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Mass Defect

  1. Oct 20, 2011 #1
    I was wondering how mesons or the strong force is accounted for in mass defect.
    Nucleons individually have more mass then when they are bound together in a nucleus of an atom.
    I saw a teacher/professor speak on youtube. He said the binding energy (strong force) was calculated as part of the nucleons mass energy when they are seperate. It would almost seem then that mesons or the strong force come out of protons and neutrons.
    I know that protons and neutrons are made of 3 quarks each; and mesons, being force carriers are made of 2 quarks each.
    I am a little confused about how the force carrier (meson) or it's energy is calculated as part of the nucleon's mass, when they are seperate and individual.
  2. jcsd
  3. Oct 20, 2011 #2
    When the Nucleons are bound it is as if though they are in a non-inertial frame. Just like an object on earth has less energy then an object further away, the nucleon has less potential energy in the bound state then they would in the free state.

    The energy is usually said to be potential energy and is chosen to be 0 in the free state. However potential energy can always be found to be tangible upon measurement.

    All fields propagate at an invariant speed, so any calculations involving fields (such as in Quantum Field Theory) must vary in frequency relative to the reference frame. A particle in different non-inertial frames will result in relativistic momentum. So the potential energy can be found to be intrinsically kinetic and therefore tangible to a relative observer.

    This is how I understand it and I may be wrong.
  4. Oct 20, 2011 #3
    Thank you LostConjugate - I think I am on my way to understanding this. The strong force (binding energy) is considered potential energy because the nucleons are in a free state - correct? Then when it is measured, or observed into being it slows down and gives up it's potential energy in the form of the strong force. Am I understanding this correctly? If so, I have another question:
    Could this potential energy be another sort of energy, or does it only become the strong force, a binding energy? I am wondering this because I had not once seen you refer to the potential energy as the strong force or binding energy - only 'potential energy'.
  5. Oct 20, 2011 #4
    The binding energy is the energy required to bring the potential energy up to zero where the potential energy in the bound states is negative.

    The change in potential energy is due to the force. If an object is outside of the range of the force then there is not much potential for the object to gain any kinetic energy. The potential is effectively zero. However the potential must increase as the distance from the lowest energy state is increased, since the object has the potential to gain kinetic energy. So the potential energy is decreased from zero from the free state as it goes into lower and lower bound states.

    The obvious question is just because some particle has the potential to gain kinetic energy is this energy tangible before it becomes kinetic? I say that it is stored within the momentum of the quantum field associated with the particle due to relativistic effects on fields.
  6. Oct 20, 2011 #5
    The potential energy for the strong force that binds nucleons is in the form of a http://en.wikipedia.org/wiki/Yukawa_potential" [Broken]. This is the potential that you get from the exchange of a massive boson. It is more shortrange than the Coulomb potential:


    The mesons (which BTW are composed of a quark and an anti-quark, not two quarks) are virtual, and are not counted in the calculation of the binding energy.

    Last edited by a moderator: May 5, 2017
  7. Oct 22, 2011 #6
    I appreciate the both of you helping me wrap my brain around the mass defect concept. It seems like the more I learn, the more questions I end up having lol. Thanks again.
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