Romanian Journal of Physics 64, 303 (2019)
ON THE NUCLEAR SHELL MODEL
ANDRZEJ B. WIĘCKOWSKI1,2
1
Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, ul. Szafrana 4a, PL-65-516 Zielona Góra, Poland
2
Institute of Molecular Physics, Polish Academy of Sciences, ul. Smoluchowskiego 17, PL-60-179 Poznań, Poland
E-mail: [email protected] Received February 12, 2019
Abstract. A historical overview of works involved in the development of the
shell model of nuclei has been made. A special attention was given to physical, geochemical and number theoretical aspects. Two sequences of nuclear magic and semi-magic numbers are known to be of major importance to the graphical construction of the periodic table of nuclides. On the basis of ordering the nucleons (protons and neutrons) according to their energy state a periodic Table of Nuclides was built up. For comparison a version of the periodic table of chemical elements and two slightly differing versions of the periodic table of nuclides are presented.
Key words: Nuclear magic and semi-magic numbers, primordial nuclides, mirror
nuclides.
1. INTRODUCTION
While the periodic table of chemical elements is known since the nineteenth century, an analogous periodic Table of Nuclides based on the nuclear shell model remains unknown till now. The electron configuration in atoms and the nucleon configuration in nuclides are described similarly by the respective shell models. In comparison with the structure of electron shells, the structure of nucleon shells is more complex, because there are two separate kinds of nucleons (protons and neutrons) and different forces are involved.
The aim of this paper is to work out a graphical presentation of the periodic table of nuclides. The centre of attention will be drawn to the shell model of nuclei.
2. PERIODIC TABLE OF CHEMICAL ELEMENTS
The principles of chemistry have a physical basis. Even the periodic table of Mendeleev apparently, as it turned out later, was built up on a property of the atomic nucleus, namely its mass, because at the time of developing the table of chemical elements, the electron structure of atoms was unknown. The building up
of the periodic table of chemical elements by Meyer [1, 2] and Mendeleev [3–7] was a milestone in the development of chemistry. In 1882 both scientists, Dmitri Mendeleev and Lothar Meyer, were honoured jointly with the Davy Medal by the Royal Society of London for their discovery of the periodic relations of the atomic
weights.
Moseley [8, 9], while investigating the X-ray spectra of different elements, gave a physical basis of the periodic table by modern truly ordering chemical elements according to their atomic numbers Z. Later with the development of the quantum mechanics (and the quantum chemistry) the location of the elements in the periodic table was connected with their electron configuration in atomic shells.
The periodic table of chemical elements is undergoing further development and study. A broad band of historical, physical, chemical and mathematical aspects of the periodic table was presented in two books edited by Kaji, Kragh and Palló [10] and by Scerri and Restrepo [11].
A version of the periodic table of chemical elements is presented in Fig. 1. n 1 1 H 2 He 2 2 He 3 Li 4 Be 3 5 B 6 C 7 N 8 O 9 F 10 Ne 11 Na 12 Mg 4 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 19 K 20 Ca 5 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 37 Rb 38 Sr 6 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 55 Cs 56 Ba 7 57 La 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 87 Fr 88 Ra 8 89 Ac 90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Es 100 Fm 101 Md 102 No 103 Lr 104 Rf 105 Db 106 Sg 107 Bh 108 Hs 109 Mt 110 Ds 111 Rg 112 Cn 113 Nh 114 Fl 115 Mc 116 Lv 117 Ts 118 Og 119 Uue 120 Ubn f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 ff4 d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 p1 p2 p3 p4 p5 p6 s1 s2
Fig. 1 – (Colour online). A version of the periodic table of chemical elements. The blocks of electron shells s, p, d, f, in atoms are in the order from right to left. The cells with darker (rose in colour)
background (column p6) correspond to the noble gases [n – period (row) number]. The lowest strip (under the periodic table) represents the number of electrons
occupying the respective energy level of electron shell.
For each period with the ordinal number of the row n the value of the length of the period L(n) is equal to:
L(n) = [2n + 1 – (–1)n]2 /8 = 2, 2, 8, 8, 18, 18, 32, 32 (1) for n = 1, 2, 3, 4, 5, 6, 7, 8.
The atomic number of the noble gases Z(n) can be calculated with the formula:
Z(n) =
∑
= n i i L 1 ) ( – 2 = [2n3 + 6n2 + 7n – 21 – 3(n + 1)(–1)n] /12 = = (0), 2, 10, 18, 36, 54, 86, 118 (2) for n = (1), 2, 3, 4, 5, 6, 7, 8.In Fig.1 the cell of helium He is repeated and appears twice, because the
helium He atom having the electron configuration 1s2 belongs to the sequence of
the noble gases Z(n) [Z(2) = 2].
3. DEVELOPMENT OF THE SHELL MODEL OF NUCLEI
3.1. WORKS BEFORE DISCOVERY OF THE NEUTRON BY CHADWICK
It was Harkins [12–16], who has studied the problem of the structure of atomic nuclei very early. Harkins [12–14] adopted the hypothesis that during building up the atomic nuclei the most stable nuclei were formed with the biggest abundance. By analyzing the abundance of chemical elements in iron meteorites, stone meteorites and on the surface of the Earth, he came to the conclusion that the elements with even atomic number are much more abundant than the odd numbered elements.
At that time the view dominated that the nuclei of elements consist of helium
(α++) and hydrogen (π+) nuclei, as well as of binding and cementing electrons (β–)
(see Harkins [15, 16]).
Harkins [17] and Rutherford [18], while discussing the constitution of nuclei in isotopes, postulated the possible existence of an atom having one binding electron in the hydrogen nucleus, which has a mass equal to unity and a zero electric charge. For this hypothetical particle Harkins [19, 20] used the name ‘neutron’; he wrote: Here the term neutron represents one proton plus one electron
(pe). (see Ref. [19], p. 315). Harkins [19] found that the most abundant isotopes in
meteorites are oxygen 16O, magnesium 24Mg, silicon 28Si, sulphur 32S and iron 56Fe.
