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Z,ELt DOVICHIya-B., PAIZER; P. (moscov~ "On Radiation Generated by-Strong Shock Waves." ,report presented at the First All-Union Congress on Theoretical and Applied Mechanics, Moscow, 27 Jan - 3 Feb 1960. ZZLIDOVICH. Ya.B., almdemik (Mooltva) ProgTOOD Madolu direct traneformation of heatlinto electricity. Pis. v shkole 20 not50-32 6-0 160, (MIRA 13:11) Mermoelectricit7) ZZLIDOTICH, Ya.B. Scattering by a singular potential in the perturbation theory and in pulse representation, Zhur.ekspA teor.fix- 38 no-3: 819-824 * 16o. (141U 13 t 7) 1. Inetitut, teoretichookoy iekoperimental 'my fisild Akademil nauk SSSR, (Scattering-Mysica)) Wi- 83729 S/056/60/036/00OZ/0 2104" f"; B019/B-070 AUTFOR., Zelldo ich, Ya. B. TITLE: Existence of Now Isotopes'of Light Nuclei and the 'Equation of State of 11autran2ji PERIODICAL- Zhurnal eksnerimentallnoy i teoreticheskoy fiziki, Vol- 38, 110. 4, PP- 1123-1131 TEXT: P. E~ Nemirovskiy (Refs. it2) studied the possible existence of isotopes in the range of 8.L-Z!L-84, and A,-T, Baz' (Ref. 3) in the range of IT~;A L-40. Both predicted the existence of unknown isotopes of which 020 has been discovered in the meantime. In the present paper, the auth-or studies the limits of stability of light nuclei, and predicts the 8 12 13 15 17 191 existence of the following isotopes. He , Be 0 , B , B , B C16 - 20"N18 - 21, Mr?20' 0 ~X` 0 The table on page 1124 gives the isoto_,sa predicted by Nemirovskiy, Baz', and the present author. The presont author has made a theoretical study of the existence of heavy nuclei consisting only of neutrons. He first mentions that if such nucle-J. exi,.-t Card 1/2 2 83719 Existence of New.Isotopes of Light Nuclei and S/056/60/038/004/012/046 the Equation of State of B0110070 at all, their density must be esentially smaller than that of the usual nuclei. He-has, therefore, studied the properties of a neutron liquid of low density. This problem,to that of a Fermi gas with resonance i5teracticr- of the particles, -the eneray of the gas beinC proportional to &j2j7~ ( W densi-ty of the gas). For finding out the equilibrium density and the coupling energy) the author bau studied the affective radius of tu~,e nuclear forces and the interaction in the state with 1 / 0. The accuracy of the calculations is not sufficient to det-armino the siEn of tho en-eTC,-1- and to answer the question of the existence of neutron-nuclei. The author Land and thanks A. I. BazI, V. I. Golldanskiy) P. E. ilemirovskiy for discussions; and D. V. Grigarlyov ~o help in the Rr work. There are I table and 16 ref renc6s, 8 Soviet e d 8 US., SUBMITT:KD: October 22, 1959 Card 2/2 83772 S1056/60~03!Y00310301045 BOO /B06, 6 ?00 AUTHOR: Zelldovich, Ya-B. TITLE: The Theory of Instable States PERIODICAL. Zhurnal eksperimental',noy i teoreticheskoy fiziki, 1960, Vol. 39, No- 3(9), PP, 176-780 TEXT: Exponentially damped states such as occur in al2ha dec y are de- scribed by a complex energy value whose imaginary part indicates -the de- cay probability. The wave function of such a state increasen exponential- ly with respect to the large-distance modulus. Thus, the ordinary methods of normalization, perturbation theory, and expansion in a series of eigen- functions cannot be applied to such a state, In the present papers the author develops a perturbation theory which yields an expression in the form of a quadrature for the change in the decay probability and the mean energy in the case of arbitrarily small potential changes. If the state is described at the first momen'. by a certain wave function, the wave function then approaches, in a long time intervalg an exponentially damped function of a certain amplitude. This amplitude is also given in quadra- tures. When treating the problem of energy perturbation and of the aq)litude Card 1/3 7- .............. 83772 The Theory of Instable States S/056/60/039/003/030/045 B~06/BO63 of the state exponentially damped in time, the author uses a term that plays the role of the norm of this state: lim 2 exp(-ar2)r2dr. First, he considers a particle moving in a aj'O T . I 0 spherical barrier potential (a - particle in the Gamov theory of alpha decay), and.shows that the perturbation-theoretical expression (11) for 6E; (where Ec = E can be derived in an elementary way and may 2 ~2 be written down in the simple form 6E1 f )e bVd T/ d-z. Then, he considers the non-steady problem, and studies the initial wave function ~P(r It-0) T(r) with the asymptoti.