Geometrical Polar-Ring Solution for Magic and Sub-Magic Numbered
Nuclei.

It is well known that if the neutron- or proton number within atomic
nuclei have the following quantities (2, 8, 20, 28, 50, 82 and 126:
the magic numbers), then the atoms are showing a more than average
stability. As an example, the most stable form of Lead PB126 is an
integration of two T= 82 and T=126 (Double Magic) structures. (figure
B)see:
http://home.planet.nl/~vuyk0022/App_Vuyk.htm#appendix7
The common "Shell Model" doesn't give a logically 3D representation
of these nucleons.

As a solution: Each magic numbered nucleon is supposed to have a
polar axis which is
occupied by an even number of nucleons.
This axis is the centre of the coaxial placed symmetrical and
globular system of circular trajectories or rings.
The planes of the rings are supposed to be concentric and
perpendicular to the polar axis.
Each circular trajectory is occupied by even numbers of nucleons, as
represented in the figures below.
These figures have to be interpreted as central sections over the
axis of the globular nucleus.
The magic number nuclei with 82 and 126 nucleons have a
second "concentric inner system" of nucleons.
Number T=82 has only one inner ring with 6 nucleons, and number T=126
has three inner rings with respectively 6,8, and 6 nucleons.

Based on this growing system we may construct and suggest the next
magic numbers= 178 and 244.
It would be interesting to study on the intermediate
transitional "jump" situations in nature, between these structures.
See the figure B:
There are 7 magic numbered ATOM NUCLEI systematically represented, as
a central section through the axis of the more or less globular
nucleus, starting with nucleon number: T=2, and in succession T=8,
20.28.50,82 and 126.
The dot sign represents an axial located nucleon.

There are two types of circular located nucleons:

Type A: outer ring located Nucleons: represented in figure B as a
closed rectangular with a number X enclosed. This represents a
circular trajectory (ring) occupied by X nucleons, concentric with he
polar axis of the nucleon.

Type B: so called Inner ring located Nucleons: represented in figure
B as a closed rectangular with an internal horizontal striping and an
external located number Y. This represents a circular trajectory
occupied by Y nucleons, concentric with the polar axis of the nucleon.
For T=2, there are 2 axial nucleons.
For T=8, There are 2 axial nucleons, and 6 ring nucleons= 8. Or, as
an alternative: 4 axial nucleons, and 4 ring nucleons=8 nucleons.
For T=20, There are 6 axial nucleons, and 14: (4+6+4) ring nucleons=
20 nucleons. Or, as an alternative : 4 axial nucleons and 2x8 ring
nucleons.
For T=28, there are 8 axial nucleons, and 20: (6+8+6) ring
nucleons=28 nucleons.
For T=50, there are 12 axial nucleons, and 386+8+10+8+6) ring
nucleons.
For T=82, there are 16 axial nucleons, and 66: (6+8+10+12+10+8+6)+
(6:in the inner ring) ring nucleons=82 nucleons.
For T=126, There are 20 axial nucleons, and 106:
(6+8+10+12+14+12+10+8+6)+(6+8+6: in the inner ring)=126 nucleons.

As a result: we may assume that all nucleons should have more or
less the same combined structure of Axial and Concentric Ring
located Nucleons, as the origin of atomic up or down polarity.

So called submagic nuclei, are nuclei which show also a more than
average stability, but less manifest than the magic numbered nuclei.
The numbers found by experiments seem to be: 14,
38,40,64,108,114,120,152, and 162. If we look at the 7 magic numbered
nucleons (see also figure B
http://home.planet.nl/~vuyk0022/App_Vuyk.htm#appendix8 ), it is
obvious that it represents 7 special Polar/Ring shaped moments within
a growing nuclear scheme. As a consequence, there should be
intermediate geometrical structures possible between the seven
different cross sections given in the figure B, with equatorial
symmetry and more or less deformed globular structures.

For T=14, it is assumed that there are 6 axial nucleons and 8 ring
nucleons.

For T=38, there are 10 axial nucleons and 28 (6+8+8+6) ring
nucleons.

For T=40, there are 12 axial nucleons, and 28 (6+8+8+6) ring
nucleons.

For T= 64, there are 16 axial nucleons and 48 (6+8+10+10+8+6) ring
nucleons.

For T=108, there are 18 axial nucleons and 90 (6+8+10+12+12+10+8+6) +
(6+6+6: in the inner ring).

T=114, is assumed to be basically identical with T=126, however
with subtraction of the two inner rings occupied with each 6
nucleons.

T=120, is assumed to be also corresponding with T=126, however with
extension of 2 extra axial nucleons (22 total) and with subtraction
of the single inner ring occupied with 8 nucleons.

T=152, is assumed to be also corresponding with T=126, however with
extension of 4 extra axial nucleons (24 total) and with addition of
an extra "double equatorial ring " (8+14=22 nucleons) adding 26 extra
nucleons to the T=126 nucleus.

T=162, is assumed to be corresponding with T=126, however with
extension of 4 extra axial nucleons (24 total) and with addition of
2x double equatorial rings (8+14+14+8=44 nucleons) and under
subtraction of two inner rings of 6 nucleons. As a result this
nucleus should have a cylindrical non-globular form elongated along
the nuclear axis.

(see; Figure B.
http://home.planet.nl/~vuyk0022/App_Vuyk.htm#appendix8 .The schematic
geometrical representation of these nucleons placed in magic number
nuclei)
Leo.
http://home.planet.nl/~vuyk0022/

So as an interesting feature, this geometric solution is able to
explain not only the series of Magic numbers: 2,8,20,28,50,82,126, but
also SUB MAGIC NUMBERS:
14,38,40,64,108,114,120,152, and 162.