Niggli [21] has investigated the chemical composition of eruption rocks and found that in the Earth’s crust the distribution curve of petrogenic elements
demonstrates maxima: (1H), 8O, 14Si, 20Ca, 26Fe, having a difference of the atomic
numbers equal to 6. On the other hand, the distribution curve of metallogenic
elements demonstrate maxima: 26Fe – 28Ni, 48Cd – 50Sn, 80Hg – 82Pb, where in each
pair the difference in atomic numbers is equal to 2. Later, the atomic numbers 28, 50, 82 were denoted ‘magic numbers’ of nucleons (protons and neutrons).
Sonder [22] proposed an expansion of the first series by the following
elements: …, 26Fe, 38Sr, 50Sn, 56Ba, 74W, (80Hg), 92U, where the differences
the abundance values of elements and by some speculations on the structure and symmetry of nuclei, Sonder [22–24] postulated the existence of a nuclear periodicity.
Beck [25] built up a scheme of known isotopes and showed regularities in the structure of atomic nuclei. He was the first who, from the distribution of some series of isotopes, postulated the possibility of the existence of nuclear shells, similar to the shells of electrons.
3.2. WORKS BEFORE THE FORMULATION OF THE NUCLEAR SHELL MODEL BY GOEPPERT MAYER, HAXEL, JENSEN AND SUESS
The discovery of the neutron has been made by Chadwick [26, 27]. He produced neutrons of mass 1 and charge 0 by the bombardment of beryllium Be or boron B with α-particles from a source of polonium Po. He has carried out the following nuclear reactions:
9
Be + 4He → 12C + 1n and 11B + 4He → 14N + 1n.
Chadwick [26] supposed that the neutron is a constituent of atomic nuclei. In a comment to this discovery Iwanenko [28] also considered the neutron as being a component of the nucleus and mused of whether the neutron can be an elementary particle like the electron and the proton. Heisenberg [29] indicated to the quantum mechanical consequences of the assumption that the atomic nuclei are composed only of interacting protons and neutrons as building stones, without participation of electrons.
Bartlett [30, 31] discussed the possible structure of light elements with small
atomic number and came to the conclusion that a regularity ends at the nucleus 16O
and this may be interpreted as a result of the formation of a closed shell. He indicated an analogy with the system of external electrons. Similar closed shells for protons and for neutrons can exist also for heavier elements. The principal quantum number is of smaller importance, because the central field is not characterized by a Coulomb potential [31]. However, Bartlett [32], following a suggestion put forward by Dirac, adopted the view that beside protons and neutrons, also electrons are present in nuclei, because the β-type decay exists. Gapon and Iwanenko [33] considered the successive building up of the nuclei in shells of protons and neutrons as being in analogy with the periodic system of elements. Elsasser [34, 35], while referring to the suggestion of Bartlett [31, 32] on the existence of consecutive shells in nuclei, pointed to the significance of this for the formulation of the role of separate shells for protons and neutrons, respectively, in the number of isotopes for atomic numbers of light elements. Elsasser [35, 36] was citing the results obtained by Guggenheimer [37], who pointed to periodic regularity of the
structure of nuclei in groups of consecutive chemical elements. Guggenheimer [37] placed emphasis on the numbers of neutrons N = 50 and N = 82, for which there exist a higher number of isotones and the shells became closed. The term ‘isotones’ was introduced by Guggenheimer [37]. Elsasser [36, 38], after analyzing the models of isotopes and isotones, supplemented these two distinguished numbers with the third number N = 126.
3.3. NUCLEAR SHELL MODEL ACCORDING TO GOEPPERT MAYER, HAXEL, JENSEN AND SUESS
Suess [39] and Goeppert Mayer [40] discussed the nuclear structure of naturally occurring chemical elements and drew the attention to isotopes and isotones with higher stability and abundance. Especially stable were elements having the special, named distinguished or excellent numbers (ausgezeichnete Zahlen [39]) of 28, 50, 82 and 126 neutrons or protons. Goeppert Mayer [40] suggested that this phenomenon is an effect of filling up the closed shells in nuclei.
Almost simultaneously and independently of each other, Goeppert Mayer [41–43] and Haxel, Jensen and Suess [44–48] have assumed for the calculation of the energy levels of protons and neutrons the single particle orbit model in which nuclear potential energy has a shape between a square well and a three-dimensional harmonic oscillator with strong spin-orbit (l, s) coupling of the nucleons (protons or neutrons). The single particle energy states are filled up according to the Pauli exclusion principle. For each nucleon the authors calculated the total angular momentum quantum numbers j = l + s (s = ± ½), the multiplicities 2j + 1, and the sum of multiplicities on each shell. The state with j = l + ½ has a lower energy than the state with j = l – ½ and the energy level with higher j is filled up first. When the number of identical nucleons is even, they couple giving a spin zero and do not contribute to the magnetic moment. When the number of identical nucleons is odd, they couple giving a spin j and a non-zero magnetic moment occurs. This scheme of occupation is the same for the shells of protons and for the shells of neutrons. The differences between the scheme for protons and neutrons are only of quantitative character. The shell model allowed the prediction of the nuclear spins, the parity and the magnetic moments (with a few exceptions). Goeppert Mayer [41] presented the spin terms of energy levels, the number of states on each energy level and the maximal occupation of each shell. The sum of the maximal occupations of shells gave the number of nucleons in closed shells; these numbers were named ‘magic numbers’: 2, 8, 20, 28, 50, 82, 126 (see [41], Table I). The distance between the energy level of closed shells filled with a magic number of nucleons and the next energy level is greater than the distances between the energy levels of other shells. Haxel, Jensen and Suess [44] obtained the following numbers for the occupation of closed shells: 2, 6, 8, 14, 20, 28, 40, 50, 70, 82, 92, 112, 126
(numbers written in bold are particularly representative; the numbers not put in bold are sometimes denoted as ‘semi-magic numbers’ or ‘sub-magic numbers’).