- solu tion t(r,t) = Aexp(-1E`t)X(r) + O(r,t)' 3/2 where O(rt) decreases for small r like t- For this purpose, he com pares the function *(r,s) - --I. r,t)OQxP(i.rt)dt, suggested by 11. A. Dmitriyev, -with the ooeffioienta A and a from the soluticn J(r,s) a X(r)l(s-El) + *1(rs), Finally~ he generalizes the formulas Card 2/3 83772 The Theory of Instable States 3/056j6O/O39/003/030/045 Boo6/BM3 obtained to states with 1/1. He thanks G. A. Drukarev, A. B. Migdal, V. A. Fok, and L. A. Khalfin for discussions, and N. A. Dmitriye]Lfor his helpful assistance. N. S. Krylov is mentioned. There are 6 references: 5 Soviet and 1 British. SUBMITTED: April 16, 1960 Card 3/3 M21 5/056/60/039/004/039/048 Boo6/BO56 o?4-, bYo AUTHOM Zalldoviah, Ya, B., Perelomov, A. M. TITLEt The Effect of Weak Intertintio4 tUpgn the Electromagnetic Propertiesl'of Particles PERIODICALs Zhurnal eksper.ima ntallnoy i teoreticheskoy fiziki, 1960, Vol- 39, No. 400), PP. 1115 -1125 TEXT: It was the purpose of the present work to investigate the contri- bution made by weak particle interaction to electromagnetic interaction. In the introduction; the pr -oblem as such is discussed, and the contents of the paper is given. In section 2, the graphs (Figs. -1-6) which make a contribution to the electromagnetic properties of.the neutrino, the leptons (e andp,), and the baryons are investigated; the contributions are determined n orders of magnitude of the weak interaction constant for individual cases. For this purpose, two variants of the theory are studiedt that of four-fermion interaction and that of the intermediate, heavy, charged X-boson. In several cases, the order of g is reduced by the introduction of the X-boson, I.e., the affect 'is increased. In gection 3, Card 1/5 - - - -- --------- 84~21 The Effect of Weak Interaction Upor the B/056/60/039/004/0"'19/048 Electromagnetic Proportion of Particlea 13006/BO56 the general electromagnetic properties resulting from the Lorentz and gradient invarianoes of the theory, from the probability and the theory of universal weak interaction, and from the theory of the two-component neutrino are dealt with. In section 4, the interaction within the frame- work.of the perturbation investigated, and the order of ,magnitude of the divergence of the integrals obtained is determined. The characteristic electromagnetic properties of the particles are numerically estimated. In the case of baryons, one assumes that strong interaction replaces weak interaction already at momenta of the order of M n (Mn nucleon mass). In section,5, the experimentally observable particle scattering effects are discussed, especially the polarization of particles in the scattering plane, because this effect is related to parity non-conservation. Neutrino scattering by nuclei as well as the effects of new electromagnetic properties in nuclear physics are dis- cussed. Section 6 deals with the.problem of the possible modifications of the initial assumptions on weak interaction, by adding the derivative of the neutral currents to the ordinary derivative of the charge currente. The conditions under which the additional term does not lead to a decay -_Card 2/3 The Effect of Weak Interaction Upon the S/056/60/039/004/039/048 Electromagnetic Properties of Particles B006/.BO56 and cannot be observed experimentally, are s,~udied, as well as the effects which are due to the scattering of electronsYby protons. The authors thank A. M. Brodskiy, G. M. Gandeltman, B.L. Ioffq, L. B. OkunIq and K. A. Ter-Vartirosyan or discussions. Ya. A. STorodinskiy, A.I.Akhiyezer IL. N. Rozentsveyg, and I. M. Shmushkevich are mentioned. There are 6 figures and 21 referencest 10 Soviet, 2 Italian, and 9 PS. SUBMITTEDt March 23, 1960 Card 3/3 W& kg~ 86930 S10561601039100510491051 Boo6/BO77 bqoo AUTHOR: Zell TITLE: The Dipole Moment of Inatable Elementary Particles PERIODICAL: Zhurnal eksperimentalinoy i teoreticheskoy fiziki, 1960, Jol, 39, No- 501), PP- 1483 1485 TEXT: The conclusion following from the theory of combined inversion of L'ZiPLandauLthat.Ahe elementary part i cl es possess no dipole moment cannot be applied to instable particleal this is shown in the present "Letter to the Editor". If a particle with spin and dipole moment is considered while the time axis is reversed it is obvious that there is no T-invari- ant relation, and considering the effect of the reversion of the time axis to an instable particle (that emits particlea and spontaneously transmutes other.partiole) one can see at once that this proof of the nonexistence of dipole moments can not be applied to such par- ticles. In order to examine the relationship between the instability of particles and the dipole moment the author considers the two reactions of a neutral spin-1/2-particle. Ao;=�B+ + C_ and A0j:tDo + Eo. The first Card 1/2 86930 The Dipole Moment of Instable Elementary S/056/60/039/005/049/051 Particles B006/BO77 reaction is assumed to be a virtual and the second a real decay. Using the results of a previous work (Ref-3) it can be shown that the viola- tion of parity (assumed to be necessary for this reaction) together