From: javadi_hossein@hotmail.com (Hossein Javadi)
Newsgroups: sci.physics.plasma
Subject: Analysis of effective nuclear charge and atom's orbits by CPH Theory
Organization: http://groups.google.com


Analysis of effective nuclear charge and atom's orbits by CPH Theory

The effective nuclear charge is the "pull" that the specific electron
"feels" from the nucleus.
Example; hydrogen atom contains one proton and one electron. The
effective nuclear charge on electron is equal 1 in hydrogen atom.
Hellium contains two protons and two electrons. But there is not the
effective nuclear charge equal 2 on each electron in hellium atom. It
is about 1.7 units.

Staler's Rule;
Of the first time Slater did give a simple rule for calculate the
effective nuclear charge on any electron in any atoms. Specifically,
Slater's Rule determines the shielding constant which is represented
by S. To determine the effective nuclear charge use this equation:

Z*=Z-S.

By according Staler's rule you must order the configuration
differently then what you are used to. Group each electron like this:

(1s)(2s,2p)(3s,3p)(3d)(4s,4p)(4d)(4f)(5s,5p)(5d)(5f)...

Electrons to the right of the electron you have chosen do not
contribute because they don't shield. In the same group, each electron
shields 0.35.
Main group electrons (s,p) n-1 contribute 0.85.
Electrons in n-2 contribute 1.00 If the desired electron is in the
(d,f) orbital, anything to the left shields completely and therefore
has a value of 1.0.

Example 1: Sc from a 4s perspective (Its nuclear has 21 protons)
S(4s) = 1 x (.35) + 9 x .85 + 10 x 1.0 = 18
So, Z*=21-18=3.

Example 2: As from a 3d perspective (Its nuclear has 33 protons);
S(3d)=20.3 and Z*=33-20.3=12.7

Clementi and Raimondi;
Clementi and Raimondi did their work on effective nuclear charges in
the early 1960s. By this time, there was a great deal of background
work that had been done on orbitals and molecules. And the computer
had been invented! This gave them the ability to incorporate
self-consistent field (SCF) wave functions for the hydrogen to krypton
atoms into their calculations. They didn't have to rely on Slater-type
orbitals which, for simplicity of calculation, didn't contain nodes.
They were thus able to go to a greater depth with a refined
mathematical model, and this allowed
them to clearly distinguish the s-orbitals from the p-orbitals in
determining their set of rules. Specifically, they had a better model
for dealing with electron penetration of the inner core.
The results of Clementi's method is diffenrence of Staler's rule. For
example Clementi calculated as Sc from a 4s perspective Z*=4.632
(Staler's is equal 3) and as from a 3d perspective Z*=17.378 (Staler's
is equal 12.7).

Remark;
Staler's rule and Clementi's method based on expriments. There is no
any analystic concept why and how the strongly of nuclear charge does
lose? The effective nuclear charge leads we have a new looking on
force and relationship between force and energy.
Is force perishable? If force is not perishable, why the effective of
nuclear charge does change of an orbit to other orbit? What happens
for the strongly of nuclear charge in during its traveling toward
electrons? Is force convertable? If force is convertable, it does
convert to what? When an electron accelerates toward a proton, then
energy of electron does increase. Question is that; what happens for
the amount of force? By according CPH theory force and energy are
equivalence. Force converts to energy and energy changes to force. I
will explain the effective nuclear charge by CPH theory.

Work is quantized;
Theoretical physics and evidence show energy is quantized. Also, when
force applied on a particle/object, energy of particle/object does
change. Relations Fdx= - dU and W=fd=deltaE show if energy is
quantized then work can not be continually. When a photon is falling
in a gravitational field, its energy does increase. But energy of
photon is quantized. So, work of gravity force must be quantized.
Also, when an electron accelerates in an electrical field, the energy
of electron does change. But energy of electron is quantized, so work
of electrical force is quantized. But d (distance) is continually, so
f (gravity force or electric force) is quantized.
How we can define a quantum of force? Before we define a quantum of
force, we must define a quantum of work. So, we need select a short
length for that. I propose Lp (Planck Length) for that. It is equal;
Lp=1.6x10 power minus 35 m.
Also, I defined a quantum of gravity force (in CPH Theory) Fg, that is
equal;
Fg=1.41x10 power minus 37 N.
So, a quantum of work is Wq=FgLp=2.26x10 power minus 72 J.
And at usual case W=nWq, n is an integer number. (n=...-2, -1, 0, 1,
2...)

