I Does the mass of a neutron vary?

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1. Nov 23, 2016

Zahidur

The mass of a neutron is approximately 1.674927471×10−27 kg, but is this always the case?

For example if a neutron undergoes negative beta decay (i.e. an electron and an electron anti-neutrino is emitted) and then positive beta decay, will this not mean that the final mass of the neutron is now lower than it initially was (since energy has been release and e= mc2)?

2. Nov 23, 2016

Orodruin

Staff Emeritus
That does not happen. The free proton is stable.

If you have a beta- decaying nucleus, the daughter does not decay via beta+ decay.

3. Nov 23, 2016

Staff Emeritus
Then after this it's gone.

4. Nov 23, 2016

Staff: Mentor

After the decay, you no longer have a neutron, but instead, a proton. A proton does indeed have a smaller mass than a neutron.

5. Nov 24, 2016

snorkack

In which senses does the mass of a neutron vary with its binding energy in the nucleus/state it is in?

6. Nov 24, 2016

Staff: Mentor

It does not vary. The overall mass of a nucleus is not the sum of masses of its constituents. That is not nucleus-specific, the same is true for a hydrogen atom (lighter than proton+electron), a nucleon itself (heavier than the three valence quarks), and every other bound system.

7. Nov 24, 2016

stoomart

Interesting. Is this extra mass a product of the energetic fusion event that brought the components together?

8. Nov 24, 2016

Staff: Mentor

It is a reduced mass. And yes, the difference is given by the energy released when fusing the nuclei together (with the speed of light squared as conversion factor).

9. Nov 24, 2016

stoomart

Are there any similarly energetic fusion events in cosmology where two or more components bind together without exploding or merging? It seems to me this may be an indicator why the standard model cannot be reconciled with QM, they look similar but have fundamentally different principles.

10. Nov 24, 2016

Orodruin

Staff Emeritus
What do you even mean by this? The Standard Model builds upon quantum field theory, which in turn is a development from quantum mechanics.

11. Nov 24, 2016

stoomart

Sorry still learning the basic terminology, I mean to say "why General Relativity cannot be reconciled with Quantum Field Theory".

12. Nov 24, 2016

Staff: Mentor

All fusion processes are processes where two or more components bind together without exploding. What exactly do you mean by "merging"? They form a new nucleus.

All this has nothing to do with general relativity.

13. Nov 24, 2016

stoomart

Was referring to black holes. I'm trying to ask if fusion occurs on the macroscopic scale.

14. Nov 25, 2016

ChrisVer

a black hole is a singularity on spacetime...no "merging" or "fusion"...

do you consider the burning of a star's elements (something that involves processes on a microscopic level) something that happens on a "macroscopic scale"? then yes...

15. Nov 25, 2016

Staff: Mentor

16. Nov 25, 2016

stoomart

Sorry, I'll stay focused on the topic.
Am I interpreting this right: atoms are lighter than the sum of their constituents' mass, and nucleons are heavier than the sum of their constituents' mass.

17. Nov 25, 2016

Staff Emeritus
No. Please reread message #6 where it says "the same is true".

18. Nov 25, 2016

stoomart

What am I missing here?

19. Nov 25, 2016

Staff: Mentor

Post #6 didn't specify the direction, I just said the mass is not the same. In post 8 I wrote that the mass of a nucleus is smaller than the sum of masses of its constituents (the nucleons).

20. Nov 25, 2016

vanhees71

The issue is not that easy and not fully understood.

What's very well understood is the theory of quite weakly bound systems like the binding of atomic nuclei out of nucleons (protons and neutrons) via the residual strong force (a kind of van der Waals force of the strong interaction acting between color neutral hadrons) or atoms out of atomic nuclei and electrons. The mass of such objects (i.e., the rest energy of these objects in the center-of-momentum frame of the constituents) is given by the sum of the mass of the constituents minus the binding energy, i.e., there is a "mass defect" $\delta M=E_{\text{B}}/c^2$.

The case of the hadron masses as bound states of either three quarks (baryons) or a quark-antiquark pair (mesons) is way more complicated. The light quarks (up and down) have a "current quark mass" of a few 10 MeV. The determination of these masses is already complicated enough since we cannot define it in the usual sense of the mass of asymptotic free particles, because there are no free quarks (nor free gluons) due to confinement. This "current quark mass" is the mass due to the Higgs mechanism of the electroweak sector of the standard model. A proton, however has a mass of about 938 MeV. The precise mechanism, how this mass can be explained as dynamically generated via the strong interaction, is pretty much unkown. That this picture is, however, quantitatively correct, is inferred from ever more accurate evaluations of QCD with help of computer simulations, called lattice QCD. Basically it's the Monte-Carlo evaluation of path integrals of Euclidean ("imaginary time") QCD with ever better algorithms and increasing CPU/GPU power. The observed hadron spectrum is pretty well described in this way, and that's why we can be pretty confident that QCD is the right fundamental theory of the strong interaction (at least as far as the Standard Model works, and to the dismay of the particle physicists there's no clear hint for "physics beyond the Standard Model" yet!).

Qualitatively one can make sense of the fact that the mass of the hadrons is so much larger than that of the valence quarks in the naive quark model in terms of the socalled MIT bag model, which however is not too successful quantitatively. Nevertheless it provides a picture: The three valence quarks of, e.g., a proton are confined to a "bag" about the size of 1 fm due to confinement (however this may work in detail), and thus there's a lot of kinetic energy of the motion of these constituents within the bag, and this motion makes the huge part of the mass of the proton not provided by the mass of the constituents. The formation of the bag is hand-wavingly depicted as a bubble of perturbative QCD vacuum in the fully interacting QCD vacuum, although as I said it's not very clear, how to make sense of this mathematically.

Confinement, chiral-symmetry breaking through the formation of a quark condensate, $\langle \bar{q} q \rangle \neq 0$, is among the most puzzling an fascinating questions of contemporary physics. It's investigated with heavy-ion collisions at various accelerators (e.g., RHIC at the Brookhaven National Lab and the LHC at CERN). There the collision of heavy nuclei like Au and Pb at very high energies (200 GeV, up to about 5 TeV per nucleon respectively) creates tiny "fireballs" (some fm in extension) of very hot strong-interaction matter for a very short time (some fm/c) were the relevant degrees of freedom become quarks and gluons, the socalled quark-gluon plasma. This fireball rapidly cools down and undergoes transitions from a QGP to a hot hadron-resonance gas and is finally freezing out in terms of the known hadrons.

During it's lifetime the fireball also spits out lepton-antilepton pairs and photons, for which the medium is pretty transparent, and thus these "electromagnetic probes" provide some information about the spectral properties of their sources, which is the strongly interacting matter and thus one can learn about the deconfinement-confinement as well as the chiral-symmetry-restoration mechanism. For transparencies of some lectures, I've given to graduate students at some lecture weeks, see

November 25-26, 2015: Two Lectures on "Electromagnetic Probes in Heavy-Ion Collisions" at the "Graduate Days" at the University of Graz, Austria
Lecture 1: Electromagnetic Probes in Heavy-Ion Collisions I: Foundations [pdf]
Lecture 2: Electromagnetic Probes in Heavy-Ion Collisions II: Phenomenology from SIS to LHC Energies [pdf]

http://th.physik.uni-frankfurt.de/~hees/hqm-lectweek14/index.html