﻿ The Correspondence of the Two Types of Estimates of the Binding Energy Due to the Formation of Neutron-Proton Spin Pairs
San José State University

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The Correspondence of the Two Types of
Estimates of the Binding Energy Due to the
Formation of Neutron-Proton Spin Pairs

Let BE(n, p) be the binding energy of a nuclide with n neutrons and p protons. The binding energy associated with the formation of a neutron-proton spin pair can be estimated by

#### FBEnpn = [BE(n+2, p) − BE(n, p)] − [BE(n+1, p) − BE(n-1, p)] and by FBEnpp = [BE(n, p+2) − BE(n, p)] − [BE(n, p+1) − BE(n, p-1)]

The first is the formation binding energy of a neutron-proton spin pair from the incremental binding energies of neutrons. The second is the formation binding energy of a neutron-proton spin pair from the incremental binding energies of neutrons. There are 42 cases in which FBEnpn can be computed and 36 where FEnpp can be computed. Their values are as follows.

Number of
Corresponding
Nucleons
FBEnpn
(MeV)
FBEnpp
(MeV)
1 5.322631 5.126394
2 19.219853 18.718516
3 4.4472 3.6318
4 13.24891 12.08681
5 5.9844 5.0659
6 11.328998 10.545383
7 8.086162 8.064255
8 8.193516 7.619396
9 3.41104 2.54828
10 7.342099 6.500419
11 4.86813 4.10965
12 6.17507 5.43902
13 4.24078 3.64089
14 7.18494 6.5705
15 4.01976 3.38425
16 4.20017 3.62542
17 3.47751 2.92864
18 3.95739 3.4154
19 4.6035 4.2743
20 4.5603 4.1606
21 2.4574 1.8506
22 3.7636 3.11
23 3.624 2.7297
24 3.947 3.3339
25 3.5988 2.5463
26 3.5274 2.8045
27 3.79 3.3546
28 4.8871 4.4222
29 2.833 2.3653
30 2.4827 2.106
31 3.017 2.504
32 3.12 2.3
33 2.97 2.5
34 2.9 2.02
35 3.28 2.7
36 3.1 2.75
37 2.271
38 2.532
39 2.9
40 2.7
41 2.5
42 2.6

These data plotted together show a close correspondence. Another way of viewing this close correspondence is as a scatter diagram. The correlation coefficient for the two variables is 0.9976. The regression equation for the data is