Force and Energy are convertable to each other;
I take a shot with mass m. I shoot it with velocity v upward the
earth. Shot takes kinetic energy. In during shot is traveling upward,
gravity force works on it. Gravity work is negative, and shot's energy
does decrease until shot does stop. Then shot falls toward the earth
and its kinetic energy increases.
When shot is moving upward, it loses energy equal 1/2mv*2 that it is
equal

1/2mv*2=nFgLp, and shot's energy converts to n quantum gravity force.
Also, when shot is falling n quantum gravity force converts to kinetic
energy.

Now suppose a charge particle accelerates in electric field and its
velocity does change. When energy of electron increases, electric
force converts to energy. And when energy of electron decreases,
energy does convert to electric force.

Force is a current;
Earth has gravity field. Gravity field formed of many gravity force
particles that are moving toward the earth. Suppose earth is alone and
there is not any interaction between earth and other bodies in
universe. When a gravity force particle reaches to earth, it absorb by
earth. But earth is not alone and it has interaction with other
bodies. Have a look at earth and moon. There are two fields; one is
around the earth and other one is around the moon. When a gravity
force particle reaches to earth, other one moves toward the moon and
pushing earth toward moon. Also when a gravity force particle reaches
to moon, other one moves toward the earth and pushing moon toward the
earth.
Suppose n1 Gravity force particles are moving from moon toward earth.
They reach to an object around the earth. Some of them (equal n2)
convert to energy and do attach to object. So, earth feels moon's
effective gravity force is Fg(n1-n2) at time t1. But there is a
current of gravity force particles between object and moon too. When
object reaches to earth, n1 gravity force particles start their travel
toward the moon (from earth and object). When they reach to moon at
time t2, moon feels earth's gravity force is equal n1Fg. If object
does not attach with earth, moon feels gravity force of earth is equal
(n1-n2)Fg.
Moon feels that earth and object are separate. Becaouse their distance
(or direction) is not same.

Effective nuclear charge;
Current of electric force is like of gravity force's current.
Difference between them is in the their's strongly. Suppose an atom
contains n protons and n electrons. Electrons are rotating in their
orbits around nucleos. Electron B is between nucleos and electron A.
Given Fe is a quantum of electric force. Now suppose n1 electric force
particles start their travel of nucleos toward electron A. n1=kn, n is
number of protons in nucleos and k is a natural number. When these
electric force particles reach to electron B, they works on it. (B is
between nucleos and electron A). Then n2 electric force particles
convert to energy, and energy of electron B does change. So, (n1-n2)
electric force particles reach to electron A, and effective nuclear
charge on A is equal Z*=Fe(n1-n2). Then electron A feels F=(n1-n2)Fe
of nucleos. If there were electrons B, C, D... between nucleos and
electron A, then n2, n3, n4 .. convert to energy and
[n1-(n2+n3+n4...)] reach to A. Then A feels eggective nuclear equal
Z*=Fe[n1-(n2+n3+n4...)].
When n1=n2+n3+n4..., then electron A never feels any effect of nuclear
charge.
Let come back to electron B and see what happened for it. When n2
electric force particles reach to B, B's energy changes, and it leaves
its orbit. But B is not alone and other electrons and nucleos have
effect on electron B. They do return B to its orbit. And its energy
converts to foce, this interaction is continually.

Atom's orbits;
If external forces that applied on an electron was beeing constant,
then its energy and orbit is stable. But the strongly (and directions)
of electric forces that applied on any electrons does change
continually. So, energy of electron (and direction) is not constant
and its velocity and orbit do change. Also, the magnetic field of
electron does change continually. So, this changing of magnetic field
has effect on other electrons and nucleos. The spin and volume of
nucleos do change, and it has effect on electrons and their orbits.
So, electron oscillates around its orbit.

Sincerely
Hossein Javadi

For more explain see;
http://groups.yahoo.com/group/cph_theory/files/PDFofCPH.pdf

References;
http://www.webelements.com/
http://www.madsci.org/posts/archives/1067535650.Ch.r.html


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