The founders of the closed shell structure of nuclei presented their works later in the publications written by Haxel, Jensen and Suess [49] and by Goeppert Mayer and Jensen [50]. Brueckner and Levinson [51] have developed approximated solutions based on a self-consistent field method for a many-body problem which justified the application of the nuclear shell model in the case of strong nucleon-nucleon interactions. A further overview of the nuclear shell models has been presented by Jensen [52]. Maria Goeppert Mayer and J. Hans D. Jensen were awarded with the Nobel Prize in Physics 1963 for their discoveries concerning
nuclear shell structure (Nobel lectures: Goeppert Mayer [53], Jensen [54]).
More detailed descriptions of earlier works in connection with the historical development of the nuclear shell model were presented by Zacharias [55], Kragh [56] and Johnson [57].
3.4. NUMBER THEORETICAL ASPECTS OF THE NUCLEAR SHELL MODEL
Bagge [58] has found that the magic numbers in the sequence N1(n) = 2, 6,
14, 28, 50, 82, 126, are given by the formula:
N1(n) = (n 3 + 5n)/3 = 2
∑
=
+ n m m 1 2 1 (3) where n = 1, 2, 3, 4, 5, 6, 7.A similar formula was proposed by Valente [59, 60]. Bagge [61] found also
that the magic numbers in the sequence N2(n) = 2, 8, 20, 40, 70, 112, are given by
the formula: N2(n) = (n 3 – n)/3 = 2
∑
= n m m 1 2 (4) where n = 2, 3, 4, 5, 6, 7.Lepsius [62, 63] has shown, how the magic numbers can be derived from the binomial coefficients occurring in the Pascal’s triangle.
Pauling [64, 65] explained the magic numbers by assuming a structure of atomic nuclei build up by layers of a mantle, an outer core and an inner core having completed shells and completed sub-shells filled up by nucleons. In this scheme the
main magic numbers are composed of numbers having the form 2k2 (similarly to
2 = 2·12 8 = 2·22 20 = 2 + 18 = 2·12 + 2·32 (28 = 2 + 18 + 8 = 2·12 + 2·32 + 8) 50 = 8 + 32 + 10 = 2·22 + 2·42 + 10 82 = 2 + 18 + 50 + 12 = 2·12 + 2·32 + 2·52 + 12 126 = 8 + 32 + 72 + 14 = 2·22 + 2·42 + 2·62 + 14
(the magic number 28 has not been included in the scheme given by Pauling [64, 65]). This explanation of the magic numbers has not found a wider acceptance.
For the calculation of all the nuclear magic numbers Weise [66] proposed to use the formula:
MN(m, k) = k·(m2 – m) + (m3 + 5m)/3 (5)
where m = 1, 2, 3, 4, … with k = 1 if m = 1, 2, 3; k = 0 if m > 3.
Herrmann [67, 68] has proved that the magic numbers in nuclear shells can be derived from group theoretical considerations of symmetry without defining the field potential shape. He found the following two sets of magic numbers:
nmagic 1 = (N + 1)(N + 2)(N + 3)/3 = (2), 8, 20, 40, 70, 112, 168, 240 (6)
for N = (0), 1, 2, 3, …
nmagic 2 = nmagic 1 – N(N + 1) = (N + 1)[(N + 2)(N + 3) – 3N] /3 =
= (N + 1)[(N + 1)2 + 5]/3 = 2, 6, 14, 28, 50, 82, 126, 184, 258 (7)
for N = 0, 1, 2, 3, …
Further number theoretical discussion on general laws of the structure of stable nuclei can be found in the monograph by Boeyens and Levendis [69].
4. PERIODIC TABLE OF NUCLIDES
4.1. CONSTRUCTION PRINCIPLE OF THE PERIODIC TABLE OF NUCLIDES
The construction principle (Aufbauprinzip) for building up the periodic table of nuclides is based on the scheme of energy levels of nucleons in the nuclear shell model given by Goeppert Mayer [41]. In Fig. 2, a comparison of the construction principles of the periodic table of chemical elements (a) and of the periodic table of nuclides (b) is shown. In the cells of the right part (b) of the comparison presented are the spin terms of nucleon shells and (in parentheses) the numbers of nucleons (protons or neutrons) filling up the closed shells. The ordering of the spin terms is in full agreement with the scheme of energy levels given by Goeppert Mayer [41]. The locations of the terms of closed shells, which are ordered in two sequences:
can be easy seen in Fig. 2. The numbers 2, 8, 20, 28, 50, 82, 126, 184 are the nuclear magic numbers, whereas the numbers 2, 6, 14, 40, 70, 112, 168, 240 are nuclear semi-magic numbers.
n (a) (b) 1 1s2 1s1/22 (2) 2 1s2 (2) 2s2 1p3/24 (6) 1p1/22 (8) 3 2p6 (10) 3s2 1d5/26 (14) 1d3/24 2s1/22 (20) 4 3p6 (18) 4s2 1f7/28 (28) 1f5/26 2p3/24 2p1/22 (40) 5 3d10 4p6 (36) 5s2 1g9/210 (50) 1g7/28 2d5/26 2d3/24 3s1/22 (70) 6 4d10 5p6 (54) 6s2 1h11/212 (82) 1h9/210 2f7/28 2f5/26 3p3/24 3p1/22 (112) 7 4f14 5d10 6p6 (86) 7s2 1i13/214 (126) 1i11/212 2g9/210 2g7/28 3d5/26 3d3/24 4s1/22 (168) 8 5f14 6d10 7p6 (118) 8s2 1j15/2 16 (184) 1j13/2 14 2h11/2 12 2h9/2 10 3f7/2 8 3f5/2 6 4p3/2 4 4p1/2 2 (240) Fig. 2 – (Colour online). Comparison of the construction principle (Aufbauprinzip) of (a) the periodic
table of chemical elements and (b) the periodic table of nuclides. 4.2. LENGTHS OF THE PERIODS AND CALCULATION OF MAGIC
AND SEMI-MAGIC NUMBERS
For each energy level with the angular momentum quantum number j the number of occupying nucleons is equal to (2j + 1). In each period with the ordinal number of the period (row) n the highest value of j is equal to:
jmax = n – ½ (8)
Calculating the number of nuclides L(n) (length of the period) in each row n we obtain: L(n) =
∑
= + max ½ ) 1 2 ( j j j = 2∑
= n i i 1 = 2 + 2 1 n = = n(n + 1) = 2, 6, 12, 20, 30, 42, 56, 72 (9) for n = 1, 2, 3, 4, 5, 6, 7, 8.
