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On the base of the astronomy and physics institute, which was formed in 1941 in Alma-Ata, the new Astrophysical Institute (APHI) was founded in 1950 thanks to academician AS USSR V.G. Fessenkov.


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N a t i o n a l s pa c e a g e n c y o f t h e R e p u b l i c o f K a z a k h s t a n N a t i o n a l c e n t e r o f t h e sp a c e r e s e a rc h a nd tec hnol ogy V . G . F e s s e n k o v A s t r o p hy s i c a l I n s t i t u t e
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Dubovichenko S.B.

Thermonuclear
processes of the

Universe
Physical models and results, mathematical and calculations methods, computer programs

Almaty 2010


PACS 26.; 25.20.-x; 24.10.-i; 21.60.-n; 21.60.Gx; 02. E d i t o ri a l b o a rd T.A. Mus sab aev (chairman) M. M. Mo l d a b e k o v , Z h . S h . Z h a n t a e v , L . M. C h e c h i n T h e b o o k wa s re c o m m e n d e d t o t h e p u b l i s h b y t h e Sc i e n t i f i c a n d T e c h n i c a l C o u n c i l o f N C S R T N S A R K , S c i e n t i f i c Co u n c i l o f V . G. F e s s e n k o v As tr o p h y s i c a l In s ti tu te a n d P re s i d i u m II A ( R K) S c ien t if ic co ns ul ta nt Doctor, professor Blokhints ev L.D. (MSU, Mo sco w, Ru ssia ) S c i e n t i f i c r e d a c to rs Doctor Uz ik ov Yu. N. (JINR, Du bna , Russi a), doctor, professor Burkova N.A. (KazNU, Almaty, Kazakhstan) Reviewers The academician NAS RK, doctor, professor Boos E.G. (PTI), academician NAS RK, doctor, professor Takibaev N.Zh. (KazNPU), academician IEA RK, winner of the state awards RK, doctor, professor Danaev N.T. (KazNU), academician IIA (RK), doctor, professor Shmygaleva T.A. (KazNU), academician IIA (RK), doctor, professor Chechin L.M. (APHI), doctor, professor Duisebaev A.D. (INP), doctor, professor Burtebaev N.T. (INP)

Dubovichenko S.B. Thermonuclear processes of the Universe. Almaty: Fessenkov Astrophysical Institute NC SRT NSA RK, 2010 -530p.
ISBN 978-601-278-331-5

The book considers some theoretical questions of nuclear astrophysics thermal energies and light atomic nuclei. For the analysis of reactions is used potential two cluster model of light nuclei with classification of states by orbital schemes. On its basis photonuclear processes in 2 3 6 7 9 12 24 ,3 4 3 4 p H, p H, p Li, p Li, p Be and p C, and also H He H He, H He and 4 12 He C channels are considered and astrophysical S - factors corresponding to them are calculated. It is shown, that used methods allow to describe well available experimental data in the field of astrophysical energies. Dubovichenko S.B., APHI, 2010 ISBN 978-601-278-331-5


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( ) .......................................... () ......................................................... () .............................................. FOREWORD (Autor)......................................................... ................................................... .............................................. SHORT CONTENTS........................................................ ..................................................................... 1. ............................... .................................................................... 1.1 ...................... 1.2 - ..................................... 1.3 CNO - ........................................... 1.4 .................................. 1.5 ..................................................................... 1.6 ......................................... 1.7 ............................................................... 2. .............................. .................................................................... 2.1 .............................................. 2.2 S - ............................ 2.3 ...................... 2.4 .................. 2.5 .............. 2.6 ................................... 2.7 .......................................... 3. S - 2 ...............................
9

13 16 18 20 22 26 30 33 40 40 41 46 51 55 57 60 64 70 70 74 78 82 85 86 89 90 95


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.................................................................... 95 3.1 .......................... 97 3.2 S - ............................. 103 3.3 ........................................................... 110 .............................................................. 128 4. 3 ......................................... 129 .................................................................. 129 4.1 ........................ 130 4.2 S - ............................. 138 4.3 S - ............................................................... 141 4.4 1/2+1/2 .......... 166 .............................................................. 203 5. p6Li .............................................................. 204 .................................................................. 204 5.1 ............................ 205 5.2 ................................................. 206 5.3. .................................................................. 211 5.4 ................................................................. 213 5.5 S - ............................. 219 .............................................................. 221 6. S - p7Li .............................................................. 223 .................................................................. 223 6.1 .................................................................. 224 6.2 ................................................................. 227 6.3 S - ............................. 232 6.4 ................................................................. 236 6.5 S - p7Li ............................................................... 246
10


