http://nukephysik101.wordpress.com/2011/02/03/changing-of-frame-ii/
this one is good~
Thursday, February 3, 2011
Isospin
This is the understanding of thus topic so far, will be subject to change when I have more understanding.
This is another degree of freedom or dimension in particle. The proton and neutron mass are very similar. And beside of the mass, and electric charge, proton and neutron are the same in everyway. Thus, it was portuslated that they are same particle and the different of mass is due to the electronmagnetic field. Which is like the Zeeman splitting of energy level on spin.
And also, the proton-neutron interaction is same as neutron neutron interaction in most cases. Thus it strongly suggest proton and neutron are same particle under strong interaction.
Without an magnetic field. Energy level of different spin are degenerated. And same thing happen on isospin : when there is no charge, no electric field, the energy level of isospin will be the same. So, proton and neutron will be the same particle when there is no field. And the strong force does not charge sensitive, thus, under the strong force, proton and neutron are the same.
spin and isospin share same mathematic description.
a magnetic moment, it can be come from spin angular momentum or orbital angular momentum, whic is current distribution.
The electric moment can be generated by isospin and electric charge distribution.
This is another degree of freedom or dimension in particle. The proton and neutron mass are very similar. And beside of the mass, and electric charge, proton and neutron are the same in everyway. Thus, it was portuslated that they are same particle and the different of mass is due to the electronmagnetic field. Which is like the Zeeman splitting of energy level on spin.
And also, the proton-neutron interaction is same as neutron neutron interaction in most cases. Thus it strongly suggest proton and neutron are same particle under strong interaction.
Without an magnetic field. Energy level of different spin are degenerated. And same thing happen on isospin : when there is no charge, no electric field, the energy level of isospin will be the same. So, proton and neutron will be the same particle when there is no field. And the strong force does not charge sensitive, thus, under the strong force, proton and neutron are the same.
spin and isospin share same mathematic description.
a magnetic moment, it can be come from spin angular momentum or orbital angular momentum, whic is current distribution.
The electric moment can be generated by isospin and electric charge distribution.
Wednesday, February 2, 2011
a review on atomic structure
http://nukephysik101.wordpress.com/2011/02/02/a-review-on-atomic-structure/
this one is half finish, sorry.
this one is half finish, sorry.
Tuesday, February 1, 2011
Sunday, January 30, 2011
Rotation operator on x, y in Matrix form
http://nukephysik101.wordpress.com/2011/01/30/rotation-operator-on-x-y-in-matrix-form/
Saturday, January 29, 2011
detail treatment on Larmor Precession and Rabi Resonance
http://nukephysik101.files.wordpress.com/2011/01/a-treatment-on-larmor-precession-and-rabi-resonance.pdf
is a pdf files, 15 pages. i think it covered most material on this subject. did i?
is a pdf files, 15 pages. i think it covered most material on this subject. did i?
Thursday, January 27, 2011
Announcement
the further post will post on WordPress.
since there can edit formula.
Google sucks, this time!! too bad. i am a big fan of you!
http://nukephysik101.wordpress.com/
since there can edit formula.
Google sucks, this time!! too bad. i am a big fan of you!
http://nukephysik101.wordpress.com/
Parity
It is Pa-ri-ty, not Par-ty.
Parity is just a reflection on every space dimension.
X -> -X
Y -> -Y
Z -> - Z
This is just a mirror reflection, although it only reflects on 1 dimension, the dimension that perpendicular to the mirror surface.
The parity transform is taking everything reverted. For example, when you stand up, your arms place horizontal and you left arm points forward and your right arm points right. After a parity transform. You right arm point left. Your left arm point backward, and you are standing on the ceiling, upside down. The result is a mirror image of your self. If we rotate the reverted-self from the ceiling to the ground.
Thus, parity also related as mirror reflection. In physics, we like to call the right-hand system (RHS) or left-hand system (LHS).