The binomial coefficient
+ 2 1 n = n(n + 1) /2 (10)
is known as the nth triangular number.
The sequence of the magic numbers N1(n) can be calculated with the formula:
N1(n) =
∑
= + − n i i L 1 ] 2 ) 1 ( [ =∑
= − n i i L 1 ) 1 ( + 2n = 2∑
= n i i 1 2 + 2n = = 2 + 3 1 n + 2n = n(n2 – 1) /3 + 2n = n(n2 + 5) /3 (11)or with the formula:
N1(n) =
∑
= − − n i i i L 1 )] 1 ( 2 ) ( [ =∑
= n i i L 1 ) ( – L(n – 1) = 2∑
= + n i i 1 2 1 – 2 2 n = = 2 + 3 2 n – 2 2 n = n(n + 1)(n + 2) /3 – n(n – 1) = n(n2 + 5) /3 (12)Finally, by applying any of the two equivalent ways of deriving the above
formulae for N1(n) we obtain the sequence:
N1(n) = n(n
2
+ 5)/3 = 2, 6, 14, 28, 50, 82, 126, 184 (13)
for n = 1, 2, 3, 4, 5, 6, 7, 8.
The sequence of the magic numbers N2(n) can be calculated with the formula:
N2(n) =
∑
= n i i L 1 ) ( = 2∑
= + n i i 1 2 1 = 2 + 3 2 n = = n(n + 1)(n + 2) /3 = 2, 8, 20, 40, 70, 112, 168, 240 (14) for n = 1, 2, 3, 4, 5, 6, 7, 8. The binomial coefficient + 3 2 n = n(n + 1)(n + 2) /6 = [(n + 1)3 – (n + 1)] /6 (15)
We have also N2(n) – N1(n) = 2 2 n = n(n – 1) (16) and N1(n) – N2(n – 1) = 2n (17)
4.3. TWO VERSIONS OF THE PERIODIC TABLE OF NUCLIDES
By putting each set of nucleons (protons or neutrons) in a given energy state into the respective cells of Fig. 2 we obtain the periodic table of nuclides, which is shown in Fig. 3. Because the order of the energy levels for protons and for neutrons is the same, the form of the periodic table is valid both for protons and for neutrons. The cells in rose colour (darker in print version) correspond to magic or semi-magic numbers of nucleons. The two lowest strips (below the periodic table) represent the number of nucleons occupying the respective energy level. The spin terms in the strips allow to give for each nuclide its nucleon configuration.
Additionally, below to the primary version of the periodic Table of Nuclides, a modified version is presented. This version shows graphically the similarities and the connection between the two sequences of the magic and semi-magic numbers
N1(n) and N2(n).
4.4. EXAMPLES OF APPLICATION OF THE PERIODIC TABLE OF NUCLIDES
The form of the periodic Table of Nuclides can be used in practice by inserting the nuclides with a chosen property into the numbered cells of the periodic tables for protons and neutrons, respectively. Some examples are given below.
In Fig. 4, part (a) for protons and part (b) for neutrons, the primordial (stable and nearly stable having natural abundances) nuclides are presented. It is seen that for odd numbers of nucleons (protons or neutrons) the number of primordial isotopes and isotones does not exceed two (only in the case of potassium K with Z = 19, the number of primordial isotopes is equal to three). For even numbers of nucleons the number of isotopes and isotones is in general higher. As expected, for magic and semi-magic numbers of nucleons the number of isotopes and isotones is noticeable high. It is well known that particularly stable are the primordial doubly magic and semi-magic
nuclides containing a number of nucleons from the sequences N1(n) or/and N2(n),
which are listed in Table 1. All these nuclides have simultaneously the highest abundance from among the component nuclides of the considered chemical element. Normally, to present the properties of nuclides in the periodic table, the nuclides have to be shown in two tables – for protons and for neutrons, separately. In Fig. 5 an excerpt is shown from the periodic Table for Nuclides with N = Z. In this case, it is sufficient to present the nuclear properties in one table only. The values of nuclear spin quantum number J and the parity π are presented. The numerical data are taken from
the Table of Nuclides presented by KAERI [70]. In Fig. 5 we find all four stable low mass odd-odd nuclides, which have a non-zero nuclear spin J: hydrogen (deuterium)
2
H (Jπ = 1+), lithium 6Li (Jπ = 1+), boron 10B (Jπ = 3+), nitrogen 14N (Jπ = 1+).