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7. 9 ......................................................... .................................................................. 7.1 .................................................................. 7.2 ................................................................. 7.3 S - ............................. 7.4 S - ............................................................... 8. p12C ............................ .................................................................. 8.1 ............................ 8.2 ................................................................ 8.3 12 ................................................................. 8.4 S - ............................. 8.5 12 ..................................................................... 9. S - 34, 34 24 .................................................................. .................................................................. 9.1 ........................ 9.2 ........................... 9.3 ............... 9.4 S - ............................. 9.5. ................................................................. 10. 4 12 .......................................................... .................................................................. 10.1 .......................... 10.2 ............................................... 10.3 ......................................... 10.4 S - ...........................
11

267 267 267 269 275 278 307 307 307 310 314 318 326 337 337 338 343 347 351 358 377 377 378 379 385 390


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............................................................... ............................................................. CONCLUSION ............................................................... ........................................................... ....................................................... ACKNOWLEDGMENTS ................................................ 1 .......................................................... 4 4 ..................................................... 2 .......................................................... 9................................. 3 .......................................................... .................................................................. 4 .......................................................... .................................................................. ..............................................

394 398 402 406 408 410 412 412 450 450 486 486 497 497 509

12


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- , , , . , . , (p + 2H) (4He + 12C) . , , . ( ), , ( ), ( ) . , . b+c S - b(c,)a, a b c. S - ( ).
13


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S - , . , , , , , S - - , . : 1) S , , ( ). 2) S - - . , . , , () . (, p + 2H p + 3H) , . 14


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15


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17


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19


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FOREWORD
Author
Nuclear astrophysics is one of the youngest branches of the modern astrophysics, which practically represents the sphere of application of the results obtained in experimental and theoretical physics to the astronomical objects with a view to explain their nature, energy sources, age and chemical composition peculiarities [1] .

Owing to the modern development of astronomy and astrophysics we have a general understanding of the Universe ­ of its evolution and structure within the distances of the order of 14 billion light years. The observations of the Universe reveal the areas of very compact matter concentration and extremely large distances between them which seem to be "empty". However, all this "empty" space is filled with gas and dust matter, atoms and various kinds of radiation including neutrino. Furthermore, the modern theories about the Universe involve such concepts as dark matter and dark energy, which determine its mass and characterize its mode of Expansion. The matter which concentrates in the stars and planets of the visible Universe and which forms the gas and dust clouds consists of nuclides, i.e. the atoms of ninety two chemical elements having different numbers of protons and neutrons in their nuclei and ranging from hydrogen to uranium. All the diversity of nuclear composition of the Universe is made up of several hundreds of nuclides and the current level of science ­ nuclear astrophysics ­ allows explaining in general the history of their formation and their relative occurrence. The world around us also consists of various chemical elements and, presently, it is generally recognized that all the elements forming the Earth, the Sun and the whole solar system were produced in the course of the stellar evolution. Our Earth is
20


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one of the eight planets of the solar system and our Sun is a common stable star of our galaxy ­ the Milky Way. According to the current estimates the Milky Way only comprises several hundred billion stars and even at present time, i.e. 14 billion years after the formation of the visible Universe, which may contain hundred billions of similar galaxies, new stars can be born [2].

21


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. . ­ ­ . [2] .

. , . , , . , S - . , .
22


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­ ­ , . . , 3 9 . ( 10, 1.4 ) . CNO - 9 ( 13 , 1.2 В 1.4 , ) - . (12 13N) 8 - , ( 1.2 В 1.4 ) 17,18F , () , . CNO - . ­ , , 10 - . 15 , , 10 , , , . , , . [1,2]

23


. .

+ 3 4 +
2

+ 4 6Li + , + 4 7Li + ,

3

[3,4] S - 4 9 . " " . , , . 16 , - 5, 6 7 6,7Li 9Be 10B
10,11 7,8

B

B

11,12



.
24


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- CNO - . - CNO - , ( 5 ),
3

He + 3He 4He + 2p .

.

25


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. , , . - [2] .

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26


. .

- - , , , , . .3 9. ( 10, .1.4) , . CNO - 9 ( 13 , .1.2 В 1.4, .. ) ­ . 12 13N .8, (. .1.2 В 1.4) 17,18F, - (), , . CNO - . ­ , , .10. 15 , . , , , , , -, . , , , , , .. . , , [1,2]

27


. .