with the conservation of the T-invariance in the instable particle Hamiltonian leads to the appearance of a dipole moment that is to an apparent-violation of the T-invariance. This result agrees with that of von Behrends (Ref.4) who investigated the decays A - n + y an6L A - p + He also ended up with a solution having terms that apparently contra- diet the T-invarianae disregarded the T-invariance of the applied Hamiltonian. There are 4 references; 2 Soviet and 2 US. SUBMITTED: September~7,-1960 Card 2/2 AI, 88457 S10561601039100610491063 B006/BO63 AUTHOR: Ze 1 dovi ch,_ -Ya 1__B TITLE: The Form Factor of P3 and Ke3 Decays PERIODICAL: Zhurnal eksperimentallnoy i teoretiche8koy fiziki# 1960, Vol- 39, No. 6(12), pp. 1766-1769 TEXT: The decay of a K-meson into a pion and two leptons may be ascribed to the weak four-fermion interaction with AS = 1. In this case, the decay proceeds via an intermediate state of a baryon-antibaryon pair. The momenta of the K-meson and the pion (p K, p.) are small compared to the baryon.masses %. Hence, the velocities of the K- and n-mesons are assumed to be the characteristic quantities. In the rest eyetem of the K-meson, the pion can reach a Velocity Of 0-870. The author discusses a hypothesis according to which the four-velooity of K- and n-mesons (U ' ud enters K symmetrically into the expression for the matrix element of the interaction between K- and n-mesons and the lepion current. As usualp the matrix Card 1/3 �457 The Form Factor of and K Decays S1056 607039100610491063 '~k 3 e3, I)- B006/BO63 element of the process is formulated by Ri - IV T ra(1+t5)Tj). Thu a pe velocities u K and u n are symmetrically introduced into this relation. The expression for the vector current, which corresponds to this hypothesis, reads as follows: Va = (P(-u en) IUKa + Una] . The form factor 9 depends on the invariant, i.e., the product u K U ' UK. = PK./mK U7ta ~ Pna/mn. The conclusions to be drawn from the fact that the divergence of the vector current vanishes are studied forthese formulations. It is shown that div V = 0 holds only in the approximation of the isotopic invariance (that is to say, if the same massis assumed for charged and neutral pions). The assumption of div V 0 and different masses of n+ and no (as done by Weinberg et al. - Ref. 2 and Marshak et al. - Ref- 3) leads to certain difficulties, 9.g., an incorrect expression for the n e3 vector current., Finally, the results obtained by G. M. Gandellman and the conclusions to be drawn from the above-described hypothesis for the reaction K+ P+ p + - + e + +V-4no + e+ + V p Card 2/3 88457 The Form Factor of K and K.3 Decays S10561601039100610491063 AL3 B006/BO63 in the Feynman perturbation theory are discussed. B. LO Ioffe, L. B. Okunt, 1. Y&. Pomeranchuk, and G. M. Gandellman are thanked for discussions. There are 8 references: 5-Sovietf 2 US, and I Italian. SUBMITTED:. July 20, 19.60 Carli -3/3 82752 S/053/60/071/004/002/004 B004/B056 AUTHORS: Zeltdovicho Ya. B., Gi~xtjhtoyn# So 8 a TITLE: Nuolehr Reactions in Cold Hydrogen. I. The Mesonic Catalysis 17 PERIODICAL: Uspekhi fizioheskikh nauk, 1960, Vol. 71, No. 4, Pp. 581 - 630 TEXT: The authors proceed from the catalysis of nuclear reactions in hydrogen by g-mesons, which was discovered in 1957 in Berkeley by L. W. Alvarez et,al. (Ref, 4). This phenomenon had been predicted also by A. Do Sakharov (Ref. 2) and Ya. B. Zeltdovich (Ref- 3). A systematic survey Is given.of the theoretical papers dealing with muon catalysis, and the possibility of a nuclear synthesis in cold hydrogen by means of "piezonuclear reactions" under high pressure is dealt with. The follow- ing reaction equations are mentioned: p + p d + e+ + ~ (2.2 Mev) (I); + P (4 Mev) B + d He + 7 (5.4 'Aev) (II); d + d lie + n (3-3 Mev) (III); 3 Ile + 7 (24 Mev) 4 Card 1/4 82752 Nualear Reactions in Cold Hydrogen. 3/053/6o/o7i/004/002/004 I, The Mesonic~Catalysie B004/BF,56 d + t - lie + n (17.6 Mev) (IV); p + t He + (20 Mev) (V)~ and 4 4 t +.t - He + 2n (10 Mev)'(VI). The quantum-mechanical tunnel effect is 4 discussed, and it is stated that with the interatomic distances existing in ordinary-molecules) no nuclear reaction' occureg but that such a.reac- tion becomes possible if the electron is replaced by a V -meson. Part 2 describes the experiments carried out in Berkeley (Ref . 4) and in Liver- pool (Raf- 5). Part 3 deals with the catalysis of nuclear reactions in hydrogen by means of g-mesons$ viz.: 1) The formation of the pg mesic atom; 2) The formation of pplL mesio molecules; 3) The transition of the g-meson from a proton to a deuteron; 4) The formation of pdg- and ddp-mesic molecules, and 5) nuclear reaction in mesic molecules. In part 4 the mesic molecular processes in hydrogen a-re dealt with on the basifj of Ref. 17. The adiabatic approximation for ordinary molecular processes is diacuaoed, a preoine dofination of the adiabatic approxima- tion for hydrogen mesio molecules is derived Fig. 69 appendix 1) a calculation of the levels of mesic molecules Rable Ily Vigo. 7,81, and of the binding energies (Table III) is given; transition of the p-moson from a light to a heavy isotope (Tables IV, V)g the scattering of mesic Card 2/4 82752 Nuclear Reactions in Cold Hydrogen. 