n (a) 0 1 1 H 2 He 2 3 Li 4 Be 5 B 6 C 7 N 8 O 3 9 F 10 Ne 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 19 K 20 Ca 4 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 37 Rb 38 Sr 39 Y 40 Zr 5 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 55 Cs 56 Ba 57 La 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 6 … 82 Pb 83 Bi 84 Po 85 At 86 Rn 87 Fr 88 Ra 89 Ac 90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Es 100 Fm 101 Md 102 No 103 Lr 104 Rf 105 Db 106 Sg 107 Bh 108 Hs 109 Mt 110 Ds 111 Rg 112 Cn 7 … 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 6 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb … 7 113 Nh 114 Fl 115 Mc 116 Lv 117 Ts 118 Og 119 Uue 120 Ubn 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 … n (b) 0 1 0 1 H 2 He 2 2 He 3 Li 4 Be 5 B 6 C 7 N 8 O 3 8 O 9 F 10 Ne 11 Na 12 Mg 13 Al 14 Si 15 P 16 S 17 Cl 18 Ar 19 K 20 Ca 4 20 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr 37 Rb 38 Sr 39 Y 40 Zr 5 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe 55 Cs 56 Ba 57 La 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 6 … 82 Pb 83 Bi 84 Po 85 At 86 Rn 87 Fr 88 Ra 89 Ac 90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Es 100 Fm 101 Md 102 No 103 Lr 104 Rf 105 Db 106 Sg 107 Bh 108 Hs 109 Mt 110 Ds 111 Rg 112 Cn 7 … 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 40 Zr 6 70 Yb 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb … 7 113 Nh 114 Fl 115 Mc 116 Lv 117 Ts 118 Og 119 Uue 120 Ubn 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 … … h9/21 h9/22 h9/23 h9/24 h9/25 h9/26 h9/27 h9/28 h9/29 h9/210 f7/21 f7/22 f7/23 f7/24 f7/25 f7/26 f7/27 f7/28 f5/21 f5/22 f5/23 f5/24 f5/25 f5/26 p3/21 p3/22 p3/23 p3/24 p1/21 p1/22 … g9/21 g9/22 g9/23 g9/24 g9/25 g9/26 g9/27 g9/28 g9/29 g9/210 g7/21 g7/22 g7/23 g7/24 g7/25 g7/26 g7/27 g7/28 d5/21 d5/22 d5/23 d5/24 d5/25 d5/26 d3/21 d3/22 d3/23 d3/24 s1/21 s1/22 h11/21 h11/22 h11/23 h11/24 h11/25 h11/26 h11/27 h11/28 h11/29 h11/210 h11/211 h11/212 … i13/2 1 i13/2 2 i13/2 3 i13/2 4 i13/2 5 i13/2 6 i13/2 7 i13/2 8 i13/2 9 i13/2 10 i13/2 11 i13/2 12 i13/2 13 i13/2 14 i11/2 1 i11/2 2 i11/2 3 i11/2 4 i11/2 5 i11/2 6 i11/2 7 i11/2 8 i11/2 9 i11/2 10 i11/2 11 i11/2 12 …
Fig. 3 – (Colour online). Periodic tables of nuclides based on the nuclear shell model of nucleons (protons or neutrons) (Z, N ≤ 168): (a) primary version of the periodic table of nuclides, (b) modified
version of the periodic table of nuclides. For protons in the cells of the periodic tables the numbers and the chemical symbols are valid; for neutrons only the numbers are valid. The cells with darker (rose in colour version) background correspond to magic and semi-magic numbers of nucleons from the sequences N1(n) and N2(n) [n – period (row) number]. In part (b) the cells of nuclides with a magic
or semi-magic number of nucleons from the sequence N2(n) are repeated and appear twice. The 0 cells
are added only for setting the pairs of magic and semi-magic numbers N1(n) and N2(n) in order.
In Fig. 6 and Fig. 7 presented are fragments of the periodic tables of selected sequences of nuclides with their values of the spin quantum number J and the parity π for protons and for neutrons. Following periodic tables were pairwise juxtaposed: n (a) 0 n 1 1 1H 2H 2 3He 4He 2 3 6Li 7Li 4 9Be 5 10B 11B 6 12C 13C 7 14N 15N 8 16O 17O 18O 3 9 19F 10 20Ne 21Ne 22Ne 11 23Na 12 24Mg 25Mg 26Mg 13 27Al 14 28Si 29Si 30Si 15 31P 16 32S 33S 34S 36S 17 35Cl 37Cl 18 36Ar 38Ar 40Ar 19 39K 40K 41K 20 40Ca 42Ca 43Ca 44Ca 46Ca 48Ca 4 21 45 Sc 22 46 Ti 47Ti 48Ti 49Ti 50Ti 23 50 V 51V 24 50 Cr 52Cr 53Cr 54Cr 25 55 Mn 26 54 Fe 56Fe 57Fe 58Fe 27 59 Co 28 58 Ni 60Ni 61Ni 62Ni 64Ni 29 63 Cu 65Cu 30 64 Zn 66Zn 67Zn 68Zn 70Zn 31 69 Ga 71Ga 32 70 Ge 72Ge 73Ge 74Ge 76Ge 33 75 As 34 74 Se 76Se 77Se 78Se 80Se 82Se 35 79 Br 81Br 36 78 Kr 80Kr 82Kr 83Kr 84Kr 86Kr 37 85 Rb 87Rb 38 84 Sr 86Sr 87Sr 88Sr 39 89 Y 40 90 Zr 91Zr 92Zr 94Zr 96Zr 5 41 93Nb 42 92Mo 94Mo 95Mo 96Mo 97Mo 98Mo 100Mo 43 (Tc) 44 96Ru 98Ru 99Ru 100Ru 101Ru 102Ru 104Ru 45 103Rh 46 102Pd 104Pd 105Pd 106Pd 108Pd 