A simple RHS and LHS are on your hands! Although our left hand and right hand has some minor different, in general, they are the mirror image of each other. And the great interesting thing is, your left hand cannot overlap the right hand. They are equal but not the same.
Another thing is spring, when a wire is rowed clockwise and going upward, it form a left-hand spring and vice aver. Thus 2 springs are not the same.
A more physical example is the polarization of light, there are lefthand rotating light and right hand rotating light, called circular polarization. And material which interact differenty with different circular polarization are called chiral material. We should stop talking about examples in here. Because in nature, there are so many things has chiral property. Never the less, potenient and drug also has chirality. One book I recommend on general science for the chirality is "right-hand, left-hand" by chris McManus.
Physics encounters parity is because we believe if the whole world is reverted, every thing just work fine and the same. For example, if our orgasms are all reflected, left goes to right, right go to left. We still alive. In fact, there are some real cases, that some peole do have reverted orgasm. Because there should be symmetric in the world.
For those which keep function as before parity transform, we called it parity positive, for those who are not, we called it parity negative.
Be reminded that the chiral material that interact circularly polarized light different still the parity positive. For example, a material which only let right hand light passes through, but not let the left hand pass. After parity transform, it lets left hand light pass through but not right hand .Thus, the left hand and right hand are work equally well!
We also cannot say our left hand is more weak then our right hand, then we called it parity negative. It is because, if we reflected ourself, our left hand is as good and right hand and the right hand is as weak as left hand.
In normal day, parity positive never break. It is seem impossible to break. How coome some thing work differently under parity transform?
However, in mathematics, there are many parity negative things. One example is the spherical harmonic. It is can be parity positive and negative depends on the parameter.
Lets take a imaginary example in parity negative. If we use photon to hit a target, all photons are going left. Now, we reflet the whole system. But now, the photons are still going left.
The first discovery of parity negative is on beta- decay from Co-60. Whe. Applied an external magnetic field from down to up, the beta particle come out at left. When we change the magnetic field, now is from up to down, the beta particle should come out at right, if parity is positive. But it is not, it still keep coming out left!
The reason of t is beyond my understanding... Sorry.
Parity is just a reflection on every space dimension.
X -> -X
Y -> -Y
Z -> - Z
This is just a mirror reflection, although it only reflects on 1 dimension, the dimension that perpendicular to the mirror surface.
The parity transform is taking everything reverted. For example, when you stand up, your arms place horizontal and you left arm points forward and your right arm points right. After a parity transform. You right arm point left. Your left arm point backward, and you are standing on the ceiling, upside down. The result is a mirror image of your self. If we rotate the reverted-self from the ceiling to the ground.
Thus, parity also related as mirror reflection. In physics, we like to call the right-hand system (RHS) or left-hand system (LHS).
A simple RHS and LHS are on your hands! Although our left hand and right hand has some minor different, in general, they are the mirror image of each other. And the great interesting thing is, your left hand cannot overlap the right hand. They are equal but not the same.
Another thing is spring, when a wire is rowed clockwise and going upward, it form a left-hand spring and vice aver. Thus 2 springs are not the same.
A more physical example is the polarization of light, there are lefthand rotating light and right hand rotating light, called circular polarization. And material which interact differenty with different circular polarization are called chiral material. We should stop talking about examples in here. Because in nature, there are so many things has chiral property. Never the less, potenient and drug also has chirality. One book I recommend on general science for the chirality is "right-hand, left-hand" by chris McManus.
Physics encounters parity is because we believe if the whole world is reverted, every thing just work fine and the same. For example, if our orgasms are all reflected, left goes to right, right go to left. We still alive. In fact, there are some real cases, that some peole do have reverted orgasm. Because there should be symmetric in the world.
For those which keep function as before parity transform, we called it parity positive, for those who are not, we called it parity negative.
