Will New Russia is turning back to socialism? Victory Parade of 9th of May

The victory parade in Moscow on 9th of May is somewhat a chilling reminder of old soviet days. The parade comes after  the annexation of Crimea. 

Ok, we all know what Nikita Khrushchev did. After all he is the man who took out his shoe in UN while addressing the general assembly. He handed Crimea to Ukraine and after Putin's annexation of Crimea back to Russia,  Russian National pride is all time high.

 However this parade was quite similar to those conducted in the former USSR, which I used to watch since 1984. I was somewhat perplexed by this flag shown below behind the military vehicles.  It has hammer and sickle in it. And not only that. Flag on the left has CCCP printed on it, which is  USSR in Russian.

 Most interesting thing is the words used by the generals and soldiers. 

The Commanding General addressed the soldiers as comrade soldiers. Then the soldiers replied to him calling him "thovarish genaral" in Russian meaning comrade general. 

Then the General reported to Defence minister the readiness of the troops to the possession.  He addressed the minister as comrade minister and minister replied to him addressing as comrade general. 

Most intriguing part is that the minister addressed the  president putin as comrade Vladimir Putin and not as his excellency the president. 

Then Putin addressed the soldiers as  comrade soldiers. Is this normal? Or is it that Russia is firmly heading back to Soviet system with some sort of a mixed capitalist system like in China. In that case this day will be a memorable one. 

---ajith Dharmakeerthi 

Quantum tunnelling and Gamow Energy

Quantum tunnelling:

Quantum tunnelling also known as the barrier penetration, is the key to the occurrence of fusion reactions in stars. If the particle's total energy is less than the potential energy of some barrier it cannot pass that barrier. Think about throwing a ball over a wall. Unless there is sufficient kinetic energy to attain a height greater than the wall, there is no way the ball will reach the other side. Kinetic energy of the ball, once transformed to gravitational potential energy should exceed the gravitational potential energy of the wall.
However this restriction does not apply to quantum mechanics. We have to consider the wave properties of the particle in quantum mechanics. The amplitude of particle's wave function goes to zero only for an infinitely high barrier although the wave function associated with a particle is attenuated by a potential barrier.

As we know that the finite potential barriers exist in reality, the wave function inside and beyond the barrier is non-zero. Hence the position probability density is also non-zero. (position probability density).  Therefore there is a small but non-zero probability that a particle will make its way through a barrier, in such a case and even though that may appear impenetrable or insurmountable in normal circumstances. If we think about the ball again, if a ball and the wall were small enough for quantum properties to dominate over the classical scenario, it would be possible for a ball to reach the other side. That is even if it did not have enough kinetic energy to overcome the gravitational potential energy at the wall's top. This seems strange but this is precisely what happens during collisions of nuclei.

For the nucleus to be stable, the nucleons in a nucleus sit in a potential well surrounded by a Coulomb potential barrier of finite height and width. There is a non-zero probability of a particle with energy less than the height of the barrier would make its way from outside the barrier to inside due to barrier penetration to reach the nucleus.

The Gamow energy

The  barrier potentials do vary with separation, i.e. V is a function of r. For the Coulomb barrier, the penetration probability may be expressed in terms of the particle energy E, and the Gamow energy EG which depends on the atomic number of the interacting nuclei, and hence the size of the Coulomb barrier:

Therefor Gamow Energy:

where α is the fine structure constant ≈ 1/137.0.  and and C is Speed of light.
The rate of nuclear fusion therefore depends on the penetration probability of the Coulomb barrier. This penetration probability in turn is described by its Gamow energy.
A higher EG reduces the probability that the barrier will be penetrated. The Gamow energy measures the strength of the Coulomb repulsion, which determines the height of the Coulomb barrier.

The Gamow energy is named for George Gamow (1904–1968), a Russian physicist and cosmologist who escaped to the USA in 1934. His paper ‘The origin of chemical elements’ (1948) by Alpher, Bethe & Gamow attempted to explain much of astrophysical nucleosynthesis in the big bang and also predicted the existence of the cosmic microwave background radiation.

The Gamow Peak: 

The fusion probability as a function of energy for nuclei.  The energy at which the fusion rate is a maximum is called the Gamow peak. The region on either side of the peak in which the fusion probability is significant is called the Gamow window.