110Pd 47 107Ag 109Ag 48 106Cd 108Cd 110Cd 111Cd 112Cd 113Cd 114Cd 116Cd 49 113In 115In 50 112Sn 114Sn 115Sn 116Sn 117Sn 118Sn 119Sn 120Sn 122Sn 124Sn 51 121Sb 123Sb 52 120Te 122Te 123Te 124Te 125Te 126Te 128Te 130Te 53 127I 54 124Xe 126Xe 128Xe 129Xe 130Xe 131Xe 132Xe 134Xe 136Xe 55 133Cs 56 130Ba 132Ba 134Ba 135Ba 136Ba 137Ba 138Ba 57 138La 139La 58 136Ce 138Ce 140Ce 142Ce 59 141Pr 60 142Nd 143Nd 144Nd 145Nd 146Nd 148Nd 150Nd 61 (Pm) 62 144Sm 147Sm 148Sm 149Sm 150Sm 152Sm 154Sm 63 151Eu 153Eu 64 152Gd 154Gd 155Gd 156Gd 157Gd 158Gd 160Gd 65 159Tb 66 156Dy 158Dy 160Dy 161Dy 162Dy 163Dy 164Dy 67 165Ho 68 162Er 164Er 166Er 167Er 168Er 170Er 69 169Tm 70 168Yb 170Yb 171Yb 172Yb 173Yb 174Yb 176Yb n (b) 0 1 H 1 1 2 H 3 He 2 4 He 2 3 6 Li 4 7 Li 5 9 Be 10 B 6 11 B 12 C 7 13 C 14 N 8 15 N 16 O 3 9 17 O 10 18 O 19 F 20 Ne 11 21 Ne 12 22 Ne 23 Na 24 Mg 13 25 Mg 14 26 Mg 27 Al 28 Si 15 29 Si 16 30 Si 31 P 32 S 17 33 S 18 34 S 35 Cl 36 Ar 19 20 36 S 37 Cl 38 Ar 39 K 40 Ca 4 21 40 K 22 40 Ar 41 K 42 Ca 23 43 Ca 24 44 Ca 45 Sc 46 Ti 25 47 Ti 26 46 Ca 48 Ti 50 Cr 27 49 Ti 50 V 28 48 Ca 50 Ti 51 V 52 Cr 54 Fe 29 53 Cr 30 54 Cr 55 Mn 56 Fe 58 Ni 31 57 Fe 32 58 Fe 59 Co 60 Ni 33 61 Ni 34 62 Ni 63 Cu 64 Zn 35 36 64 Ni 65 Cu 66 Zn 37 67 Zn 38 68 Zn 69 Ga 70 Ge 39 40 70 Zn 71 Ga 72 Ge 74 Se 5 41 73 Ge 42 74 Ge 75 As 76 Se 78 Kr 43 77 Se 44 76 Ge 78 Se 79 Br 80 Kr 45 46 80 Se 81 Br 82 Kr 84 Sr 47 83 Kr 48 82 Se 84 Kr 85 Rb 86 Sr 49 87 Sr 50 86 Kr 87 Rb 88 Sr 89 Y 90 Zr 92 Mo 51 91 Zr 52 92 Zr 93 Nb 94 Mo 96 Ru 53 95 Mo 54 94 Zr 96 Mo 98 Ru 55 97 Mo 99 Ru 56 96 Zr 98 Mo 100 Ru 102 Pd 57 101 Ru 58 100 Mo 102 Ru 103 Rh 104 Pd 106 Cd 59 105 Pd 60 104 Ru 106 Pd 107 Ag 108 Cd 61 62 108 Pd 109 Ag 110 Cd 112 Sn 63 111 Cd 64 110 Pd 112 Cd 113 In 114 Sn 65 113 Cd 115 Sn 66 114 Cd 115 In 116 Sn 67 117 Sn 68 116 Cd 118 Sn 120 Te 69 119 Sn 70 120 Sn 121 Sb 122 Te 124 Xe f7/2 1 f7/2 2 f7/2 3 f7/2 4 f7/2 5 f7/2 6 f7/2 7 f7/2 8 f5/2 1 f5/2 2 f5/2 3 f5/2 4 f5/2 5 f5/2 6 p3/2 1 p3/2 2 p3/2 3 p3/2 4 p1/2 1 p1/2 2 g9/2 1 g9/2 2 g9/2 3 g9/2 4 g9/2 5 g9/2 6 g9/2 7 g9/2 8 g9/2 9 g9/2 10 g7/2 1 g7/2 2 g7/2 3 g7/2 4 g7/2 5 g7/2 6 g7/2 7 g7/2 8 d5/2 1 d5/2 2 d5/2 3 d5/2 4 d5/2 5 d5/2 6 d3/2 1 d3/2 2 d3/2 3 d3/2 4 s1/2 1 s1/2 2
Fig. 4 – (Colour online). Periodic tables of primordial (stable or nearly stable) nuclides; (a) table of isotopes for protons (Z ≤ 70) and (b) table of isotones for neutrons (N ≤ 70), respectively.
Table 1
The primordial doubly magic and semi-magic nuclides, number of protons Z, number of neutrons N, and abundance [%]
Nuclide Z N Abundance [%] 4 He N1(1) = N2(1) = 2 N1(1) = N2(1) = 2 99.999866 12C N 1(2) = 6 N1(2) = 6 98.93 16 O N2(2) = 8 N2(2) = 8 99.757 28 Si N1(3) = 14 N1(3) = 14 92.223 40 Ca N2(3) = 20 N2(3) = 20 96.94 (48Ca) N2(3) = 20 N1(4) = 28 (0.187) 90 Zr N2(4) = 40 N1(5) = 50 51.45 120 Sn N1(5) = 50 N2(5) = 70 32.58 208 Pb N1(6) = 82 N1(7) = 126 52.4
– periodic Table of Nuclides with N = Z – 1 for protons and periodic Table of
Nuclides with Z = N – 1 for neutrons,
– periodic Table of Nuclides with N = Z + 1 for protons and periodic Table
of Nuclides with Z = N + 1 for neutrons,
– periodic Table of Nuclides with N = Z – 2 for protons and periodic Table of
Nuclides with Z = N – 2 for neutrons,
– periodic Table of Nuclides with N = Z + 2 for protons and periodic Table
of Nuclides with Z = N + 2 for neutrons,
1 N = Z 1 2H 1+ 2 4He 0+ 2 3 6Li 1+ 4 8Be 0+ 5 10B 3+ 6 12C 0+ 7 14N 1+ 8 16O 0+ 3 9 18 F 1+ 10 20 Ne 0+ 11 22 Na 3+ 12 24 Mg 0+ 13 26 Al 5+ 14 28 Si 0+ 15 30 P 1+ 16 32 S 0+ 17 34 Cl 0+ 18 36 Ar 0+ 19 38 K 3+ 20 40 Ca 0+ 4 21 42Sc 0+ 22 44Ti 0+ 23 46V 0+ 24 48Cr 0+ 25 50Mn 0+ 26 52Fe 0+ 27 54Co 0+ 28 56Ni 0+ 29 58Cu 1+ 30 60Zn 0+ 31 62Ga 0+ 32 64Ge 0+ 33 66As 0+ 34 68Se 0+ 35 70Br 0+ 36 72Kr 0+ 37 74Rb 0+ 38 76Sr 0+ 39 78Y 0+ 40 80Zr 0+ d5/21 d5/22 d5/23 d5/24 d5/25 d5/26 d3/21 d3/22 d3/23 d3/24 s1/21 s1/22 f7/21 f7/22 f7/23 f7/24 f7/25 f7/26 f7/27 f7/28 f5/21 f5/22 f5/23 f5/24 f5/25 f5/26 p3/21 p3/22 p3/23 p3/24 p1/21 p1/22 Fig. 5 – (Colour online). Periodic Table of Nuclides (Z, N ≤ 40) fulfilling the condition N = Z.
