The Periodic Table Possible Coincided with an Unfolded Shape of Atomic Nuclei

The periodic table seems to correspond to folding nuclei, a visible proton (nucleon) distribution, that can grow vertical 4 a (representative), 4 b (transition), and 8 c (inner transition) axes (α-clusters) bound with valence neutrons standing a core (1st period) of likely expanding in Co, Ni, Rh, and Pd, which was naturally within proton and neutron drop lines, and roughly able to fit in with nuclear fission phenomena, including α-cluster decay. It was observed in analysis molecular structures that crosses nuclear, atomic, and molecular three levels, which provides a convenient way that will enable the nature of the periodic table promisingly to become easier understanding.


Introduction
The periodic table with the elements accumulated today is well-known and plays a basic role in physical science.Its nature (shape, Z, the atomic number) that is bewildering was traditionally explained by Bohr (1913), an atomic periodicity, though about in the meantime it has been proven to result from the proton number (Moseley, 1913).This seems possible to attribute to that a real cubic distribution of Z in a nucleus might have not been revealed (Bohr & Wheeler, 1939), to the author's knowledge.However, it may be a flaw to pay little attention on the proton number that could convey a nuclear periodicity to some extent.For example, magic nuclei 2, 8, 20, 28, 50, 82, and 126 (Haxel, Jensen, & Suess, 1949) are almost inconsistent with noble nuclei (gases) 2, 10, 18, 36, 54, 86, and  118, while noble nuclei appear to close naturally that can display a cubic Z.
It was observed in analysis molecular structure starting from a curiosity that whether an atomic mass has an influence upon molecular bond energy about in the summer of 1987.Because an element occurs some isotopes and then had no intention of taking their relative mass what want to see nucleons how to distribute in a molecule (atom), every element is represented by its maximal abundant isotope selected from U.S. National Nuclear Data Center, (Nudat 2).Actually, it was an integrative result of atomic dot structure of Lewis, (1916) and nuclear alpha particle model (Hafstod & Teller, 1938) plus valence neutrons (Table 1, Figures 1a-c and 2a-b, most notes in their captions).
To test this there is an attempt to interpret fission, mainly concentrating on fragment origin and yield, as it can direct reflect details of a nuclear structure.Furthermore, it tends to consider that α and cluster (nucleon number, A ＞ 4) decay (Rose & Jones, 1984) were similar to fission (like super asymmetric fission) (Poenaru, Ivascu, &  Sandulescu, 1979), despite indirect somewhat.Therefore, at this stage that their roots remain poorly understood a brief interpretation may be effectual.In the following, basic, light, mid, and heavy nuclei individually in the 1, 2-3, 4-5, and 6-7 (periods/layers) steps will be illustrated to emerge different shapes and folding.

Nuclear 4 steps and 16 Axes
Basic nuclei 1,2,3 H, 3,4 He, neutron, and di-neutrons appear in nuclei that can be separated into core, middle, and skin, core + middle = c m ; skin particle, s p , its particle structures and distributions was called skin configuration.
Collectively, c m is a noble nucleus and core is a 4 He in range Z = 3-26, for it will expand in Z = 27.On the other hand, in nuclear growth a nucleon behavior seems to loom up a tetrahedral shape having some "nucleon valence" (~ 4) to bind other nucleons or basic nuclei (Figure 2a) with an explicit direction, suggesting that a molecular bond may result essentially from this character (Figure 2b).