Be reminded that the chiral material that interact circularly polarized light different still the parity positive. For example, a material which only let right hand light passes through, but not let the left hand pass. After parity transform, it lets left hand light pass through but not right hand .Thus, the left hand and right hand are work equally well!
We also cannot say our left hand is more weak then our right hand, then we called it parity negative. It is because, if we reflected ourself, our left hand is as good and right hand and the right hand is as weak as left hand.
In normal day, parity positive never break. It is seem impossible to break. How coome some thing work differently under parity transform?
However, in mathematics, there are many parity negative things. One example is the spherical harmonic. It is can be parity positive and negative depends on the parameter.
Lets take a imaginary example in parity negative. If we use photon to hit a target, all photons are going left. Now, we reflet the whole system. But now, the photons are still going left.
The first discovery of parity negative is on beta- decay from Co-60. Whe. Applied an external magnetic field from down to up, the beta particle come out at left. When we change the magnetic field, now is from up to down, the beta particle should come out at right, if parity is positive. But it is not, it still keep coming out left!
The reason of t is beyond my understanding... Sorry.
on Relaxation in NMR
If we only switch on the transverse magnetic field for some time tau. after the field is off, the system will go back to the thermal equilibrium. it is due to the system is not completely isolated.
instead of consider a single spin, we have to consider the ensemble. and an ensemble is describe by the density matrix.
the reason for not consider a single spin state is, we don’t know what is going on for individual spin. in fact, in the previous section, the magnetization is a Marco effect. a single spin cannot have so many states, it can only have 2 states - up or down. if we insist the above calculation is on one spin, thus, it only give the chance for having that direction of polarization. which, is from many measurements.
so, for a single spin, the spin can only have 2 states. and if the transverse B field frequency is not equal to the Larmor frequency , and the pule is not a pi-pulse, the spin has chance to go to the other state, which probability is given by a formula. and when it goes to relax back to the minimum energy state, it will emit a photon. but when it happen, we don’t know, it is a complete random process.
However, an ensemble, a collection of spins, we can have some statistic on it. for example, the relaxation time, T1 and T2.
instead of consider a single spin, we have to consider the ensemble. and an ensemble is describe by the density matrix.
the reason for not consider a single spin state is, we don’t know what is going on for individual spin. in fact, in the previous section, the magnetization is a Marco effect. a single spin cannot have so many states, it can only have 2 states - up or down. if we insist the above calculation is on one spin, thus, it only give the chance for having that direction of polarization. which, is from many measurements.
so, for a single spin, the spin can only have 2 states. and if the transverse B field frequency is not equal to the Larmor frequency , and the pule is not a pi-pulse, the spin has chance to go to the other state, which probability is given by a formula. and when it goes to relax back to the minimum energy state, it will emit a photon. but when it happen, we don’t know, it is a complete random process.
However, an ensemble, a collection of spins, we can have some statistic on it. for example, the relaxation time, T1 and T2.
NMR
NMR is a technique to detect the state of nuclear spin. a similar technique on electron spin is call ESR ( electron spin resonance)
The principle of NMR is simple.
by analyzing the T1 and T2 and also Larmor frequency, we can known the spin, the magnetization, the structure of the sample, the chemical element, the chemical formula, and alot many others thing by different kinds of techniques.
For nuclear physics, the use of NMR is for understand the nuclear spin. for example, the polarization of the spin.
The principle of NMR is simple.
- apply a B-field, and the spin will align with it due to interaction with surrounding and precessing along the B-field with Larmor frequency. the time for the spin align with the field is call T1, longitudinal relaxation time.
- Then, we send a pule perpendicular to the B-field, it usually a radio frequency pulse. the frequency is determined by the resonance frequency, which is same as the Larmor frequency. the function of this pulse is from the B-field of it and this perpendicular B-field with perturb the spin and flip it 90 degrees.
- when the spin are rotate at 90 degrees with the static B-field, it will generate a strong enough signal around the coil. ( which is the same coil to generate the pule ) and this signal is called NMR signal.