5/053/60/071/004/002/004 1. The Mesonic Catalysis B004/BO56 atomson nuclei (Table VI),,the formation of miesic molecules (Table VII)v and the transitions among the levels of mesio molecules are discussed. Furthermore, the calculated probability for the various mesic molecular processes are compared with experimental data, and in this way agree- ment? at least as regards the order of magnitude, is found. Part 5 deals with the nuclear reactions in mesic molecules. The following reaction constants are eriumerated: CIII - 2.10-16 CM3/sea; CIV - 2.10-14 CM3/sea and'C,, 1a25-10-22 OM3/sec, and,for the pr9bability of the nuclear reaction, the equation w,.- CJ'a( 0)12 (C - reaction constant, G(O) = value of the wave function at a nuclear distance R - 0) (Tables VIII, IX) is written down. The nuclear reaction 11--'.the pdg and ptp mesic molecule is then discussed. In part 6 it is stated that no continuous nuclear reac- tion occurs. Part 7 mentions further experimental research work in the field of the p-catalysis as being desirable. In appendix II, a calcula- tion of mesic molecules with the same nuclei, and in appendix III a calculation of the spin states of mesic molecules is given. The authors Card 3/4 82752 Nuclear Reactions in Cold Hydrogen. S/053 60ZO71100410021004 I. The Mesonic Catalysis B A56 mention papers by Panovskiy (Ref. 24) and A. B. Migdal (Ref- 44). There are 9 figures, 9 tables, and 44 references: 17 Soviet, 16 US, 6 British, 2 German, 2 Italian, 2 Japanesep and 1 Swiss. AUTHORS: TITLE: PERIODICAL: S/0,53/60/072 /002/002/005 B006/BO67 Bazl, A~ I.~ Golldarskty,, V, I., and Zelldovich. Ya.B, Some Isotop;~s of Light Nuclei UEipekhl f1z1chq9k1ikh nauk, '1960, Vol, 72, No, 2, pp. 2144 - 234 TEXT: At present about 300 isotopes of light nuclei (Z!:'L36) are -;f -which abundant experimental material has already been ,311ected. The present paper gives a survey of these data, After a sh~)rt Int::oduction the neutron-deficient isotopes (Z> N) are dealt -1-h in chapter 2. Their properties can be predicted by the fact wl t - which follows from charge invariance - that the properties of two iso-top-ically conjugate nuclei (nucleus AZ 1Ni la the isctopically 1 conjugate nucleus of nucleus' A,Z N if Z_N zin d 11 - Z 2 1 2 1 2 ;.-xar-.tly coincide up to the Coulomb corrections and the corrections fn~r the neutron-proton mass difference. Since these corrections are relatively easy to consider, the main properties of the isotopes can Card 1/3 Some Isotopes of Light Nuclei S/053/60/072/002/00?/005 B006/BO67 dete.-mined with Z> N from the known properties of the isotopon with X> Z. Fig. I givos a scheme of the difference of the binding energy of the Z-th neutrons in the nuoltvas (A A-:Z) and the bindtng energy of the Z-16-h prolvon in the nucle~.zs (A;.Z~.. In a simt-lar scheme Fig. 3 illustrates the region of 'he stable nuclei. The mcst promising method of producing neutron-deficient isotopes of light nuclei are the react-ions (pxn) and (He3,.tn)., as well as reactions induced by multiply chargt.~d ion bombardmont. New physical phenomena are assumed to be obael-vable in noutrGri-4,41"'ifint nuclol, proton and two-proton radio- act-ivity; these phenomena are dealt with in part 3 of tho 1),,Iper in which among others the region -where such phenomena may ocour, Is bri.efly outlinod, and th -a ..n roperties of two-prcton radioactivity are described. The reaction NO -,014 f2 i~~ discussed more thoroughly. 17(18?) S-921(22?) 25(24?) 29'(28?5, 33(34?) j48. r ~ Mg 7 ~ , S , A! Ca , T ,42 44(43?) 46(47?) 53(54?) 63(62?) 67(66?) Fe , Ni , Zn ; G,59(58?), Se j Kr are also counted among the 2p-active nucle 4~ In part 4 'he nuclei Card 2/3 Some Isotopes of Light Yuclei S/053/60/072/002/002/005 B006/BO67 with high neutron excess are dealt with, In this case 'above all problems of neutron binding energy in the nucleus are discussed (Fig. 6 shows En as a function of Z for a large number of N-values). Also experimental results are presented and discussed. The possibilities of an experimen- tal determination of the bineutron (reaction (n2,a) e.g. N14.i n2--s B'J 2+a +13.2 Mov, n2j, 2n decay onIpassage ofn 2 throu h tter and meaourement of the neutron directional correlation, Fig-75 amr1e, diacussed. Furthermore experiments for determining 0 and HO are dis- cussed. In part 5 considerations are made on the stability limits and a five-page table containing a survey of various propertleB tN,A,(MQA), E p , En9~E PO T1/2P ) of isotopes with-neutron excess as well as of neutron- deficient electrons for the region 2- Z!!