Ref: Stellar Evolution and Nucleosynthesis - Sean G Ryan, Andrew J Norton

Predicting the Abundances and Successes of the Standard Model

Predicting the Abundances: 
There are a few complications predicting the abundances. One of the complications is tracking the abundances of few dif ferent nuclei instead of just a single element hydrogen. Next problem is that neutrons are unstable when not in a nucleus. They have a half-life of about 11 minutes. Third, several light nuclei end products have very small binding energies, therefore delaying the freeze-out.

BBN has it's own shortcomings earlier on like not being able to produce the observed abundances of all of the element isotopes, primarily due to the unstable nuclei with atomic number A = 5 and A = 8. Therefore as Burbidge et al. (1957) correctly noted stellar nucleosynthesis caught attention of the astrophysicists. If we assumes that 4He is entirely of stellar origin, then we should be able to find places in the universe in which the 4He mass fraction 25% . The data for 4He ( The helium(Y) vs oxygen (O=H) abundances in extragalactic HII regions emphasized
the lack of low 4He regions. [ref: Olive (1999)] shows the fact that no such region with low 4He has been observed and that leads to a conclusion that BBN nucleosynthesis is responsible for 4He abundance and should be part of any cosmological model.

The element abundances depend on the number of baryons per photon, or on or  .
 Big Bang nucleosyntheis therefore makes very clear predictions for the
primordial abundances of elements created in the first half hour of the Universe's
existence. These predictions can be tested, and the overall level of agreement with
observations is one of the many successes of the Big Bang model. However, the
tricky part of the experiment is to determine primordial abundance of baryonic
matter that has remained in its primordial condition for the ~ 13.7 billion years
since the nucleosyntheis epoch.

Burles et al. (1999b) noted that, the predicted abundances of the light elements

 have been used to test the consistency of the hot big bang model at very early times (t ~0.01200sec). Fields et al. (1996) pointed out that the abundances of 4He and 7Li alone are su cient to probe and test the theory

and determine the single remaining parameter in the standard model, the baryon to
photon ratio.

Successes of the Standard Model

The assumptions that the standard model is based on are the laws of physics, which have been verifi ed at the present time by experiments, are also valid in the early universe. The cosmological principle described above holds. The temperature at early time t1 is greater than and contents of the universe are in thermal equilibrium.

It is suggested that (t1) is very close to 1. A baryon asymmetry is consistent with
observed radiation density.  It is assumed also that the initial density fluctuations gave rise to later formation of structures. The standard cosmology model nonetheless achieved success.

Close connections have been developed between theory and observations for Standard Big Bang Nucleosynthesis (SBBN), and observations are more and more reliable now. The BBN model leads to a deeper understanding of the creation of primordial elements and the predictions of the CMB. The most important of all is predicting abundances of   and explaining it through a single free parameter  .  The value of baryon density    agrees with other estimated values. Astrophysicists up to now used SBBN predictions and measured abundances to successfully estimate best values for cosmological parameters of baryon density  and baryon to photon ratio   . Generally one uses the low D/H ratio as the decent estimator for find for the baryon density. The next chapter will show that, the observed abundances of elements D, 4He and 7Li are close to the primordial abundances predicted by SBBN.

References:
1.E. M. Burbidge, G. R. Burbidge, W. A. Fowler, and F. Hoyle. Synthesis of
the elements in stars. Rev. Mod. Phys., 29:547{650, Oct 1957. doi: 10.1103/
RevModPhys.29.547. URL http://link.aps.org/doi/10.1103/RevModPhys.
29.547.
2. S. Burles, K. M. Nollett, J. W. Truran, and M. S. Turner. Sharpening the predictions of big-bang nucleosynthesis. Physical Review Letters, 82:4176{4179, May 1999b. doi: 10.1103/PhysRevLett.82.4176.
3. B. D. Fields, K. Kainulainen, K. A. Olive, and D. Thomas. Model independent
predictions of big bang nucleosynthesis from ^4He and ^7Li: consistency and
implications. New A, 1:77{96, July 1996. doi: 10.1016/S1384-1076(96)00007-3.

BBN - Reactions Explained

Deuterium bottleneck - At high temperatures and densities, according to Hawley and Holcomb (1997) neutrons and protons can fuse directly to form deuterium (also called heavy hydrogen) nuclei, or deuterons.

