it is for and from a beginner. hopefully, everyone who interested can understand. Physics is about concept, mathematics follows naturally.
Thursday, January 27, 2011
Parity
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
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
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.
Tuesday, January 25, 2011
On mass deficit
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
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..
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| a scratch on the nuclear potential. there are a Coulomb Barrie. ( by wolframalpha.com) |
Saturday, January 22, 2011
Spin
Spin is a intrinsics property of elementary particle, such as electron, proton, and even photon. Intrinsics means it is a built-in property, like mass, charge. Which extrinsic properties are speed, momentum.
Spin is a vector or tensor quality while charge and mass are scaler.
Spin can react with magnetic field, like charge reacts with electric field or mass react with force produce acceleration. Thus, spin is like a bar-magnet inside particle, counter part of charge.
The magnitude of spin is half integer or integer of reduced Planck's constant h_bar or hb. Particles with half integer of spin are classified as Fermion, and those with integer spin are Boson. they follow different statistic while interact together, thus, this creates different physics for different group.
we are not going to the mathematic description this time.
the effect of spin causes the magnetic moment, that's why it react with magnetic field. the other thing that creates magnetic moment is angular momentum for charge particle, like electron orbiting around nucleus. So, both spin and angular momentum can be imagined as a little magnet, thus, they can interact, in physics, we call the interaction between spin and angular momentum is coupling. for example, spin-orbital coupling, spin-spin coupling, etc..
when the spin interact with external magnetic field, it will process around the magnetic field with Larmor frequency. and the direction of the spin while undergoes procession can only be certain angle. for spin half, like electron or proton. there are only 2 directions, and we called it up and down.
Wednesday, January 19, 2011
alpha decay
i assume we know what is alpha decay, which is a process that bring excited nucleus to lower energy state by emitting an alpha particle.
The force govern this process is the strong force, due to the force is so strong, the interaction time is very short, base on the uncertainty principle that large change in energy leads to short time interval. however, the observed alpha decay constant is about 1.3 × 1010 year, which is about the age of our universe. That's why we still able to find it at the beginning of nuclear physics : discovery of radioactive matter.
The reason for such a long decay time is due to the Coulomb barrier of the nuclear potential. since the proton carry positive charge, thus. it creates a positive potential wall in the nucleus. that potential not only repulse proton from outside but also the proton from inside which try to get out. thus, the inside protons are bounded back and forth inside the nucleus. due to the momentum carried by the protons, it has frequency 6 × 1021 per sec.
Due to the Quantum tunneling effect, the probability of tunneling is 4 × 10-40. which is a very small chance. But , don't forget there are 6 × 1021 trails per sec. Thus, the chance per sec is 2.4 × 10-18 . and the mean life time is inverse of the probability, thus it is approx 1.3 × 1010 year.
Tuesday, January 18, 2011
terminology
Nucleus : (noun) is the core of element, which contain protons and neutrons
Nuclei : (noun) many of nucleus
Nuclear : (adj) to relate something to nucleus. e.g. nuclear energy, nuclear plant, nuclear phsyics
Nucleon: (noun) is the thing make the nucleus, which is a single word. a nucleon can be a proton or neutron
Nuclide: ( noun) [from google translate : A distinct kind of atom or nucleus characterized by a specific number of protons and neutrons ] (what??)
Detector
there are 3 main principles on particle detection.
- by the ionization between particle and gas
- by the excitation of energy level
- by the detection of photon
here is a diagram from WIKI, which summarized
Friday, January 14, 2011
Type of accelerator (Ring type)
- the particle circulate inside the accelerator, so, it can be accelerate infinite time in principle.
- The space require is smaller compare with similar energy output Linac.
- particle can have every high energy
- high intensity of beam
- it can have some section only for linear motion with accelerate.
- it is not limited by the B field. since the narrow of the beam, a higher forcing B field can be applied.
particles identification
there are 3 main principles in PID.
- decay mood
- time of flight
- energy loss to surrounding
Sunday, January 9, 2011
Informations we can extract
- the number of particles counted at particular solid angle. ( when you have a unit sphere, the area on the surface is called solid angle)
- The polarization (spin)
- charge
- energy
- momentum (time of flight)
magic number
Thursday, December 16, 2010
type of accelarator I (Linac)
There are basically 2 types, one is called Linear Accelerator (Linac) , another type is called Circular Accelerator.
in fact, there are many other type of accelerator, as long as they can accelerate particle, by definition, it can be called as accelerator. for example, The vacuum tube in old day TV is an electron accelerator! However, most other type of accelerators can only speed up particle at low speed, not comparable to speed of light. So, in modern nuclear physics, we don`t use them. Nevertheless, the mechanism of them may be reviewed and other type of accelerator may be invented in future, who know!
so, far, all Accelerator can only handle charged particle.
Linac
The particle being accelerated in Linac is moving in a straight line. that is why the name Linear. Linac constitutes of many sectors, each sector is a mini accelerator, which speed up the particle by adding energy into it.
The simplest type of Linac is 2 parallel plate with a hole at the middle, and has the electric potential different V. when an electron passed through it, it will gain eV of energy and then speed up. so, if there is n sector, and each sector are identical, the final energy is neV. This LINEAR behavior also address the name.