Along with nuclear crystal growing to the 4 th layer, its skin area will increase enough to hold another 4 b α-clusters in between 4 a α-clusters; further, its core will be intensified in old group 8B to support increasing mass.In terms of electron distributions, a proton distribution of 21 Sc is 2 p l of 19 K and 20 Ca on 2 a axes, and p l of 21 Sc on b axis, but it seems to be questionable for nucleon arrangements of subsequent elements; i.e., 3 p l of 19 K, 20 Ca, and 21 Sc may simultaneously glide upon b axes.In comparison, a pair distributions of electrons and protons is 21 Sc-e(18)ds 2 /p(18)d 3 (in proton distributions, a = s+p that in range Z = 3-26, 2 p and 2 n of basal tetrahedral α-particle that 4 a axes stand on have not been distinguished, b = d, and c = f, respectively).Furthermore, 4 p l of 27 Co, 28 Ni, 45 Rh, and 46 Pd will sink into the core (Figure 1b), which may be ended that a total of 6 p l (Z = 1, 2, 27, 28, 45, and 46) with 6 n are to form an innermost close-packed core (Figure 2a).However, this performance will enable a nucleus to possess a definite hub, a Coulomb repulsion center, otherwise its shape cannot be opened, like a tiny liquid drop.Parallel to this was that per nucleon binding energy ~ 8.7 MeV is maximal, as nuclear mass increase to A ~ 60 (Nudat 2), which would imply that though at Fe-Co-Ni region nuclear core has been intensified immediately, a sharp change of nucleon distributions, its curve remains to fall from Fe, a last element owning c-2+2 that may play a critical role in chemical element distributions of universe.Additionally, ferromagnetic only occurs in Fe, Co, and Ni at room temperature that possibly has a link to a structure and vibratory pattern of their nuclei.A nuclear coordinate was introduced to describe fission that the serial numbers of axes and layers are after a, b, and c letters; for valence neutron is n that it is clockwise rotating from a1 axis to the origin point: 1→4, 1→8, and 1→16 in the 2-3, 4-5, and 6-7 steps, respectively.This figure suggests that in 1-1/4-8 fission (from n1-6 through 1/4 core to n8-6), 1-8 and 8-1 sectors are light (A L ) and heavy (A H ) fragments, some of 6 n v (n1-6, 1-4, 1-2 and n8-6, 4-4, 2-2) became prompt neutrons in the split line, and angular distributions of α-particle were 90-22.5°forA L and 90+22.5°f or A H coming from c1-6 or c4-6.(b) In the center is a 16 O c-2+2 4242 and the farthest are 2 1 H, suggesting that its chemical valence and their angle are rooted in the 2 d.If 2 d of 16 O 4242 (99.757%) were replaced by 1 or 2 t, it is 17 O 4342 (0.038%) or 18 O 4343 (0.205%) One of extraordinary feature in the periodic table is old group 8B existence, implying that nuclei contain an expansible core, the other is the number of inner transition metals, from where a particular place, 57 La-e(54)ds 2 /p(54)f 3 , start to grow out between 4 a and 4 b α-clusters, implying that nuclei are folding.The extrapolation is that, if inner transition p l were on 6 faces or 12 sides of Figure 1a, it needs 12 or 24 p l , what is both impractical.Thus, it may averagely vacate 4 of 12 sides to grow 16 elements.On the other hand, whether inner transition contains 14 elements?If so, given that α is one of particles to construct a nucleus, as such an odd number of 7 α will be asymmetric in a nuclear shape (coordinate).So far, it is thought that nuclear shapes might have not been so easy to recognize, whereas in here are visible that almost are tetrahedral in the 2-3 step ( 12 C, 28 Si) and cubic in the 4-5 step ( 74 Ge, 120 Sn), but in the 6-7 step ( 208 Pb), their shapes would be kept in a phase between cubic and flat, which might relate to a nuclear vibratory form.