Deuterium is the isotope of hydrogen, and it contains one proton and one neutron

in its nucleus. The reaction that formed the deuterium is shown here is on of the first reactions

of key fusion reactions . The in this reaction represents a photon.This reaction liberates the binding energy (energy equal to the energy liberated when a nucleus is created from other nucleons or nuclei -Wikipedia)  of the deuterium nucleus in the form of photon. Deuterium then fuses with a proton or another deuterium as in here shown in the second reaction, 

 to form the helium nucleus 3He or as shown in below 3rd reaction, 

fuses with neutron to create a tritium 3H. As shown in following reaction 4 

 both these nuclei (3He and 3H) then react with additional particles, 3He with a neutron or a deuteron, and the tritium with a proton or a deuteron, to form 4He. This is the most common isotope in the universe and almost all helium in the universe was created in this nucleosynthesis epoch, shortly after the big bang.

We can fi nd that the equilibrium Hydrogen density is proportional to exp(B/kT) where B = 13:6eV is the binding energy of the hydrogen atom. The most strongly bound light nucleus is 4He, with binding energy B4 =28:5MeV . So most of the nucleons end up as Helium in equilibrium and that's why we should have Helium abundances now. As the universe cooled down and expanded di fferent nuclear reactions froze out, leaving the relic abundances of the stable nuclei.

Key Fusion Reactions:

Below are the Key fusion reactions of Big Bang nucleosynthesis taken from lecture

from Steven Weinberg:

4He is a very stable nuclei with close to 28MeV binding energy. However, a nuclei with atomic number A = 5 is unstable. Therefore the further fusion is rare with lower binding energies. However this would be overcome and the production of 7Li will proceeds through. These further reactions with Li production are shown here:

The weak interaction rates responsible for n - p equilibrium freeze -out at 

T ~0:8MeV . The neutron to proton ratio at this is about 1/6. However when taking

into account the fact that free neutron decays prior to deuterium formation, this

ratio drops to n/p ~ 1/7. Then the 4He mass fraction is  ~ 0:25.

Reference:

1. J. Hawley and K. Holcomb. Foundations of Modern Cosmology. Oxford University Press, USA, 1997. ISBN 9780195104974. URL http://books.google.co.uk/

books?id=eBFawfP8ak8C.

2.http://star-www.st-and.ac.uk/ kdh1/cos/cos17.pdf

3 http://en.wikipedia.org/wiki/Steven Weinberg

Big Bang Nucleosynthesis (BBN) -Historical background

Historical background: The early universe behaved like a nuclear explosion or like a fusion bomb, creating the temperatures required for the creation of light elements. After that first minute with the temperature close to perhaps a billion kelvins nuclear reactions started. Approximately 180 seconds after the big bang, the temperature of the universe was  according to Hawley and Holcomb (1997). The content of the Universe consisted of a dilute gas of free streaming neutrinos , photons ,
 electron positron pairs
 and trace amount of nucleons(the protons and neutrons) as noted by Boesgaard and Steigman (1985). The temperature and densities were still very high, but dropped sufficiently so that the nuclei of atom could remain stable. The creation of atomic nuclei through nuclear reactions called nucleosinthesis, thought to be commenced at this point. Hence, this period in the big bang is known as the nucleosynthesis epoch. Olive (1999) noted that Big Bang Nucleosunthesis (BBN) is the theory explaining the origins of the light elements D;3 He;4 He and 7Li and their primordial abundances. Ellis (2011) commented that, the theoretical framework for BBN is based on Friedmann-Lemaitre-Robertson-Walker cosmology and a network of nuclear reactions.

BBN requires temperatures greater than 100keV and corresponds to time scales less than 200 seconds. It was necessary to achieve a density n  . The current density of visible matter is

 and we can estimate  the current temperature of the universe as  ~ 10K. 

In the early Universe at temperatures T < or ~ to 1MeV , conditions for the synthesis of the light elements were attained. Weak interactions were in equilibrium at higher temperatures. The following processes fix the ratio of number densities of neutrons to protons. 

(a neutron plus a positive electron (positron)  create  a proton and an anti-nuetrino and vice-versa, a neutron plus a nuetrino create a proton and electron,  from a  nuetron  a proton, electron and antinuerino is fixed).