- since the spins are not isolate, when it interact with environment, they will go back and align with the static B-field. the time for this is called T2, transverse relaxation time.
by analyzing the T1 and T2 and also Larmor frequency, we can known the spin, the magnetization, the structure of the sample, the chemical element, the chemical formula, and alot many others thing by different kinds of techniques.
For nuclear physics, the use of NMR is for understand the nuclear spin. for example, the polarization of the spin.
Wednesday, January 26, 2011
Changing of frame
sometimes, i will confuse on changing frame, especially between rotating frame and lab frame.
Tuesday, January 25, 2011
On mass deficit
The mass deficit is due to the potential energy loss.
But, why there are potential?
Coz there is a force associate with a potential.
Or in more correct way, the potential energy is due to the force. When 2 bodies in space has a attractive force, then it naturally go together. And the force accelerate the body and increase their kinetic energy.
Thus, we think the force created a field, which stored potential energy. When the force accelerates body, the potential energy converted into kinetic energy.
Imagine there are 2 bodies, A & B, Which at different location and have different force. If A is further away, when it comes at B, it has more kinetic energy than B, coz B is at rest at that position. Thus, further away, higher the potential.
Can thus potential be as high as infinite? In reality, because thing has surface, has size. The minimum distance between the 2 bodies is the sum of their radius. And if we sum up all potential, from the surface to infinity. We found that it is finite. And we like to set the potential at infinity is zero. Thus, it makes all attractive force has negative potential.
But, electric and positron do not has size, so, and electron and a positron can come together and the potential energy they can release is infinite! Since when they are apart infinite and the attractive force accelerate it, when they meet, their speed will be infinite!
Wait! The speed cannot be infinite, the highest speed is the speed of light and for an object has mass, it never move at the speed of light!
So, when electron and positron hit each other from infinity. However, relativity does not limit the energy and the kinetic energy. The result is, it can release infinite energy.
But at first, infinite exist. In reality, we can just approximate the "infinite" by far far away. When the potential change very little. But far far away is still very short compare to infinite. Thus, we don't have infinite energy source.
In laboratory, we can accelerate electron and position at very high speed and contain several GeV. Thus when those particles annihilate, they release GeV energy due to the kinetic energy and their mass, which is just 0.000511GeV. Does not help much.
Monday, January 24, 2011
Mass of particles and nucleus
in Nuclear physics, the particle we deal with are so small and so light, if we use standard unit, then there will be many zero and we will lost in the zeros. for example, the electron has mass:
Mass( electron ) = 9.11 × 10-31 kilograms
Mass( proton ) = 1.67 × 10-27 kilograms
see? as the special relativity give us a translation tool - E = m c^2, thus, we can use MeV to talk about mass.
Mass ( electron ) = 0.511 MeV
Mass ( proton ) = 938.3 MeV
thus, we can see, Proton is roughtly 2000 times heavier then electron ( 1000 : 0.5 ).
Mass( neutron ) = 939.6 MeV
neutron is just 1.3 MeV heavier then proton.
The nucleus is formed by proton and neutron. so, in simple thought, an nucleus with Z proton and ( A-Z ) neutron should have mass
Z x Mass( proton ) + ( A - Z ) x Mass ( neutron ) = Mass ( A, Z )
where A is the atomic mass number, which is equal the number of nucleons in the nucleus, and Z is the proton number.
However, scientists found that it is not true.
Z x Mass( proton ) + ( A - Z ) x Mass ( neutron ) > Mass ( A, Z )
Some of the mass is missing! But that is explained why nucleus will not break down automatically. since it need extra energy to break it down.
we called the mass different is Mass Deficit. or Blinding energy.
