Chapter 643 The Atomic Bomb Theory Is Complete! (Part 2)

Chapter 643 Atomic Bomb Theory. Completed! (Part 2)

After deciding on the internal grouping.

Chen Nengkuan and others stopped procrastinating and immediately began to calculate their own data.

"."

At this moment.

Looking at the blank calculation paper spread out in front of him, Chen Jingrun's mood could not help but surge and stir.

He is actually a very introverted person. When he meets a crowd of people, he will be nervous and blush. In the words of later generations, he is very "socially anxious".

For example, a few years ago.

Because of his excellent academic performance in Xiamen University, he obtained the qualification to teach at Capital No. 4 Middle School and was sent to Capital No. 4 Middle School to give a speech.

That speech was not just a sharing of experience, but also related to Chen Jingrun's subsequent work at No. 4 Middle School.

As a result, when facing dozens of students in the audience, Chen Jingrun was too nervous and panicked, causing the prepared speech to be incoherent.

Under such circumstances, Capital No. 4 Middle School decided not to accept Chen Jingrun and sent him back to Xiamen University.

So you can see such a work resume in Chen Jingrun's personal profile in later generations - [In 1953, he graduated from Xiamen University and was assigned to teach at Capital No. 4 Middle School. In 1954, he served as a data clerk at Xiamen University. ]

Although Wang Yanan, the president of Xiamen University, still took good care of him after being "returned", and pushed him to the Institute of Mathematics of the Chinese Academy of Sciences as an intern researcher four years ago.

But to be honest, Chen Jingrun's life was not very happy.

Because under his seemingly simple inner appearance, he has always had a passionate heart.

His favorite poem comes from Li He's "Thirteen Poems of Nanyuan", which is the famous "Why don't men take Wu Gou and take over fifty states of Guanshan?"

This poem was excerpted no less than fifty times in his life. The study, entrance, and bedroom were all posted with banners excerpted by hand, which shows his love for this poem.

However, due to his personality, Chen Jingrun knew very well that he might not have the opportunity to carry a gun on the front line in this life. No, it should be said that he didn't even have many opportunities to contribute to the country.

The result was unexpected.

Not long ago, the organization suddenly found him and transferred him from the Department of Mathematics of the Chinese Academy of Sciences to the 221 Base far away in the Jinyintan Grassland.

What surprised him even more was that the project responsible for this base was actually

the atomic bomb? !

He probably would never forget the day he arrived at the base, when the base director Li Jue patted him on the shoulder and said:

"Comrade Jingrun, the motherland needs your brain."

So from that day on, Chen Jingrun made a decision:

He would do his best to expand the territory for the motherland in the smokeless battlefield of mathematics!

The fountain pen is his weapon, and the calculation paper is his shield. He calculates whatever data the base needs.

In the past, he had assisted Xu Yun in many small battles as a member of the mathematics group.

But today is different.

What they are facing today is a decisive battle at the Huaihai level!

Although it seems that there is only one step left, the bald guy who clamored for the advantage has "recovered lost ground" and received it on the other side.

Therefore, I must be extremely alert and never repeat someone's mistakes.

"."

Then Chen Jingrun took a deep breath and focused his attention on the manuscript in front of him.

He and his teacher Hua Luogeng were responsible for the calculation of explosion pressure, which is also a more complicated parameter in the atomic bomb.

Because the critical mass of the same type of nuclear material is inversely proportional to the square of the density, the critical mass depends to a great extent on the conditions of explosion compression. This is a concept that has been mentioned a long time ago - although it is estimated that not many people remember it.

And this compression condition cannot be evenly distributed in space, so the highest explosion pressure value must be calculated.

This is actually not difficult to understand.

Just like when you cook rice with a pressure cooker, the internal pressure of the container has a limit. If it exceeds the maximum limit, the pressure cooker will turn into Melody's head and explode into countless pieces in an instant.

The same is true for the explosion pressure value. The only difference is that the direction of this explosion pressure is controllable and calculable.

In fact, the research group at the base had already calculated the explosion pressure parameter before today, but the accuracy of that parameter was limited, so Chen Jingrun had to push it back two decimal points.

Although [pushing back two decimal points] seems simple, it is actually very difficult. Let's put it this way, look at the balance of your bank card, and think about how difficult it is to add two zeros to the integer position.

So soon.

Chen Jingrun wrote a formula on the paper:

[△P=0.084/R+0.27/R+0.7/R].

This is the basic calculation formula for the overpressure of the shock wave of a point explosion, which is the most basic concept in the field of shock waves.