~=40 is given which is highly valuable for practical work in this field. P. E. Nemirovskiy and A. T. Varfql~ ~re mentioned. There are 8 figures, 1 table, and 25 references: 14 Soviet, 10 US, and I Canadian. Card 3/3 ZELIDOVICHA-Ye.- B.-, -Dro "Thaory of the detonation and formation of abnormal shook waves for which the Chapman-Janguet conditions are not effective," "Emission of light by i9hook waves and their Btructur*00 To be submitted for the Scientific Research, National Center of-International Colloquium on Detonation Waves- Gif-sur-Yvette (Seine-et-Oise), France, 28Aag- 2 Sep 1961. Institute of Chemical Physics, Aoademj;.of Sciences USSR. 3091 S/1;5/61/002/003/001/009 _9 0 r4 1yo J 6 IF) E030/E111 AUTHORs Zelldovi - V-S. TITLE Chain reactions in burning flames an approximate theory of flame velocity PERIODICAL: Kinetika i katali.z, v.2, no*3W ig6i, 305-318, TEXT: This article was presented at the All-Union Conference on Combustiom January 10, 1961. The test theories hitherto have led to exact differential equations which can be solved, in general, only by numerical integration for each case. Here, a series of approximate theories are developed for each type of flames arid these are used to give physical insight into the process and to provide interpolation formulae for regions intermediate between those for which exact formulae exist. All are based on the relations from heat theory, 2 T b - T - RT b Q where Tb is the temperature of burning and Q the activat'lon energy, and the Michelson relation for the distribution of temperature by diffusion in the reaction zonei Cnrd 1/5 30917 Chain reactions in burning flames S/195/61/002/003/001/009 E030/Elll T = To + I(Tb - T0)- exu/D (1) where* x is spatial coordinate, To initial temperature; u, burning velocity, D thermal diffusion coefficient. The reaction velocities are introduced from the kinetics of the processes, and by using the Frank-Kamenetskiy integration method Ref-7t D.A, Frank-Kamenetskiy,,Diffusion and Heat Transfer in Chemical Kinetics) Izd-vo AN SSSR, 1947) one obtains the quantity of substance in the reaction zone, and the burning velocity, The four considered cases are as follows- 1) Unbranched chain reaction, in which the forming of active'centres does not continue in the products of burning (it stops in the reaction zone). In this case the formula for burning velocity given by the expression U -Q/RTb V Dke a2 (8) is identical with that of Spalding (Ref 5: Spalding, Phil. Trans. Roy. Soc. v,249, 957, 1956) apart from ;~~2- which must,therefore be introduced as a multiplier in all the subsequent approximations- Card 2/5 'WIq5/6l/oO2/oo3/001/009 Chain reactions in burning flames E030/Elll 2) Unbranched chain reaction with excess of substance forming active centres,,in which case the forming of active centres continues in the products of burning. Let A be the initial substance, B the active centres, and X any reacting molecule; then A + X 2B + X (9) The transformation of A i nto end-product C is given by the reaction: A + B C + B and depends on B. For a flame velocity dependent on activation energy according to Arrhenius, 4 2 _(Ql + Q2)/RTb 2 2 u = D A Xk k e 2cx CX (18) 0 1 21 112 agreeinx again with Spalding, but for q2- , and giving velocity independent of pressure.. However, for excess of B, u varies as pe-(QI+Q2)/4RTb Card 3/ 5 Chain reIactions in burning flames,- S/1190M 1/002/003/001/009 E030/Elll 3) Branched chain, no sharp edge to reaction. Also in this case the velocity u is independent of pressure; it depends only on the kinetics of development of the chains, and not on the kinetics of the reaction of transformation of the initial substance in the final one by activity of the centreso In connection with the experiments.of S.Ya. Pshezhetskiy and his team (Ref.11i V.L. Cheredinchenko, I.N. Pospelova, S.Ya. Pshezhetskiy, Zh. fiz. khimil, v.32, 2674, 1958) the influence of the initial concentration of active centres was considered. Normally the concentration of active centres may be small. If this is called B. and the flame velocity u1, then if further active centres are introduced - by ionizationj say - up to quantity Bm actually in the reaction zone, one obtains a flame velocity u', and the expre SS4 on (u 2 Bo - I - (41) U1 ) + ~7m As the quantity of active centres introduced is known, the important quantity Bm may be measured, i.e. the concentration of centres at which under rea1 conditions (BO = 0) the reaction in Card V 5 Chain reactions in burning flames 30,917 s/195/61/002/003/001/009 E03O/EllI the flame arises. 4) Highly branched reaction, in whick.