In fact, originally this nuclear pattern was two dimensional using Go game stones to put on the floor, however, it was so coincidental that when it was folded into three dimensional.Folding nuclei were suggested from the 16 axes that in Table 1 show to correspond to the groups, which is almost same in a tri-group, regardless of group A, B, and C, such as skin configuration 4443 in tri-group 7 (7A, 7B, 13-14C: 165 Ho c-4443-4343 and 166 Er c-4443-4443 ).In tri-group 3, a di-neutrons may serve as a proton in skins of 45 Sc and 89 Y in 3B that each of them has 3 p l to stay on 3 of 4 b axes, then a di-neutrons will substitute for a proton to occupy a surplus axis to form a stable b-tetrahedron out of their c m , i.e., 40 Ar+b-1112 ( 45 Sc, 100%) and 84 Kr+b-1112 ( 89 Y, 100%).In stable nuclei, 45 Sc is likely emerging di-neutrons for the first time, which seems a unique structure that its proton distribution differs with of electron, as earlier mentioned.In group 1A, a 7 Li (92.5%) may prefer a-111 to a-3 (a single triton) in its skin, including below 23 Na 111 (100%), 39 K 111 (93.3%), 87 Rb 111 (27.83%), 135 Cs 111 (2.3×10 6 y), and 225 Fr 111 (3.95 m), because skin particle masses will smoothly increase from 1 to 4 along with sweeping tri-groups from 1 (1A, 1B, 1-2C) to 8 (8A, 8-10B, 15-16C).Apparently, there is a correspondence between atomic and nuclear periodicity, such as a-4443 in 19 F, 35 Cl, 79 Br, and 127 I in group 7A that all their chemical main valence is 1.Perhaps, it cannot be excluded that the element properties were related to that long a, mid b, and short c axes extend a different depth in nuclei (Figure 2a).For example, lanthanide contraction may be relevant to inner transition 16 p l trapped in 8 c axes where is low lying between 4 a and 4 b axes.Also, in 23 Na 35 Cl, thin a-111 in 23 Na ( 20 Ne+a-111) may be looser to its m c than thick a-4443 in 35 Cl ( 20 Ne+a-4443), somewhat like that nucleon halo, if involved nuclear force, a factor possible influence on their atomic radii (0.15 and 0.09 nm), implying that nuclear radii might link to atomic radii.
In addition, possible to result in even-Z fragment that its energy release is greater than odd (fine structure of fragment masses, interval A ~ 5, n v +α) (Thomas & Vandenbosch, 1964), part of s p might be fused in glide, since in 235 U (n,f), its skin having no an innate α-particle, has occurring polar α-particle emission, about 0° or 180°with respect to the fission axis (Piasecki, Dakowski, Krogulski, Tys, & Chwaszczewska, 1970).Moreover, the yield is over 3 times for A L to A H flight directions (Piasecki & Nowicki, 1979), which is in favor of s p to glide upon A L again.
At leftmost bottom sides of a double peak curve, A ~ 80 and ~ 130, are two vanishing points of A L , A H (Unik et  al., 1973), neutron (Bowman, Milton, Thompson, & Swiatecki, 1963), and α-particle (Schmitt, Neiler, Walter, &  Chetham-Strode, 1962), which both point to a sector where its 2 edges are enclosed by long 2 a axes, i.e., 2 a 1 b 2 c (A L ) and 3 a 2 b 4 c (A H ) α-clusters.Take neutron yields for example, in where 53 129 is a minimal 3 a 2 b 4 c and 45 123 is a complementary 1 a 2 b 4 c to yield maximal neutrons (~3) (Bowman,  Milton, Thompson, & Swiatecki, 1963), suggesting that maximal neutron yield is from a sector of short 2 c axis edges.In 254 Fm (sf) that both 252 Cf and 254 Fm neutron shells were n p -114+n v -40 shows a similar result of neutron yield: minimum at A 129-130 of A H and maximum at A 123-124 of A L (Gindler, Flynn, Glendenin, & Sjoblom,  1977).

