in Phys. Rev. A 67, 030701 (2003), and their\nback-of-the-envelope calculations give rough agreement with the Yukawa\nforce between nucleons.\n\nHowever don\'t get carried away. These calculations are based on\nperturbation power-series-expansion solutions of the QFT equations,\nwhich almost always lead to nonsensical results on the initial attempt,\nand can only be coaxed unwillingly by renormalization techniques to\ngive any sensible answer at all. Any result obtained this way needs a\nreality check. There is another way of picturing the Casimir effect,\nthe Feynman-Hellman picture, which places qualitative bounds on\npossible solutions. It was first put forward by Hirschfelder and\nEliason [J. Chem. Phys. 47, 1164-1169 (1967)] and has been recently\nreviewed by Peterson and Metzger [Int. J. Chem. 7, 1 (2004)].\n\nThe Feynman-Hellmann theorem says that, when you anchor a charged\nparticle to a force-measuring apparatus, the force measured is exactly\nequal to the classical force which would act on that particle from the\nexpectation charge distribution. Neutral aggregates of matter placed\nclose to one another experience an attraction, because their proximity\nallows their component oppositely-charged particles to approach just a\nlittle bit closer to one another. The source of the energy is the\nreduction of the ground-state energy of the electromagnetic field.\n\nNotice that I say \'ground-state\' and not \'zero-point\'. To get any\nCasimir force at all, you need to modify the spectrum of\nelectromagnetic modes. This requires \'mirrors\', which are necessarily\nmade out of matter containing electrons and nucleons. In some quantum\nmechanics text books, the word \'vacuum\' is used to describe an\nunexcited system, for example a piece of silicon at absolute zero\ntemperature, rather than in the sense in which it would have been\nrecognized by Torricelli.\n\nTo get back to forces in the nucleus, the Ninham-Bostrom proposal is\nthat a Casimir-type interaction can counteract the electrostatic\nrepulsion between, say, two protons, and turn it into an attraction.\nHowever, the Feynman-Hellmann picture says that the charge cloud would\nhave to be rearranged so that to each particle, the charge of the other\none would appear to have changed sign. This appears rather improbable.\nCheers,\n\nZigoteau.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hi, Jimi,

> I've read about the Casimir effect and was wondering if it plays a
> part in the confinement of protons and/or quarks in an atomic nucleus
> as they are extremely close to each other. Could anyone run a
> calculation to estimate the force of this effect if any?

You're not the only one who's had this idea. Ninham and Bostrom have
proposed it in Phys. Rev. A 67, 030701 (2003), and their
back-of-the-envelope calculations give rough agreement with the Yukawa
force between nucleons.

However don't get carried away. These calculations are based on
perturbation power-series-expansion solutions of the QFT equations,
which almost always lead to nonsensical results on the initial attempt,
and can only be coaxed unwillingly by renormalization techniques to
give any sensible answer at all. Any result obtained this way needs a
reality check. There is another way of picturing the Casimir effect,
the Feynman-Hellman picture, which places qualitative bounds on
possible solutions. It was first put forward by Hirschfelder and
Eliason [J. Chem. Phys. 47, 1164-1169 (1967)] and has been recently
reviewed by Peterson and Metzger [\Int. J. Chem. 7, 1 (2004)].

The Feynman-Hellmann theorem says that, when you anchor a charged
particle to a force-measuring apparatus, the force measured is exactly
equal to the classical force which would act on that particle from the
expectation charge distribution. Neutral aggregates of matter placed
close to one another experience an attraction, because their proximity
allows their component oppositely-charged particles to approach just a
little bit closer to one another. The source of the energy is the
reduction of the ground-state energy of the electromagnetic field.

Notice that I say 'ground-state' and not 'zero-point'. To get any
Casimir force at all, you need to modify the spectrum of
electromagnetic modes. This requires 'mirrors', which are necessarily
made out of matter containing electrons and nucleons. In some quantum
mechanics text books, the word 'vacuum' is used to describe an
unexcited system, for example a piece of silicon at absolute zero
temperature, rather than in the sense in which it would have been
recognized by Torricelli.

To get back to forces in the nucleus, the Ninham-Bostrom proposal is
that a Casimir-type interaction can counteract the electrostatic
repulsion between, say, two protons, and turn it into an attraction.
However, the Feynman-Hellmann picture says that the charge cloud would
have to be rearranged so that to each particle, the charge of the other
one would appear to have changed sign. This appears rather improbable.
Cheers,

Zigoteau.