+ 3 4 +
2

+ 4 6Li + , + 4 7Li + ,

3

[3,4] S - .4, .9. , " " . , , , , . , , .. - , 16. 16 , , -, . , 6,7Li 9Be 10B , .5, 6 7
28 7,8

B


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10,11

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11,12

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- CNO - , ( 5 ),
3

He + 3He 4He + 2p .

, .

29


. .

SHORT CONTENTS
The progress in studies about the Universe is substantially associated with the achievements in the nuclear and elementary particle physics. It turned out that the laws of microcosm allow understanding what is going on in the Universe. This unity of micro- and macrocosm is a remarkable and edifying example of the unity of Nature [2] .

Before proceeding to the main results we would like to present a summary of the book. In the first chapter we will consider briefly and simply all the major thermonuclear reactions which may take place in the stars at different stages of their formation and evolution. Then we will expand on the analysis of the main thermonuclear processes involving radiative capture ­ processes in which two colliding particles fuse together to form one particle and emit - quantum. They are mediated by electromagnetic interactions which somewhat simplifies their consideration from the theoretical point of view. Further on, in addition to the properties of bound states of light atomic nuclei participating in thermonuclear reactions, we will consider the principal characteristics, in particular S - factors, of radiative capture of protons and other particles by such nuclei at astrophysical energies. Now we are going to give an overview of possible reactions in three major thermonuclear cycles for stable stars of the Main Sequence and then indicate which processes will be considered in this book and which ones will be analyzed in the nearest future. The first cycle is the proton - proton chain, which includes five two - particle processes (according to the input channel) mediated by strong or electromagnetic interactions, three of which belong to radiative capture processes. Two such processes will be considered in the present book and the results will be given in chapters 3 and 9. The other five reactions of this cycle (in total
30


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there are 10 of them as it is shown in fig. 1.4) are mediated by weak interactions and we will not consider them either in this book or in the nearest future. The stellar CNO - cycle consists of 9 similar reactions (13 in total, see table 1.2 В 1.4, four of which are mediated by weak forces), six of which involve radiative capture. The first of these reactions (12 13N) is considered in chapter 8 and the two last reactions (see table 1.2 В 1.4) lead to a formation of 17,18F nuclei which are not p - shell nuclei and the applicability of the potential cluster model (PCM), which was used for all further calculations, has never been tested for such cases. Therefore, only three of remaining CNO - cycle reactions will be considered in future. The triple alpha process represents two reactions, one of which involves a two - particle radiative capture, which is analyzed on the basis of the potential cluster model in chapter 10. As a result, we have 15 basic thermonuclear reactions with two - particle input channels mediated by strong and electromagnetic forces, 10 of which are the radiative capture processes, with 4 being considered in this book, the next 4 to be considered in future and two, seemingly, out of consideration within PCM. In addition to the abovementioned processes there are some other radiative capture reactions which supposedly took place at the prestellar stage of evolution of the Universe, i.e. within the first seconds of its existence. They include, for instance [1,2]: + 3 4 + or
2

+ 4 6Li + , + 4 7Li + ,

3

which could take place during the primordial nucleosynthesis [3,4] and the astrophysical S - factors of which are considered in chapters 4 and 9. In conclusion we would like to note that the general title of
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the book "Thermonuclear processes in the Universe" is chosen so as to account for the future expansion of the book. In the nearest future we are planning to finish the consideration of all possible thermonuclear reactions of radiative capture type on light nuclei, and first of all the four reactions directly associated with the thermonuclear cycles. The results obtained will be published in the second edition of the book which presently deals with nine capture reactions. In total there are 16 basic radiative capture processes, which lead to p - shell nuclei and can be considered within PCM, including the primordial nucleosynthesis reactions and reactions of the type 6,7Li or 9Be 10B considered in chapters 5, 6 and 7, and
10,11 7,8

B ,

B

11,12

.

They are all out of the standard thermonuclear cycles of pp or CNO - chains. Then we will consider the remaining thermonuclear processes of proton - proton and CNO cycles which are associated with the rearrangement of channels (in total there are 5 such reactions), for example
3

He + 3He 4He + 2p . these proclight nuclei schemes in cluster sys-

And it is supposed to carry out the analysis of all esses on the basis of the potential cluster model for and classification of orbital states according to Young case of states forbidden by Pauli principle in some tems.
32


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Introduction
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35


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[7] 10-5 . , [2]. , , [5], . , , . , .

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37


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38


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39