1 N = Z–1 1 1H 1/2+ 2 3He 1/2+ 2 3 5Li 3/2– 4 7Be 3/2– 5 9B 3/2– 6 11C 3/2– 7 13N 1/2– 8 15O 1/2– 3 9 17F 5/2+ 10 19Ne 1/2+ 11 21Na 3/2+ 12 23Mg 3/2+ 13 25Al 5/2+ 14 27Si 5/2+ 15 29P 1/2+ 16 31S 1/2+ 17 33Cl 3/2+ 18 35Ar 3/2+ 19 37K 3/2+ 20 39Ca 3/2+ 4 21 41Sc 7/2– 22 43Ti 7/2– 23 45V 7/2– 24 47Cr 3/2– 25 49Mn 5/2– 26 51Fe 5/2– 27 53Co 7/2– 28 55Ni 7/2– 29 57Cu 3/2– 30 59Zn 3/2– 31 61Ga 3/2– 32 63Ge 3/2– 33 65As 3/2– 34 67Se 5/2– 35 69Br 1/2– 36 71Kr 5/2– 37 73Rb 3/2– 38 75Sr 3/2– 39 77Y 5/2+ 40 79Zr 5/2+ 1 Z = N–1 1 1n 1/2+ 2 3H 1/2+ 2 3 5He 3/2– 4 7Li 3/2– 5 9Be 3/2– 6 11B 3/2– 7 13C 1/2– 8 15N 1/2– 3 9 17O 5/2+ 10 19F 1/2+ 11 21Ne 3/2+ 12 23Na 3/2+ 13 25Mg 5/2+ 14 27Al 5/2+ 15 29Si 1/2+ 16 31P 1/2+ 17 33S 3/2+ 18 35Cl 3/2+ 19 37Ar 3/2+ 20 39K 3/2+ 4 21 41Ca 7/2– 22 43Sc 7/2– 23 45Ti 7/2– 24 47V 3/2– 25 49Cr 5/2– 26 51Mn 5/2– 27 53Fe 7/2– 28 55Co 7/2– 29 57Ni 3/2– 30 59Cu 3/2– 31 61Zn 3/2– 32 63Ga 3/2– 33 65Ge 3/2– 34 67As 5/2– 35 69Se 1/2– 36 71Br 5/2– 37 73Kr 3/2– 38 75Rb 3/2– 39 77Sr 5/2+ 40 79Y 5/2+ 1 N = Z+1 1 3H 1/2+ 2 5He 3/2– 2 3 7Li 3/2– 4 9Be 3/2– 5 11B 3/2– 6 13C 1/2– 7 15N 1/2– 8 17O 5/2+ 3 9 19F 1/2+ 10 21Ne 3/2+ 11 23Na 3/2+ 12 25Mg 5/2+ 13 27Al 5/2+ 14 29Si 1/2+ 15 31P 1/2+ 16 33S 3/2+ 17 35Cl 3/2+ 18 37Ar 3/2+ 19 39K 3/2+ 20 41Ca 7/2– 4 21 43Sc 7/2– 22 45Ti 7/2– 23 47V 3/2– 24 49Cr 5/2– 25 51Mn 5/2– 26 53Fe 7/2– 27 55Co 7/2– 28 57Ni 3/2– 29 59Cu 3/2– 30 61Zn 3/2– 31 63Ga 3/2– 32 65Ge 3/2– 33 67As 5/2– 34 69Se 1/2– 35 71Br 5/2– 36 73Kr 3/2– 37 75Rb 3/2– 38 77Sr 5/2+ 39 79Y 5/2+ 40 81Zr 3/2– 1 Z = N+1 1 3He 1/2+ 2 5Li 3/2– 2 3 7Be 3/2– 4 9B 3/2– 5 11C 3/2– 6 13N 1/2– 7 15O 1/2– 8 17F 5/2+ 3 9 19Ne 1/2+ 10 21Na 3/2+ 11 23Mg 3/2+ 12 25Al 5/2+ 13 27Si 5/2+ 14 29P 1/2+ 15 31S 1/2+ 16 33Cl 3/2+ 17 35Ar 3/2+ 18 37K 3/2+ 19 39Ca 3/2+ 20 41Sc 7/2– 4 21 43Ti 7/2– 22 45V 7/2– 23 47Cr 3/2– 24 49Mn 5/2– 25 51Fe 5/2– 26 53Co 7/2– 27 55Ni 7/2– 28 57Cu 3/2– 29 59Zn 3/2– 30 61Ga 3/2– 31 63Ge 3/2– 32 65As 3/2– 33 67Se 5/2– 34 69Br 1/2– 35 71Kr 5/2– 36 73Rb 3/2– 37 75Sr 3/2– 38 77Y 5/2+ 39 79Zr 5/2+ 40 81Nb 3/2– d5/21 d5/22 d5/23 d5/24 d5/25 d5/26 d3/21 d3/22 d3/23 d3/24 s1/21 s1/22 f7/21 f7/22 f7/23 f7/24 f7/25 f7/26 f7/27 f7/28 f5/21 f5/22 f5/23 f5/24 f5/25 f5/26 p3/21 p3/22 p3/23 p3/24 p1/21 p1/22 Fig. 6 – (Colour online). Periodic Tables of Nuclides (Z, N ≤ 40) fulfilling the condition: |N – Z| = 1.