-recombination of centres is principally responsible for evolution of heat. For strong recombination (under high pressure and,low burning temperature), U varies as (rX)- where r is the recombination constant. For weak recombination, 2 u = h A0 Dr X (73) where h is a dimensionless number6 Ackhowledgments are expressed to G.I. Barenblatt and V I. Kondratlyev for their interest in-the work. There are 4 figures and 11 references: 9 Soviet-bloc and 2 non- Soviet-bloc. The English language reference reads as follows: Ref.5. Spaldingg Phil, Trans. Roy. Soc., v.249, 9057, 1956. ASSOCIATION: Institut khimicheakoy fiziki AN SSSR (Institute of Chemical Physics, AS USSR) SUBMITTED: February 4, 1961 Card 5/5 ZELIDOVICH Ia,B9 Symmetric compooite model of otrongly interacting elementary particleo,,- Zhur, ekop. i teor, fiz, 40 no.1.319-323 Ja 161. (MIRA 3.4:6) (Particles (Nuclear phyeics)) AUTHOR: TI TLE: S/056/61/040/002/037/047 B,112/B214 ZelldoviCh, Ya. B. Theory of formion masses PERIODICAL: Zhurnal eksperimentallnoy i tooreticheakoy fiziki, v-40, no. 2j 1961, 637-640 TEXT: The particle mass can be determined from the interaction of the particle with dissimilar or-similar particles. The resulting mass of the par~t,icle may in general also come out to be infinite. In order to obtain a finite massq it is necessary to subject the interaction formulation to important limitations. A theory of the fermion mass is discussed in the present paper, It is based on Dirac's equation for a particle of nonvanishing rest mass. The four--dimensiunal state vector (wave function) breaks up into two two-dimensional spin vectors ~T For a vanishing rest mass of the particle, Dirac's equation is reduced to two independent equations for (p, and ~ whi--h describe the motion of Card 1/2 Theory of fermion masses S/056/61/040/002/037/047 B112/B214 a system of particles with oppositely directed spin orientations ("right particles" with spin+1/2 and "left particles" with spin -1/2). In the general cased the maes-appears as a factor in the Lagrango operator and.characterizeB the relationship between the "right" and "left" particles~ Particles of finite mass may be considered to be superpositions of ~Ileftll and "right" partioles~ The case of an interaction is considered which canbe schematically characterized by the symbols Q + It is found that the mass of I a given particle with the wave functioney, 7, appears in the resillt of four-fermion interaction only when the particle enters the interaction in a two-fold way by means of T and This result is in 'contradic- tion with a principle of In'. Gell-Mann and R. P. Feynman, due to the fact that the particle possesses a polarization different from V/0. L. D. Landau, B~ L. Ioffe, L.-B.~ Okun', and I. Ya. Pomeranchuk are thanked for discussions. There are 2 figures and 7 references: 1 Soviet-bloc and 3 non-Soviet-bioc.. SUBMITTED: September 3, 1960 (initially) (Vovember 11, 1960 (after revIsion) Card 2/2 ZELIDOVICH, YaIB. Un3table particle in the Lee model. Zhur. eksp. i teor. fiz. 40 no.4-1155-1159 AP '61. (MIRA 14:7) (Nuclear models) (Quantum theory) ORIBCV, V.N.; ZELTOVICH, Ya.B.; PERELOMOV, A.M. Maximum charge for a given mass in the bound state. Zhur. eksp. i teor. fiz. 40 noM1190-1198 Ap 161. (KERA 14:7) (Nuclear reactions) (Particles (Nuclear physics)) Al" 28763 S/056 61/041/003/016/020 B125 102 o ~0' /Sw) AUTHORS: Zelldovioh, Ya. B., Smorodinskiy, Ya. A. TITLE; The upper limit of neutrino, graviton, and baryon density in the universe PERIODICAL: Zhurnal eksperimentalinoy,i tooretichookoy fiziki# v- 41, no, 3(9)~ 1961t 907-911 TEXT: To estimate the maximum energy density of neutrinos, gravitons and baryons in the universe the gravitational effect of these particles on the expanding universe has been investigated by the authors According to B. M. Pontekorvo and Ya. A. Smorodinskiy (ZhETF, 41, 239, 1961) it is very difficult to determine the cosmic neutrino density. Direct tests have shown that the mass-energy density in the form of neutrinos may be 104 to jo5 times higher than the rest-mass-energy density in an ordinary form. The authors, and also F. Raines, have already shown that these estimates depend on hypothe 'ses concerning the neutrino spectrum. Another method for calculating the maximum energy density is based on determining the gravitational effect and fits-all unknown, weakly interacting fields, also Card 1/4 2876, 10 01056J611041100310161020 'The upper limit of neutrino ... B125/BI02 for the density of high-frequenoy oscillations of the gravitational field (gravitone According to G. M. Oandellman and V Pinayev (ZhETPe a? 1072P 1959~'j the bromeatrahlung of gravitons is 1 times smaller than the radiation of V-; pairs. For the suggested estimate, the density Q of' all kinde of matter-energy determines the past of the universe. The critical density Qk Of the