Discussion
To explain fission phenomena rely on what a nuclear model was based on.However, this work seems flexible to fit.Namely, a nuclear fission, asymmetric limited within Z 94±6 nuclei as a rule, is likely that its 16 α-clusters are splitting into different ratios from 15:1 (1 c , α decay; 1 b or 1 a , cluster decay, essentially similar to three large fragments in a fission) to 8:8 to produce different mass fragments, and n v in a split line will prevail over n p to convert prompt neutrons.For example, if 16 α-clusters were splitting into 9:7, a pair fragment mass difference is Z A ≥ 20 40 (±1 a axis, 2 clusters of 5 α) in 235 U+n→ 137 Ba+ 97 Kr+2n.In addition, among LCP most probable emission is α that its angle differs from polar emission is perpendicular to fission axis, nearly 90±22.5° to A H and A L , respectively, where 22.5°= 360°/16.Since a fission nucleus is almost impossibly complete unfolded, its α emitting angle is within 67.5°-112.5°thatcame from one of inner transition 8 α-particles, which is satisfactorily in agreement with Fig. 9 of Fluss, Kaufman, Steinberg, and Wilkins (1973).
In addition, the yields of various fragments suggest to vanish in the same two points: 3 a 2 b 4 c (A ~ 130) and 2 a 1 b 2 c (A ~ 80) α-clusters.Currently, fragment A ~ 130 and A ~ 80 were explained near Z-50, N-82 and Z-28, N-50 doubly magic shells, respectively, which seem that there has no a distinction of proton and neutron shells.Perhaps, their shells are the same only in magic number 2 ( 4 He), 8 ( 16 O), and 20 ( 40 Ca) (Table 1); for the 28, 50, and 82, it is to differ because of valence neutron emergence.To N-126 shell in Figure 2a shows to derive from n p -86+n v -40, a frame to grow  2a-b).And, it is undeniable that all magic nuclei together with their neighbor nuclei able to grow is so smooth in Table 1, which will be helpful to account for magic number phenomena in the future.
On the other hand, a nucleus might emerge different structures in ground and excited states.For example, a 16 O in ground state is 16 O c-2+2 4242 and in excited state is 4 α-structure that skin 2 d of 16 O c-2+2 4242 were combined 1 α; otherwise in ground state a 4 α-structure of 16 O is inconceivable to carry two hydrogen atoms to build a water molecule.Whereas a 1 H 2 16 O will have in the main understood at a glance in Figure 2b.Also, it appears straightforward, if alternating single and double bonds of a benzene ring ( 12,13,14 C 6 1 H 6 ), a buckyball ( 12,13,14 C 60 ), and diamond ( 12,13,14 C n ) were rooted in a tetrahedral nucleus of 12,13,14 C. Obviously, this covered atomic scope that was broadened to proton distribution, which presents another way to explain Z that was shown to occupy constant spatial positions not only in nuclei, but in molecules (Figure 2b).
In conclusions, the compelling evidences suggest that a special shape of the periodic table is rooting in atomic nuclei that can only grow 1 α-particle in the 1 st layer intensified by 4 p l of 27 Co, 28 Ni, 45 Rh, and 46 Pd, and then grow 2 3 , 2 4 , and 2 5 α-particles together with nearly same number valence neutrons in the 2-3, 4-5, and 6-7 layers, respectively, that noble nuclei demonstrated perfect nucleon distributions, which is well consistent with the line of beta stability.Furthermore, the number of the elements [2(2 3 +2 4 +2 5 ) besides groups 9-10B] and valence neutrons (2 3 +2 4 +2 5 ) in the 2-3, 4-5, and 6-7 steps being a square relation therefore indicates that a nucleus unusually is a two-dimensional structure in a nuclear phase, a folding nucleon disc that may be the heavier, the flatter, a possible reason resulting in super heavy element lives becoming shorter and shorter.Also, so that gives rise to it, a crude nucleon aspect was seemingly suggested from macrocosm.However, though here is an empirical nucleon distribution that could avoid stuck on details to some extent, it provides a visible nuclear image for the first time, which will benefit to further clarify and/or integrate nuclear, atomic, and molecular structures.It is significant, especially, in the present nanoparticle time.