﻿ An Investigation of the Stability of Neutrons in Nuclei
San José State University

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 An Investigation of the Stability of Neutrons in Nuclei

One of the major puzzles of nuclear physics is why neutrons, which as free particles decay with a half-life of slightly over ten minutes, are so stable within nucllei. The decay of a neutron into a proton and an electron releases energy.

#### Mass energy of a proton = 938.27231 MeV Mass energy of a proton = 0.510999906 MeV Combined mass energy of a proton and an electron = 937.7613101 MeV Mass energy of a neutron = 939.56563 MeV Difference in mass energy =1.804319906 MeV ch

There is evidence from nuclear fission that compound nuclei do contain neutrons as particles. When a uranium U235 nucleus splits upon being penetrated by a neutron there are two or three neutrons produced as well as a krypton Kr89 nucleus and a barium Ba144 nucleus. This is the basis for the nuclear chain reaction.

One possible explanation of the stability of neutrons in nuclei is that it might be that the conversion of a neutron into a proton in a nucleus requires an energy input because of the energy level of the nucleus containing one more proton is greater than that of the original nucleus.

This hypothesis was tested using nuclear binding energy as a proxy for potential energy and computing the energy that would result from a conversion of a neutron into a proton and electron. That is to say an energy difference D was computed as

#### D = BE(n-1, p+1) − BE(n, p)

If D is positive then energy would be liberated as a result of the decay of a neutron into a proton and electron, not counting the mass of the neutron in excess of the mass of the proton and electron. If D is negative the conversion would require an input of energy and thus its nonoccurrence is explainable in energy terms.

There were 2657 nuclides for which D could be computed. The average energy difference was −1.439 million electron volts (MeV). This is on the order of the energy liberated when a free neutron decays into a proton and an electron.

The standard deviation of these difference was 7.37 MeV. The histogram for the differences is shown below. The range of this distribution of D is a resounding rejection of the hypothesis that the stability of neutrons in nuclei has anything to do with energy balance. The near-normality of the distribution suggests that the values of D are the result of a large number of random influences.

## Spin Paired and Non-Spin-Paired Neutrons

The value of D for a nuclide may be affected by whether there are any unpaired neutrons or unpaired protons. The following tables give the number of the various cases and the average value of D, the change in binding energy that would result from the decay of a neutron.

The Number of Cases of the Computed Change
in Binding Energy that would result from a Conversion
of a Neutron into a Proton and Electron
Neutron number
Proton
number
OddEven
Odd668662
Even663665

The Average Change in Binding Energy
that would result from a Conversion of a
Neutron into a Proton and Electron
(MeV)
Neutron number
Proton
number
OddEven
Odd-3.66233-1.52701
Even-1.05903+0.65682

Apparently the change in binding energy that would occur for a conversion of a neutron in a nucleus to a proton and electron does depend upon whether there is an unpaired neutron and/or an unpaired proton. For the odd-odd case a neutron conversion would result in the disappearance of a neutron-proton spin pair and the creation of a proton-proton spin pair. If there is an unpaired neutron and no unpaired proton the conversion would result only in the creation of an unpaired proton. If there is no unpaired neutron and an unpaired proton the conversion of a neutron would result in the disappearance of a neutron-neutron spin pair and the creation of a neutron-proton spin pair. For the even-even case the conversion of a neutron would result in the disappearance of of a neutron-neutron spin pair and the creation of an unpaired proton.