## 1987l

The following is the abstract of a paper by H. Aspden as published by the
Institute of Physics (U.K.) in the PROGRAMME and ABSTRACTS of a Conference on
Nuclear Physics and Particle Physics held at the University of Birmingham on 6-8
April 1987. (Paper No. Q1 on p. 84).

### A THEORETICAL DERIVATION OF NEUTRON LIFETIME

Summary: The measured mean lifetime of the neutron of approximately 898
seconds is shown to be determined from a theory of the proton dating from 1975.
The model requires the neutron to have a lifetime jointly determined by
characteristic transition times which the theory assigns to both the electron
and the proton.

Abstract: Theory of prior record (Aspden & Eagles, 1972,
1975)
gave:

α^{-1}=A(2s)^{1/2}
(4/3)(π)(2)(μ)=A^{3}s^{4}
M=2(μ)[(3/2)^{1/2}-1]^{-1}where A=108π and
(1/s)^{3}=1843. Here α is the fine structure constant, μ is the
muon-electron mass ratio and M is the proton-electron mass ratio.
The number A is a measure of the cell spacing in a cubic lattice given in
units of Thomson electron charge radius (two-thirds of the classical electron
radius). The number s represents a calculable energy quantum in electron
rest-mass energy units mc^{2} deemed to occupy each lattice site in the
calculation of record. A muon pair is supposed to be created cyclically and
annihilated in successive periods h/mc.

It is found that the chance of an encounter between a positive muon and an
electron occurs at intervals of [3/4(π)]A^{3}(h/mc^{2}),
approximately 10^{-13} seconds. This matches the observed electron
tunneling frequency.

The chance of a simultaneous encounter between the negative muon and the
proton, close enough to develop a proton-antiproton energy threshold offset by
negative potential of the interaction, involves a combined time period of:

[3/4(π)]^{2}A^{3}(2A/3)^{3}[M-μ]^{3}(h/mc^{2})With
M=1836, μ=207 and h/mc^{2}=8.09x10^{-21}, this gives a decay
time of 900 seconds.
This happens to be the lifetime of the neutron, which is of interest when
taken in conjunction with the earlier results of the theory. Taken together, the
proton and electron have a mass approximating the neutron and are electrically
neutral. This lifetime calculation may, therefore, help us in our further
understanding of neutron composition. Hence it is relevant to draw attention to
this new result which updates an earlier proposal on this subject (Aspden,
1981).

ASPDEN H and EAGLES D M, Physics Letters, v. 41A, 423 (1972).

ASPDEN H and
EAGLES D M, Il Nuovo Cimento, v. 30A, 235 (1975).

ASPDEN H, Lett. Nuovo
Cimento, v. 31, 383 (1981).

*****

Note that these three references are items [1972a],
[1975a]
and [1981b],
respectively, of this section of these Web pages.