matter-energy) which has been introduced by the authors, characterizes the transition from an open to a closed model of the universet at Q Qk f however, this expansion will change over into contraction. The times T counted from the instant of maximum density of the universum until now LTG 40 f ollows V [(k + V) arctg k 11, k (2q + q Q/2Qk' T is.calculated for resting matter and a pressure p 01 r' is calculated according to L. D'. Landau for negligible rest mass, i.e., for particles moving at vel,oDity of light and P 613 denotes the energy Card 2/4, The upper limit of neutrino 28763 s1r)56161 /041/003/oi 6/020 B125/B102 density). For T 10 10 years, one obtains -T> 0-4 and) therefrom, qt*5 and -28 30 Q< 2-10 g/om . An independent investigation yields q el%O for distant galaotics systems. Equal results are obtained in a third estimate of the maximum density by studying the star densityin the galaxies. It is possible that the density of neutrinos, gravitons, eto., in the universe is higher than the mean nucleon density observed (10-29 g/cm3) but more than 10 to 20 times. The similarity of 1 Or29 g/om3 for ordinary matter suggested a comparatively young age of the universe.- At equal order of magnitude of neutrino mass and nucleon mass densities, 'he value for the density will be smaller than _ 10-29 glow3p and correspond to - jo-5 nucleons per cm3. The number of nucleons may be much larger than the given value since the gravitational mass defect A M of a star after the gravitational colldpee may be of the same order of ma,3nitude as 'he sum of the rest masses of thenucleons contained in "he star. At present, there is no correct theory on gravitational callapsos. L. D. Landau and Ye. M. Lifshits have esbimated the critical mass to be 76% of the solar mass. When a gravitational collapse of.s. star occurav the energy might be emitted in the form of neutrinos and antineutrinos. The mean nucleon Card 3/4 S1056 /61/041 /00,3/016/020 The upper limit of neutrino ... B-1 2 /3102, 5 density in collapsed stars will be no more than 10 to 20 times higher than known,densities of ordinary nucleccns. All these eii'.imates are only correct for not too early collapses. There are 15 rafereivies: 9 Soviet and 6 non-Soviet. The four most recent reforeniiia -.o Eiigli8h-language publications read as follows: F. Reines, C. L. Ccwar,, JX,q F. B. Harrison, A. D. Me. Cuire, H. W. Kruee, Phya. 117~ 159, 1960; H. Y. Chin, P. Morrison. Phys. Rev. Lett., M. Gell-Mann. -~, 53, '1750, Phya. Revo Lett. 6,,709 1961. F. Hoyle. Pro~~. Ylhya. 1, 1961. SUBMITTED: April 14, 1961 Card 4/4 WN T-M - ZELIDOVICH, Ya.B. Correlation of electron and positron polarization in relativiB4,.-ic pairs. Zhur.ekspA toor.M. 41 n'o.3s9l2-913 3 161. (1,MU 14:10) (Electrons) (PositromB) 267111 S/056/61/041/005/026/030 0 7/ 9 6 -317 B102/B138 S AUTHOR: Zelldovich, Ya. B. TITLE: Equation of state at ultra-high densities and its relativistic limitations PERIODICAL: -Zhurnal eksperimentallnoy i teoreticheakoy fiziki, v. 41, no- 501), 19619 1609-1615 TEXT: The author develops a relativistically invariant theory to describe the state of heavy stare after gravitational collapse. The theory of neu* tron condensation (L. D. Landau, Ze. Sow. Phys., Ij 2851 1932) and the approximation of rigid nucleon repulsion lead to results which are in contradiction to the theory of relativity. From special relativity the inequality 3p'-6 results, where p is the pressure and a the energy density which includes the part icle I s rest mass. - (3p < E f or free non- interacting particles, 3P - F_ for an electromiLgnetic field). In the theory proposed here 3p > E- is possible and p - et is the limit. As an example, a classical vector field with mass, interacting with classical. point charges at rest, is considered. For Card 1/5 26711 S 056/61/041/005/026/038 Equation of state at. ultra-high... 'B102/B138 2AL St i S Ld's, (2,1) L TB -3%- 8n OAA 0-rh 0, Flt aAk ax, - aAj / axh. -- -------- (with o I and the metric A 2 A2+A2 A iAo 0 iyt, m p4, thq mass of the k 4 4 field quantum) the field e ation* U14 aAl A, + 4. (2.4) ail, is foundl its solution is Y-ge74'/r, ;t-0. The interaction energy of two charges is given by gr rl(r 2) = 92 epr12 /'121~ energy and 2 2/ 2 nE Mn + 2ng n Ii (3-5) p =.-aE,/3(1/n) = 2ng 2n2/,,2 (3.6). From this it can be seen that for large densities, n, p -F-. For a meson mass m much less than the baryon mass M the coupling constant is in the range Card 2/5 C_ 7,921TV Pi. 26?32 S/05 61/041/005/026/038 Equation, of stat' ultra-high... B102YB138 AO (m/M) 2 < g2 1. The -paper was discussed in April 1961 Card 4/5, IMAM 26711 5/056/61/041/0()5/026/038 Equation of state at ultra-high... B102/B138 in Nor-Amberd at a physics school organized by the Inatitut fiziki AN Armyanskoy SSR (Institute of Physics AS Armyanskaya SSR). The author thanks G. S. Saakyan for discussions. There are 10 references: 7 Soviet and 3 non-Soviet. The two references to English-language publications read as follows; A. G. W. Cameron. Astroph. J., jjO, 884, 1959; E. E. S,alpeter. Ann. of Phys. 11, 393, 1960. SUBMITTED,. May 312 1961 Card 5/5 25335 S/020/61/138/006/011/019 a 4, 3 9,6-6 21 3104/B214 AUTHORS: Zelldov -Ld- ~i ~Ya. B., Academician, Kormer. S. B., Sinitsyn, _T1. V.