However, this formula mainly describes the longitudinal wave with a strong discontinuity of air parameters, which is not suitable for nuclear explosion conditions, so Chen Jingrun has to make some minor changes to it.

Swish swish swish——

One minute later.

A simple formula with some changes appeared on the paper:

[△P=ρ1(Du1)At(u2u1)12g04g000g00μg0νR+ρ1(Du1)At(E2+u222E1u122)13g23g101g00μg0νR+p2Au2tp1Au1t19g33g202g00μg0νR+21g29g303g00μg0νR +12g10g000g00μg1νR】

Then looking at this formula, Chen Jingrun secretly set a time for himself to solve it:

three minutes!

While Chen Jingrun and others were calculating their respective tasks.

Xu Yun on the side also dutifully poured a glass of water into Da Yu's tea cup:

"Come on, Da Da, have a drink of water."

no way.

As an outsider in the non-atomic energy field, Xu Yun really couldn't do much with the computing tasks they were currently responsible for - after all, the span of expertise was really too large.

If it were someone else, Xu Yun would still think about whether he could get started in computing, but now he is partnering with a humanoid self-propelled supercomputer larger than

If he insists on helping, there is no guarantee that he has just calculated a certain result, and it has already been calculated three or five steps later.

Therefore, Xu Yun could only honestly build a water pouring machine to ensure that larger water cups would not bottom out.

In fact, Xu Yun believes that his work is quite important - no matter how powerful the CPU is, it needs water cooling to match it, right?

Our water-cooling level is not to mention the second and third generations of Dragon God, but it can still be regarded as a Valkyrie GL360. It costs hundreds of dollars.

Well, An and Yu are really strong together!

And opposite Xu Yun.

Da Yu was stunned for two seconds when he heard the words, and then took the water poured by Xu Yun:

"Oh, okay, thank you, Comrade Xu Yun."

"Comrade Yu, you're too polite. This is a trivial matter."

When Xu Yun heard this, he immediately waved his hand and at the same time poked his head towards Da Da's arithmetic paper:

"Da Da, where have you been?"

When Yu Yu heard this, he glanced at Chen Nengkuan and others beside him, and deliberately lowered his voice in order not to disturb other companions:

"You see, the phase data of secondary fission have been calculated and two parameters have been optimized."

Xu Yun nodded slightly.

Although he does not know much about the field of atomic energy, he still knows some contextual concepts - although knowing these concepts is actually meaningless.

Just like many military fans in later generations have a clear understanding of some firearms modules, but when it comes to the development of weapons, they are completely confused.

The phase data of secondary fission is greater than the secondary cylinder parameters that need to be calculated. This is an internal progressive structure of the atomic bomb, mainly involving high-energy neutron flow.

Its structural design requires about seven to nine parameters, seven are the minimum and nine are the best. In future generations, it will also be a standard problem that requires supercomputing to solve.

However, the name Yu itself represents a miracle, and no matter how difficult this problem is, it is still easier than the hydrogen bomb, so Xu Yun is not too surprised that Yu can continue to calculate.

No, to be precise it should be.

It takes so much time to calculate only two parameters, but it is a bit slow.

From Xu Yun's point of view, I don't know why, but Yu Yu seems to be a little out of shape today.

If I remember correctly, Da Da did not fall in love at the base.

However, things like status are not static. It is normal for academic masters to occasionally get low scores, so Xu Yun did not delve too deeply into it.

After filling Da Da with water.

He quietly left his seat and pushed the wheelchair to Lu Guangda's side:

"Director Lu, how are you doing here?"

"Oh, it's Xiao Xu."

Lu Guangda was originally staring at a calculation with furrowed eyebrows without saying a word. When he saw Xu Yun, his expression suddenly brightened:

“Here, come on, look at this problem—I’m stuck.”

Xu Yun blinked:

"Stuck? Director Lu, I remember you are calculating the optimization of the six-factor formula, right?"

Lu Guangda nodded:

"That's right."

Students who know Baidu should know it.

U235 releases approximately 1V per fission. The energy released comes from mass loss. The value can be calculated through Lao Ai's mass-energy equation.

There are two types of U235 fission: spontaneous fission and induced fission. Spontaneous fission has a half-life, and induced fission requires external supply of neutrons.

If certain conditions are met, U235 can be self-sufficient - this is the so-called critical and supercritical concept.

The purpose of a reactor is to maintain criticality, and the purpose of a nuclear bomb is to be as supercritical as possible.