Mass Deficit = Mass( A, Z) - Mass ( proton + neutron )
some one may think that the blinding energy is the energy for holding the nucleus together. in order to hold the nucleus, some mass was converted into the energy to holding it. this is INCORRECT. the correct argument is, the blinding energy is th energy require to break it down.
think about a simple 2 bodies system, like sun and earth. at far far away, when both of them are at rest, the total energy is Mass( sun) + Mass ( earth ) + Potential energy.
when the earth moves toward to sun, the potential energy converted to the Kinetic energy, so the earth moving faster and faster. but, in order to stay in the orbit, some K.E. must be lost so that it does not have enough ( or the same) energy to run away. Thus, the total energy of the system is lesser then the total mass.
another analogy is electron orbit. when an electron was captured by an atom, it radiate energy in order to stay in some energy level. thus, the total energy of the system again less then the total mass.
any any case, the mass of the sun and earth and electron does not change, but the potential changes to negative, thus it makes to total energy lesser.
similar idea hold for nucleus, but the potential of it are great different, because there are a Coulomb Barrier. Thus, in order to make a nucleus. we have to put so many K.E. to again this barrier, then the resultant nucleus release the Mass Deficit energy and also the input K.E..
Mass( electron ) = 9.11 × 10-31 kilograms
Mass( proton ) = 1.67 × 10-27 kilograms
see? as the special relativity give us a translation tool - E = m c^2, thus, we can use MeV to talk about mass.
Mass ( electron ) = 0.511 MeV
Mass ( proton ) = 938.3 MeV
thus, we can see, Proton is roughtly 2000 times heavier then electron ( 1000 : 0.5 ).
Mass( neutron ) = 939.6 MeV
neutron is just 1.3 MeV heavier then proton.
The nucleus is formed by proton and neutron. so, in simple thought, an nucleus with Z proton and ( A-Z ) neutron should have mass
Z x Mass( proton ) + ( A - Z ) x Mass ( neutron ) = Mass ( A, Z )
where A is the atomic mass number, which is equal the number of nucleons in the nucleus, and Z is the proton number.
However, scientists found that it is not true.
Z x Mass( proton ) + ( A - Z ) x Mass ( neutron ) > Mass ( A, Z )
Some of the mass is missing! But that is explained why nucleus will not break down automatically. since it need extra energy to break it down.
we called the mass different is Mass Deficit. or Blinding energy.
Mass Deficit = Mass( A, Z) - Mass ( proton + neutron )
some one may think that the blinding energy is the energy for holding the nucleus together. in order to hold the nucleus, some mass was converted into the energy to holding it. this is INCORRECT. the correct argument is, the blinding energy is th energy require to break it down.
think about a simple 2 bodies system, like sun and earth. at far far away, when both of them are at rest, the total energy is Mass( sun) + Mass ( earth ) + Potential energy.
when the earth moves toward to sun, the potential energy converted to the Kinetic energy, so the earth moving faster and faster. but, in order to stay in the orbit, some K.E. must be lost so that it does not have enough ( or the same) energy to run away. Thus, the total energy of the system is lesser then the total mass.
another analogy is electron orbit. when an electron was captured by an atom, it radiate energy in order to stay in some energy level. thus, the total energy of the system again less then the total mass.
any any case, the mass of the sun and earth and electron does not change, but the potential changes to negative, thus it makes to total energy lesser.
similar idea hold for nucleus, but the potential of it are great different, because there are a Coulomb Barrier. Thus, in order to make a nucleus. we have to put so many K.E. to again this barrier, then the resultant nucleus release the Mass Deficit energy and also the input K.E..
 |
| a scratch on the nuclear potential. there are a Coulomb Barrie. ( by wolframalpha.com) |
When the nucleus is radioactive and undergoes decay. this mean, it Mass deficit is positive. thus, it will automatically break down to another nucleus until it mass deficit is negative again. during this process, the emitted particle carry K.E. which is from the potential. Not the mass for one nucleons.
Remember, Mass( nucleus ) = Mass ( protons + neutrons ) + Potential
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