﻿ The Magnetic Moments of the Odd p Even n Nuclides from Iodine (53) to Berkelium (97)
San José State University

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Thayer Watkins
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The Magnetic Moments of
the Odd p Even n Nuclides
from Iodine (53) to Berkelium (97)

## Background

The magnetic moment of a nucleus is due to the spinning of its charges. One part comes from the net sum of the intrinsic spins of its nucleons. The other part is due to the rotation of the positively charged protons in the nuclear structure.

However nucleons form spin pairs with other nucleons of the same type but opposite spin. Therefore for an odd p, even n nucleus there should be the net magnetic moment due to the intrinsic spin of one proton. The magnetic dipole moment of a proton, measured in magneton units, is 2.79285.

## Analysis of the Magnetic Moment Due to the Rotation of a Nucleus

The magnetic moment of a nucleus μ due to the rotation of its charges is proportional to ωr²Q, where ω is the rotation rate of the nucleus, Q is its total charge and r is an average radius of the charges' orbits. The angular momentum L of a nucleus is equal to ωr²M, where M is the total mass of the nucleus. The average radii could be different but they would be correlated. Thus the magnetic moment of a nucleus could be computed by dividing its angular momentum by its mass and multiplying by it charge; i.e.,

#### μ = α(L/M)Q = (αQ/M)L

where α is a constant of proportionality, possibly unity. Angular momentum may be quantized. This would make μ directly proportional to Q and inversely proportional to M. But Q and M can be expected to be proportional to each other. That means that if L is quantized then μ is quantized. This means means that μ should approximately be a constant independent of the scale of the nucleus.

There could be a slight variation in μ with the neutron number n because of its effect on the ratio (Q/M).

## The Data

Here is the graph of the data for the magnetic moments of the odd p, even n nuclides from Iodine (53) to Berkelium (97): .

The data themselves are:

Magnetic Moments of the Even n, Odd p Nuclides
from Iodine (53) to Berkelium (97)
53 64 3.1
53 66 2.9
53 68 2.3
53 70 2.818
53 72 2.821
53 74 2.81327
53 76 2.621
53 78 2.742
53 80 2.856
55 64 5.46
55 66 0.77
55 68 1.377
55 70 1.409
55 72 1.459
55 74 1.491
55 76 3.53
55 78 2.582025
55 80 2.7324
55 82 2.8513
55 84 2.696
55 86 2.438
55 88 0.87
55 90 0.784
57 76 7.5
57 78 0
57 80 2.695
57 82 2.7830455
59 80 6.6
59 82 4.2754
59 84 2.701
61 82 3.8
61 84 3.8
61 86 2.58
61 88 3.3
61 90 1.8
63 76 6.1
63 78 3.494
63 80 3.673
63 82 3.999
63 84 3.736
63 86 3.576
63 88 3.4717
63 90 1.5324
63 92 1.52
63 94 1.5
63 96 1.38
65 82 1.7
65 84 1.35
65 86 0.919
65 88 3.44
65 90 2.01
65 92 2.01
65 94 2.014
67 86 6.81
67 88 3.51
67 90 4.35
67 92 4.28
67 94 4.25
67 96 4.23
67 98 4.17
69 88 0.476
69 90 3.42
69 92 2.4
69 94 -0.082
69 96 -0.139
69 98 -0.197
69 100 -0.231
69 102 -0.228
71 98 2.297
71 100 2.305
71 102 2.28
71 104 2.2323
71 106 2.239
73 100 1.7
73 102 2.27
73 104 2.25
73 106 2.289
73 108 2.3705
73 110 2.36
75 104 2.8
75 106 3.19
75 108 3.168
75 110 3.187
77 106 2.36
77 108 2.605
77 112 0.13
77 114 0.1507
77 116 0.1637
79 104 1.97
79 106 2.17
79 108 0.535
79 110 0.494
79 112 0.1369
79 114 0.1396
79 116 0.1487
79 118 0.145746
79 120 0.261
81 106 1.55
81 108 3.878
81 110 1.588
81 112 1.591
81 114 1.58
81 116 1.58
81 118 1.6
81 120 1.605
81 122 1.62225787
81 124 1.63821461
81 126 1.876
83 116 4.6
83 118 4.8
83 120 4.017
83 122 4.605
83 124 4.081
83 126 4.1103
83 128 4.5
83 130 3.89
85 122 3.75
85 124 10
85 126 9.56
85 128 3.8
87 120 3.89
87 122 3.95
87 124 4
87 126 4.02
87 134 1.58
87 136 1.17
87 138 1.07
87 140 1.5
89 126 7.82
89 128 3.83
89 138 1.1
91 140 2.01
91 142 4
93 144 3.14
93 146 2
95 144 2.6
95 146 1.58
95 148 0.951
97 152 2

## The Effect of the Neutron Number

The graph of magnetic moments versus neutron numbers does reveal critical values at 126 and 82.

The criticality of neutron numbers near 126 shows up in the data.

 p n μ(magnetons) 81 126 1.876 83 116 4.6 83 118 4.8 83 120 4.017 83 122 4.605 83 124 4.081 83 126 4.1103 83 128 4.5 83 130 3.89 85 122 3.75 85 124 10 85 126 9.56 85 128 3.8 87 120 3.89 87 122 3.95 87 124 4 87 126 4.02

It just happens that when n is near 126 the proton number is near 82.

A similar criticality is found near a neutron number of 82.

There does not seem to be a criticality of proton numbers near 82.

There is not an appearance of the constancy of the magnetic moment for proton and neutron numbers not near a critical number.