1 N = Z–2 1 – – 2 – – 2 3 4Li 2– 4 6Be 0+ 5 8B 2+ 6 10C 0+ 7 12N 1+ 8 14O 0+ 3 9 16F 0– 10 18Ne 0+ 11 20Na 2+ 12 22Mg 0+ 13 24Al 4+ 14 26Si 0+ 15 28P 3+ 16 30S 0+ 17 32Cl 1+ 18 34Ar 0+ 19 36K 2+ 20 38Ca 0+ 4 21 40Sc 4– 22 42Ti 0+ 23 44V 2+ 24 46Cr 0+ 25 48Mn 4+ 26 50Fe 0+ 27 52Co 6+ 28 54Ni 0+ 29 56Cu 4+ 30 58Zn 0+ 31 60Ga 2+ 32 62Ge 0+ 33 64As 0+ 34 66Se 0+ 35 68Br 3+ 36 70Kr 0+ 37 72Rb 1+ 38 74Sr 0+ 39 76Y 1– 40 78Zr 0+ 1 Z = N–2 1 – – 2 – – 2 3 4H 2– 4 6He 0+ 5 8Li 2+ 6 10Be 0+ 7 12B 1+ 8 14C 0+ 3 9 16N 2– 10 18O 0+ 11 20F 2+ 12 22Ne 0+ 13 24Na 4+ 14 26Mg 0+ 15 28Al 3+ 16 30Si 0+ 17 32P 1+ 18 34S 0+ 19 36Cl 2+ 20 38Ar 0+ 4 21 40K 4– 22 42Ca 0+ 23 44Sc 2+ 24 46Ti 0+ 25 48V 4+ 26 50Cr 0+ 27 52Mn 6+ 28 54Fe 0+ 29 56Co 4+ 30 58Ni 0+ 31 60Cu 2+ 32 62Zn 0+ 33 64Ga 0+ 34 66Ge 0+ 35 68As 3+ 36 70Se 0+ 37 72Br 1+ 38 74Kr 0+ 39 76Rb 1– 40 78Sr 0+ 1 N = Z+2 1 4 H 2– 2 6 He 0+ 2 3 8Li 2+ 4 10Be 0+ 5 12B 1+ 6 14C 0+ 7 16N 2– 8 18O 0+ 3 9 20F 2+ 10 22Ne 0+ 11 24Na 4+ 12 26Mg 0+ 13 28Al 3+ 14 30Si 0+ 15 32P 1+ 16 34S 0+ 17 36Cl 2+ 18 38Ar 0+ 19 40K 4– 20 42Ca 0+ 4 21 44Sc 2+ 22 46Ti 0+ 23 48V 4+ 24 50Cr 0+ 25 52Mn 6+ 26 54Fe 0+ 27 56Co 4+ 28 58Ni 0+ 29 60Cu 2+ 30 62Zn 0+ 31 64Ga 0+ 32 66Ge 0+ 33 68As 3+ 34 70Se 0+ 35 72Br 1+ 36 74Kr 0+ 37 76Rb 1– 38 78Sr 0+ 39 80Y 4– 40 82Zr 0+ 1 1 4Li 2– 2 6Be 0+ 2 3 8B 2+ 4 10C 0+ 5 12N 1+ 6 14O 0+ 7 16F 0– 8 18Ne 0+ 3 Z = N+2 9 20Na 2+ 10 22Mg 0+ 11 24Al 4+ 12 26Si 0+ 13 28P 3+ 14 30S 0+ 15 32Cl 1+ 16 34Ar 0+ 17 36K 2+ 18 38Ca 0+ 19 40Sc 4– 20 42Ti 0+ 4 21 44V 2+ 22 46Cr 0+ 23 48Mn 4+ 24 50Fe 0+ 25 52Co 6+ 26 54Ni 0+ 27 56Cu 4+ 28 58Zn 0+ 29 60Ga 2+ 30 62Ge 0+ 31 64As 0+ 32 66Se 0+ 33 68Br 3+ 34 70Kr 0+ 35 72Rb 1+ 36 74Sr 0+ 37 76Y 1– 38 78Zr 0+ 39 80Nb – 40 82Mo – d5/21 d5/22 d5/23 d5/24 d5/25 d5/26 d3/21 d3/22 d3/23 d3/24 s1/21 s1/22 f7/21 f7/22 f7/23 f7/24 f7/25 f7/26 f7/27 f7/28 f5/21 f5/22 f5/23 f5/24 f5/25 f5/26 p3/21 p3/22 p3/23 p3/24 p1/21 p1/22 Fig. 7 – (Colour online). Periodic Tables of Nuclides (Z, N ≤ 40) fulfilling the condition: |N – Z| = 2.
In each set of two consecutive tables for protons and for neutrons the respective values of the nuclear spin J and the parity π are identical and the set
contains isobars being mirror nuclides (an incompatibility is for Jπ(16N) = 2– and
Jπ(16F) = 0–). The numerical data are taken from the Table of Nuclides presented
by KAERI [70].
5. CONCLUSIONS
It has been shown that the properties of nuclides can be adequately presented in the periodic table of nuclides by showing them in two tables identical in form: one for protons and another for neutrons.
The application of the periodic Table of Nuclides was exemplified by presentation of primordial nuclides and isobars being mirror nuclides. The use of the periodic Table of Nuclides forms an alternative method for presentation of the properties of nuclei in scientific and educational applications. The periodic Table of Nuclides gives an informative graphical impression and a visual understanding of the regularities in nuclear shells. The periodic table has also an educational significance and can be helpful in giving a more understandable and adequate illustration of the properties of nuclides in teaching nuclear physics and nuclear chemistry.
A disadvantage of the proposed periodic table of nuclides is that the properties of nuclides should be presented in two tables, one for protons and another for neutrons.
The author is aware that the presented periodic Table of Nuclides is an idealized one and it should undergo further modifications in the future.
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