The specific numerical calculation is a four-factor or six-factor formula, which is the fuel reproduction ratio, neutron reproduction ratio, neutron reproduction ratio, neutron utilization rate, neutron loss factor and burn-up rate.

This is also a very complicated problem, otherwise Lu Guangda would not be responsible for the calculation himself.

Xu Yun had learned a bit about the six-factor formula in his elective course back then. Although he couldn't say he was very familiar with it, it was at least within the scope of what he could understand.

So he stretched his head and glanced at the paper a few times, but soon he was slightly startled:

"Eh? Director Lu, don't you have no problem?"

At this time, Lu Guangda saw a series of formulas written on the calculation paper in front of him. His ideas seemed to belong to his own school, and only some derivation processes were left to reach the final result.

Although these derivation processes are a bit complicated, to Lu Guangda, when the idea is determined, it is no different from elementary school mathematics.

"Hey, who said it was a problem with the six-factor formula? I thought of something else during the optimization process."

Xu Yun said "Oh" (second sound):

"Oh? Tell me?"

Lu Guangda quickly pulled the chair next to him away, so that Xu Yun had enough space to place the wheelchair, and explained:

"Look here, it's the neutron multiplication ratio."

"When our atomic bomb explodes, neutron capture will occur, and it can happen about three times during fusion."

"So I was thinking, if we can synthesize a nuclide and allow neutron capture to occur completely, then what will happen?"

Xu Yun was stunned.

Lu Guangda seemed to be in the mood, and he quickly pulled out a new piece of calculation paper:

"For example, U235 has 92 protons and 143 neutrons, while U236 has 144 neutrons and can capture up to 146."

"What if we have the technology to allow it to continue capturing neutrons? For example, 160, 180 or even 200?"

"Didn't Jensen propose the concept of magic numbers in 1948? I personally think that if we start from this perspective, this new nuclide may have some extremely unique stable states."

"Of course, this is just my personal guess, after all, the Coulomb barrier is a big problem."

Perhaps because Lu Guangda was too involved, he didn't notice that Xu Yun's expression had become a little dull at this time.

WTF

Lu Guangda actually thought of this?

All the students who were not pissed off by their junior high school chemistry teachers should know this.

Elements with proton numbers greater than 103 are called superheavy elements. Superheavy elements are extremely unstable, and their half-lives are generally only a few minutes at most, and only a few milliseconds or even microseconds at the shortest.

But this is not absolute.

Maria Mayer, the 1963 Nobel Prize winner, discovered while working at Argonne National Laboratory that the number of nucleons in high-abundance isotopes has a regularity:

Atomic nuclei with nucleon numbers of 2, 8, 20, 28, 50, 82, and 126 are particularly stable.

So she named these numbers magic numbers.

Later, Jensen successfully explained the existence of magic numbers under the assumption of strong spin-orbit coupling, and proposed that the existence of magic numbers reflects that the nucleus has a shell structure:

When magic numbers exist in the nucleus, the nucleons fill a certain energy level, and no nucleons transition to a higher energy level, so these nuclei are quite stable.

If we use the number of neutrons in the nucleus as the horizontal coordinate and the number of protons as the vertical coordinate, and mark all stable and radioactive nuclides on the nuclide map, then we can clearly see that the known atomic nuclei in nature are distributed along the β stable line, forming a continuously distributed peninsula in the plane formed by the number of neutrons and protons as coordinates.

And the magic numbers are 2, 8, 20, 28, 50, 82, and 126, which are all at the top of this peninsula.

Finally, based on this theory, a famous theory or conjecture emerged in the physics community:

If there is an atomic nucleus that is a double magic nucleus material with neutrons and protons filling the closed shell, then wouldn’t its nucleus be so stable that it can support an ear without collapsing?

This theory is the famous island of stability conjecture.

In the future life that Xu Yun traveled through.

The more recognized stable island nuclides are the nuclides with Z=114 and N=184, which are the so-called element 114.

However, at that time, the chemical community had only synthesized element 118, Og, and 11 was still being synthesized.

Of course.

Seeing this, some students may be surprised:

No, 118 is greater than 114, which means that nuclide 114 has been synthesized, so why is the island of stability still a conjecture?

The reason is very simple. Don't forget the N at the end, which is the number of neutrons.

Just one Z is not enough, it must be Z+N=298.

So far.

Scientists have obtained seven isotopes of element 114, ferroxene, with the smallest atomic weight being 284 and the largest being 290 - and the atomic weight predicted by the island of stability is 298.

Therefore, this theory is still a long way from being confirmed.

But

Once the nuclide Z=114, N=184 is really discovered and confirmed to be in line with the island of stability theory, then it will be fun.