Working Principle
Now, imagine you have many plates, when the particle passed plate 1, a voltage applied on plate 2 to speed up the particle. after the particle passed plate 2, you have to turn off the voltage and apply the voltage on plate 3, and the process go on. thus, the voltage on each plate is oscillating, which is the working frequency of Linac. Moreover, when the particle speed up, the time for it with in each section will be smaller and smaller, thus, the working frequency has to be increase and matching the particle speed. the other way around it, building each sector in different length, but this method will set a definite frequency of the Linac and the output energy.
The advantage of Linac is that :
1) it can produced continuous beam
2) less energy lost during acceleration. where all charged particle will radiate energy while accelerating.
The disadvantage is :
1) limited length, so the Maximum energy is limited
2) The working frequency has to be tuned so accurate. it is harder to operate a Linac.
Method
we have no choice but just bombard the nucleus with electrons, protons, neutrons, etc... if we are Alice, who become much bigger then our earth and touch the moon easily. How do we understand human world? we simply pick a human, hitting on each other, see what is going on, what is the result. If we want to know how elevator work, we put a human, let him ride on it and see the result. but sometime, we will accidentally, put a car in elevator.
so, Most nuclear experiment is SCATTERING EXPERIMENT.
and the machine to conduce this kind of experiment is called Accelerator.
Size and Unit
Let us transform ourself, like Alice in Wonderland, i guess Alice is just 100 times smaller. but this time, we goes much much smaller, become same same as an atom. Hydrogen atom, which is the smallest one, is about 1 meter hight, and Uranium is about 2 meters. and Alice, now becomes mush better then the earth and she can touch the moon easily.
how large is proton in this scale? it is just a diameter of our hair! and electron is still much smaller, so far, we believe that it is just a point, no size. so no matter how powerful your microscope, you never see it! which also means, electron has no internal structure. Thus, you may ask the structure of proton. um... we talk this later.
When someone want to talk about physics, he has to bring up ENERGY. that make his sound professional. and we are going to do the same. However, our unit of energy is different from day usage, like Calorie, or kilo-Watt-hour (kWh). we use MAGA-ELECTRON-VOLT (MeV). before we get some idea about these units. we should understand kilo [k] = 1000, maga [M] = 1000 X 1000.
1 Calorie, which is the energy require the raise 1 degree of 1 kg water. in a cold winter, say 10 degree. if you drink tap water of 350ml, then you lose about 9 Calorie. if you drink 350ml water at 60 degree. then, you gain, 17.5 Calorie. according to this website : If your body mass is 64 kg and you walk at a speed of 5.63 km/hr then you will burn approximately 4.6 Calories/minute - if you walk for one hour you will burn 60 × 4.6 = 276 Calories. well, not much help for the hot water.
1 kWh is equal to 3.6 mage joule. so, what is joule? joule is another energy unit, 1 Calorie = 4.2 kilo joule. Thus, 1 kWh = 860 Calorie = about 3 hour walk. next time when you check your electric bill, you can imagine how far you have to walk to consume this energy.
as you may see, 1 Cal can raise 1 kg water up 1 degree. how many water molecules in 1 kg of water? It is 3 × 1025 !! the world population is just 6 × 109. if this number is money, then every one is a billion billionaire!! So, you can see, each molecule only share very very little among of energy. in order to save some zero in front of 1. we use a very small unit. maga-electron-volt.
according to Einstein Energy-Mass equation: E = m c2, we found that a proton is about 940 MeV/ c2. which is to say, if we want to make a proton out of no where, we have to at least give 940MeV. um, pretty small compare to our daily life. But it is very big in nuclear physics.
from this, we can know electron mass is about 0.5 MeV/ c2.
the reason why we use "energy" unit on "mass", is not just because Einstein tell us we can do so, but it has a practical reason. We always deal with relativity and using MeV as a unit of mass bring huge convenient, both on calculation and imagination.
Objects of Interest
electron, proton , neutron, deuteron, tritium, etc... those are objects in nuclear, we call them "particle". the most simple particle in here is electron, proton and neutron.
The different between nuclear and atom is:
Nuclear core (sit in the center) + Electrons (moving around) = Atom
the mass of atom is almost contributed by nuclear. This is because the mass of proton is about 1830 times bigger than electron, and neutron's mass is only heavier a bit then proton.
There are many properties contained in each particle. there are electric charge, mass, spin, kinetic energy, etc... and the objective of nuclear physics is understand all these properties and how these properties affect the inter-reaction among them. for example, how a proton and neutron form a nuclear core in deuteron? how they attract each other?
these properties, some may say, are ASSIGNED to the particles. Basically, we can only measure the effect or the result from each interaction. we think, there is a FORCE to make particles able to INTER-ACT with each others. simple to say, when an electron meets another electron, they affect each other by ELECTROMAGNETIC force. but when consider an electron meet a neutron, they don't interact by electromagnetic(EM) force. in order to distinguish these. we assign an electric CHARGE to electron, and no charge for neutron.
so, basically, Nuclear Physics is study the PROPERTIES of particles and the INTERACTION among them.
There are 3 major forces/interactions, Weak force, EM force and Strong force. Until this moment, we only know the weak and EM force and not fully understand the strong. We neglect the gravity in here, because it is very weak and do no observable effect.
Force | Strength | Range |
Strong | 10,000 | 10-15m |
EM | 1000 | long |
Weak | 1 | 10-18m |