(Leo) wrote in message . com...
Geometrical Polar-Ring Solution for Magic and Sub-Magic Numbered
Nuclei.

It is well known that if the neutron- or proton number within atomic
nuclei have the following quantities (2, 8, 20, 28, 50, 82 and 126:
the magic numbers), then the atoms are showing a more than average
stability. As an example, the most stable form of Lead PB126 is an
integration of two T= 82 and T=126 (Double Magic) structures. (figure
B)see:
http://home.planet.nl/~vuyk0022/App_Vuyk.htm#appendix7
The common "Shell Model" doesn't give a logically 3D representation
of these nucleons.

As a solution: Each magic numbered nucleon is supposed to have a
polar axis which is
occupied by an even number of nucleons.
This axis is the centre of the coaxial placed symmetrical and
globular system of circular trajectories or rings.
The planes of the rings are supposed to be concentric and
perpendicular to the polar axis.
Each circular trajectory is occupied by even numbers of nucleons, as
represented in the figures below.
These figures have to be interpreted as central sections over the
axis of the globular nucleus.
The magic number nuclei with 82 and 126 nucleons have a
second "concentric inner system" of nucleons.
Number T=82 has only one inner ring with 6 nucleons, and number T=126
has three inner rings with respectively 6,8, and 6 nucleons.

Based on this growing system we may construct and suggest the next
magic numbers= 178 and 244.
It would be interesting to study on the intermediate
transitional "jump" situations in nature, between these structures.
See the figure B:
There are 7 magic numbered ATOM NUCLEI systematically represented, as
a central section through the axis of the more or less globular
nucleus, starting with nucleon number: T=2, and in succession T=8,
20.28.50,82 and 126.
The dot sign represents an axial located nucleon.

There are two types of circular located nucleons:

Type A: outer ring located Nucleons: represented in figure B as a
closed rectangular with a number X enclosed. This represents a
circular trajectory (ring) occupied by X nucleons, concentric with he
polar axis of the nucleon.

Type B: so called Inner ring located Nucleons: represented in figure
B as a closed rectangular with an internal horizontal striping and an
external located number Y. This represents a circular trajectory
occupied by Y nucleons, concentric with the polar axis of the nucleon.
For T=2, there are 2 axial nucleons.
For T=8, There are 2 axial nucleons, and 6 ring nucleons= 8. Or, as
an alternative: 4 axial nucleons, and 4 ring nucleons=8 nucleons.
For T=20, There are 6 axial nucleons, and 14: (4+6+4) ring nucleons=
20 nucleons. Or, as an alternative : 4 axial nucleons and 2x8 ring
nucleons.
For T=28, there are 8 axial nucleons, and 20: (6+8+6) ring
nucleons=28 nucleons.
For T=50, there are 12 axial nucleons, and 386+8+10+8+6) ring
nucleons.
For T=82, there are 16 axial nucleons, and 66: (6+8+10+12+10+8+6)+
(6:in the inner ring) ring nucleons=82 nucleons.
For T=126, There are 20 axial nucleons, and 106:
(6+8+10+12+14+12+10+8+6)+(6+8+6: in the inner ring)=126 nucleons.

As a result: we may assume that all nucleons should have more or
less the same combined structure of Axial and Concentric Ring
located Nucleons, as the origin of atomic up or down polarity.

So called submagic nuclei, are nuclei which show also a more than
average stability, but less manifest than the magic numbered nuclei.
The numbers found by experiments seem to be: 14,
38,40,64,108,114,120,152, and 162. If we look at the 7 magic numbered
nucleons (see also figure B
http://home.planet.nl/~vuyk0022/App_Vuyk.htm#appendix8 ), it is
obvious that it represents 7 special Polar/Ring shaped moments within
a growing nuclear scheme. As a consequence, there should be
intermediate geometrical structures possible between the seven
different cross sections given in the figure B, with equatorial
symmetry and more or less deformed globular structures.

For T=14, it is assumed that there are 6 axial nucleons and 8 ring
nucleons.

For T=38, there are 10 axial nucleons and 28 (6+8+8+6) ring
nucleons.

For T=40, there are 12 axial nucleons, and 28 (6+8+8+6) ring
nucleons.

For T= 64, there are 16 axial nucleons and 48 (6+8+10+10+8+6) ring
nucleons.

For T=108, there are 18 axial nucleons and 90 (6+8+10+12+12+10+8+6) +
(6+6+6: in the inner ring).

T=114, is assumed to be basically identical with T=126, however
with subtraction of the two inner rings occupied with each 6
nucleons.

T=120, is assumed to be also corresponding with T=126, however with
extension of 2 extra axial nucleons (22 total) and with subtraction
of the single inner ring occupied with 8 nucleons.

T=152, is assumed to be also corresponding with T=126, however with
extension of 4 extra axial nucleons (24 total) and with addition of
an extra "double equatorial ring " (8+14=22 nucleons) adding 26 extra
nucleons to the T=126 nucleus.

T=162, is assumed to be corresponding with T=126, however with
extension of 4 extra axial nucleons (24 total) and with addition of
2x double equatorial rings (8+14+14+8=44 nucleons) and under
subtraction of two inner rings of 6 nucleons. As a result this
nucleus should have a cylindrical non-globular form elongated along
the nuclear axis.

(see; Figure B.
http://home.planet.nl/~vuyk0022/App_Vuyk.htm#appendix8 .The schematic
geometrical representation of these nucleons placed in magic number
nuclei)
Leo.
http://home.planet.nl/~vuyk0022/