The ratio of neutrons to protons at equilibrium at temperature T is given by a Boltzman factor: 

where Nn and Np are number densities of neutrons and protons, delta m

 is the neutron proton mass difference,1.3 MeV. Olive (1999) notes that, when the temperature  the ratio of neutron to proton was

.

Reference: 

1. K. A. Olive. Primordial big bang nucleosynthesis. ArXiv Astrophysics e-prints, Jan. 1999. URL http://arxiv.org/abs/astro-ph/9901231.

2. A. M. Boesgaard and G. Steigman. Big bang nucleosynthesis - theories and observations. ARA&A, 23:319{378, 1985. doi: 10.1146/annurev.aa.23.090185.001535.

3. G. F. R. Ellis. Inhomogeneity eff ects in cosmology. Classical and Quantum Gravity, 28(16):164001, Aug. 2011. doi: 10.1088/0264-9381/28/16/164001.

The Thermal History of the universe - 2

Continuing from previous post: about the Thermal history of the universe. When the time is around

and a temperature of

the weak interaction (see previous post)  thought to be decoupled from the electromagnetic force. Now all four forces mentioned earlier were separated. During the transition the carrier particles of the uni fied electroweak force were transformed (hypothetically) into 4 new particles.
Three of them are called bosons

which acquired mass and the other one is massless photon. 

To discuss this further, according to Phillips (1994), it is generally accepted that, within the first nano seconds the universe was filled with a gas of fundamental particles
like leptons, anti-leptons, quarks, anti-quarks, neutrinos, ant-neutrinos, gluons and photons. We assume that quarks, anti-quarks and gluons annihilated and transformed to less massive particles when the temperature fell below . However, the number of quarks very slightly exceeded the number of anti-quarks. The small number of quarks remaining were thought to be responsible for the present number of protons and neutrons of the universe. when the temperature decreased further the heavier leptons and anti-leptons were annihilated as well.

When the cosmic time was

quarks formed neutrons and protons while 

Therefore between a millisecond to a second after the big bang the universe was consisted of electrons, positrons, neutrons, protons, neutrinos, antineutrinos and photons. At about 1s when

neutrinos started to decouple.

Soon after this, all of the positrons and most of the electrons were removed by annihilation of electron-positron pairs. This seems to have occurred when cosmic time was approximately 4 seconds and

. Phillips (1994) further states that, when 

t~3min and 

neutrons combined with protons to form light nuclei - Helium and other light particles, which lead to a universe with approximately 75% of its mass consisting of hydrogen and 25% of helium. 

After around 300,000 years later

and the temperature was around 4000k, it was a low enough temperature for the formation of stable atoms, and photons to decouple. Hydrogen and helium nuclei combined with electrons and

formed neutral hydrogen and helium atoms which lead to photons stopping to interact strongly with matter. The universe became transparent to electro-magnetic radiation which cooled down to about 3k at present time because of the expansion of the universe. This is the so-called cosmic microwave background detected by Penzias and Wilson. Olive (1999) claimed that, the connection between the BBN and the CMB is a key test to the Standard Big Bang Model.

About Penzias and Wilson: The accidental discovery of cosmic microwave background radiation is a major development in modern physical cosmology. Although predicted by earlier theories, it was first found accidentally by Arno Penzias and Robert Woodrow Wilson as they experimented with the Holmdel Horn Antenna. The discovery was evidence for an expanding universe, (big bang theory) and was evidence against the steady state model. In 1978, Penzias and Wilson were awarded the Nobel Prize for Physics for their joint discovery. http://en.wikipedia.org/wiki/Discovery_of_cosmic_microwave_background_radiation

Reference: 

1. J. Hawley and K. Holcomb. Foundations of Modern Cosmology. Oxford University

Press, USA, 1997. ISBN 9780195104974. URL http://books.google.co.uk/

books?id=eBFawfP8ak8C.

2. A. Phillips. The Physics of Stars. Manchester Physics Series. John Wiley &

Sons, 1994. ISBN 9780471941552. URL http://books.google.co.uk/books?

id=4SZpQgAACAAJ.

3. K. A. Olive. Primordial big bang nucleosynthesis. ArXiv Astrophysics e-prints, Jan.

1999. URL http://arxiv.org/abs/astro-ph/9901231.