
#1
Nov1610, 01:09 PM

P: 1,555

Can we calculate the difference in mass between a Proton and Neutron?
If so, how? [ Moderator: why did you move this from QM to general physics? ] 



#2
Nov1610, 01:23 PM

P: 28

Hi Passion Flower.
neutron is slightly heavier Mass of proton : 1,6726 x 10^(27) kg Mass of neutron: 1,6749 x 10^(27) kg Mass of electron: 0,00091x10^(27) kg The mass of a neutron is greater than the mass of a proton because the neutron contains a proton, contains an electron with some subatomic particles. neutron = proton + electron + subatomic particles 



#3
Nov1610, 01:25 PM

P: 1,555





#4
Nov1610, 01:28 PM

P: 28

Proton and Neutron mass
In energy units (using E = mc^2), the masses are: Proton: 938.272 MeV, neutron:
939.566 MeV, mass difference = 1.293 MeV, electron: 0.511 Mev. 



#5
Nov1610, 01:33 PM

P: 1,555





#6
Nov1610, 03:49 PM

Sci Advisor
P: 5,942

From Wikipedia
Outside the nucleus, free neutrons are unstable and have a mean lifetime of 885.7±0.8 s (about 14 minutes, 46 seconds); therefore the halflife for this process (which differs from the mean lifetime by a factor of ln(2) = 0.693) is 613.9±0.8 s (about 10 minutes, 14 seconds).[2] Free neutrons decay by emission of an electron and an electron antineutrino to become a proton, a process known as beta decay:[6] n^{0} → p^{+} + e^{−} + ν_{e} 



#7
Nov1610, 03:57 PM

P: 1,555





#8
Nov1610, 04:23 PM

Mentor
P: 11,254





#9
Nov1610, 04:29 PM

P: 546





#10
Nov1610, 04:47 PM

P: 1,555

At any rate, yes, so if the answer is yes I like to see some formulas. 



#11
Nov1610, 05:02 PM

Sci Advisor
HW Helper
PF Gold
P: 2,606

We now understand that protons and neutrons are composed of quarks. The proton is composed of 2 up quarks and 1 down quark, while the neutron is composed of 2 down quarks and 1 up quark. There's no simple explanation for the exact difference in the mass between the proton and neutron. It's known that the down quark is slightly heavier than the up quark, so the neutron could be predicted to be slightly heavier than the proton. However, the difference between quark masses only explains a small amount of the neutronproton mass difference. The remaining mass difference can only be explained by the strong interaction between the constituent quarks of each particle. This interaction within the proton is stronger, since the proton is stable and the neutron is not. So the proton has more binding energy, again leading to a smaller mass than the neutron. However precisely computing the mass difference is not as simple as writing down a formula, since just about all approximation schemes break down when considering the strong interaction at low energies. Lattice QCD is the most promising computational method for answering such questions, and it gives correct results for nucleon masses to within a few percent. 



#12
Nov1610, 05:05 PM

P: 1,555

Within a few percent is ok. So what is the formula? 



#13
Nov1610, 05:20 PM

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PF Gold
P: 2,606





#14
Nov1610, 05:40 PM

Admin
P: 22,708

From the second paper:




#15
Nov1610, 05:44 PM

Sci Advisor
PF Gold
P: 4,863





#16
Nov1610, 05:47 PM

P: 1,555

Can we do the full calculation in Maple or mathematica (I prefer Maple). If the answer is no then what software is used to calculate it? We certainly can do path integrals, Wick rotations and Monte Carlo stuff in Maple. Discretizing on a lattice I am not sure. What is quenched approximation? It seems if we use that then "the Standard Model explains" is not very relevant statement to the method of calculation or do I see that incorrectly? 



#17
Nov1610, 06:08 PM

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PF Gold
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#18
Nov1610, 06:13 PM

P: 1,555

A side question then would be how computationally intensive is the full calculation. So do I understand correctly that there are two main approaches, e.g. perturbation and QCD lattice and that quenched optimization is a shortcut for the second approach which is a shortcut to the perturbation method?
So how computationally intensive is it? Wasn't this done decades ago? As far as I understand the computing power decades ago can now easily be reproduced on even a laptop. 


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