Not to mention the impact of this new nuclide on the physical and chemical model, just one of its applications is enough to make people's heart beat faster - its lifespan is as long as 1049 years, and it is a nuclide that can be used for controlled nuclear fusion.

Although this is only one of the theoretical directions, no one can know whether it is true or false, but it is undeniable that its research value is still very high.

Take a step back.

Even if controlled nuclear fusion is not considered, the theory of stable island is also very helpful for the cognition of microscopic particles.

Now the rabbits have a series electrostatic accelerator, and what they lack is actually some theories.

Just like you have a lot of modern weapons in your hands, it seems that you can go up to F2A, but in fact, if you can have one or more correct tactical systems, the effect on the battlefield will obviously be higher.

So Xu Yun thought about it and asked Lu Guangda:

"Director Lu, do you know the shell model?"

Lu Guangda turned the pen twice:

"Shell model. Is it the atomic nuclear model proposed by Mayer and Wigner?"

Xu Yun nodded:

"Yes, it is that model-Mayer is also the originator of the concept of magic number."

Shell model.

This is a nuclear model proposed by Meyer, Wegener and Jensen in 1949. They later won the Nobel Prize in 1963 for it.

This model states that similar to electrons in atoms, there are many shells in the nucleus.

Corresponding to different energy levels, protons and neutrons move in different shells and "jump" back and forth, and they also satisfy the Pauli exclusion principle.

The reason why a noble gas is chemically stable is that its outermost shell is filled with electrons, so it has greater stability. Similarly, when the shell in the nucleus is filled with protons and neutrons, it will also have greater stability. stability.

The shell model better explains the stability of some nuclides, and can also better predict or explain the spin and parity of the ground state of the nucleus.

Take oxygen 17 as an example.

8 protons fill 3 proton shells, 8 neutrons fill 3 neutron shells, and there is 1 extra neutron.

That is, the total angular momentum of the inner full shell is 0, and the total parity of 8 protons and 8 neutrons is +1.

This means that the spin of the oxygen 17 nucleus and its parity are completely determined by the spin of the 9th neutron.

Xu Yun then drew a simple diagram on the paper and said:

"Director Lu, the current shell model has proven its accuracy. If you introduce this model into your idea, what do you think will happen?"

This time.

Lu Guangda thought for a long time and then said carefully:

"Protons and neutrons must obey the Pauli exclusion principle. At the same time, the electromagnetic repulsion between protons is offset by the strong interaction force, and the semi-classical binding energy formula holds."

"That is, if the Coulomb barrier can be broken, it should be fed back into the change in the magnetic moment of the atomic nucleus—at least a partial change?"

Snapped!

Xu Yun smiled and snapped his fingers:

"bingo!"

According to the idea of ​​​​the shell model, the inner layer of an atom can be regarded as a sphere.

The nuclei in the outer valence space bulge high, just like a towering iceberg rotating at high speed around a large water ball.

Because protons are positively charged, this "iceberg" will also bring "tidal waves" of electric current.

Therefore, the larger the magnitude of the iceberg, the larger the energy level of the tide will be.

This part of the changed energy level is actually the Coulomb barrier that Lu Guangda was hesitant about, which is part of the magnetic moment of the atomic nucleus.

At the macro level, or at the data level, the value of this change is.

Electric quadrupole moment.

In today's case where the base is used for tandem accelerators, it is still very simple to verify this change.

After all, most of the nuclides after No. 102 in later generations were successfully synthesized inside the accelerator.

After figuring this out, Lu Guangda's expression suddenly became much more joyful.

After all, for people like him, if a problem remains unresolved, they will be troubled and unable to sleep.

I saw him looking at Xu Yun with gratitude, and patted Xu Yun's shoulder hard:

"Xiao Xu, thank you for clearing up the confusion."

Xu Yun's injury was not fully healed at this time. After being patted on the shoulder by Lu Guangda, he couldn't help but bared his teeth:

"Director Lu, you are too polite, it hurts, it hurts, it hurts."

Lu Guangda couldn't help laughing.

Then Lu Guangda brought his mind back to reality and began to calculate the optimization content of the six-factor formula.

But now we have reached this point.

Whether it is Lu Guangda or Chen Nengkuan, the rest is basically just a matter of mathematical derivation.

After the theoretical ideas are solved, the test is purely about personal calculation ability - and this is a quality that almost everyone in today's theory group possesses.

Three hours later.

Bada——

Yu Yu gently put down the pen in his hand and rubbed his aching eyes:

"Huh, it's finally done."