-ga-nd-Yu-s-hko, K. B. TITLE: An investigation of the optical properties of transparent substances at superhigh pressures PERIODICAL: Akademiya nauk SSSR. Doklady, v. 158, no. 6, 1961 1336 1333 TEXT: The propagation of strong shook waves in tranaparont inedia permitu_~_ to study the properties of substances at pressures of some thouaande or millions of atmospheres (Zelldovich et al., DAN 122, no, 1, 48(1958)~ At pressures not too high if the compressed substance remains transparent throughout its thickness the refractive index may be determined geometri- cally. The authors first studied water, plexiglass, and glass. A diagram of the experimental set-up with which -the reflection of light by the shock wave can be determined, is shown in Fig. 1. The reflected rays II - V wqre recoided by a fast photochronograph. Water was found to re- main trausparent under pressures of 89 144 thousand atmospheres. Glass become8 opaque at a pressure of 200,000 atmospheres. The exact values 'Card 1 103 25335 S10201611138100610111019 An investigation of the optical... B104/B214 for water are collected in Table 1. In the discussion of the results the authors used the data of V. Raman and K. S. Venktaraman (Proc. Roy. Soc., 171, 137 (1939))and gave the following relation for the temperature and density dependence of the refractive indext n = 1-334 + 0~334(~-I) - 1.90-10-5T~ (1), T being in OC. Fig. 3 shows graphically a comparison of the values of n calculated by (1) with those determined by geometrical methods. The dotted line in this diagram corresponds to the Lorentz - Lorenz formula. The deviations of the results obtained photometrically can be partly explained by the Increase in viscoBity of water at high pressure. L. V. AlItshuler (Ref. 6) had detected a decrease of the intensity of the reflected light at pressures above 115,000 atm. and shown it to be related to the phase transformation at this pressure. This effect could not be detected by the present authors. They are of the opinion that water remains transparent up to 300,000 atm, A. G. Oleynik, V. 14. Mineyev, and R. M. Zaydellare mentioned. The authors thank V. P. Arzhanov, 0. V. Krishkevich for carrying out the experiments and A. G. Ivanov, R. M. Zaydell, A. G. Oleynik,and V. N. Mineyev for valuable discussions. There are 3 figures, 1 table4 and 10 referqnces: 5 Soviet- Card 2/P S 25849 5/026/61/139/004/009/025 B104/B209 Zelldovich, Ya. B., Academician TITLE: Moleoular symmetry, melting of a crystal, 114', 1 structure of liquids PERIODICAL: Akademiya nauk SSSR. Doklady, v. 139, no~ 4'?1f1961, 841-843 TEXT: The author studied the effect of molecular symmetry pon the melting process of crystals and on the orderly structure of liquid, Tt is pointod out that the higher the symmetry of a molecule the better 0j 11 this triole- cule fit into a crystal lattice. 114oreover, the symmetry f the molecules exerts a noticeable influence on the melting point of a crystal, ,-ihich i's due to the thermal agitation since the latter depends on this symnetry. In particular, the author studied the three isomers of C6H 4Cl (orThoo meta, and para-chlorobenzene). Among these, Para-chlorobenzene ?as tne highest symmetryg and therefore also the highest melting point (+52,500. The symmetries in meta-chlorobenzene (-24-40C) and in ortho-chlorobenzene (-17.50C) are lower. This situation is considered to be characteristic of many organic compounds. However, there are also exceptions to this rule Card 113 ol'ecular symmetry, malting of ... M S 2 61/139/004/009/025 B 0 ~20 Z 4 9 that are due to the effect of lattice energy. Thus, for instance, the a- and the P-derivatives of naphthalene have the same symmetry but different melting points. The theoretical treatment is based on the assumption that the molecules in th6 crystal are arranged and aligned regularly, The entropy of tile crystal at absolute zero is assumed to vanish, The inter- molecular spacings in liquids are of the same order of magnitude as those in crystals, but there is no mutual alignment uf the molecules in the former case. For this reason, molecular interacLion in a liquid greatly affects the translatory motion, the rotary motion, however. only slightl.,_ This fact is accomplished by the elementary concept of the molecules vibrating in a crystal, revolving in a liquid, and performing a rotary aa well as a Brownian movement in a gas. It is stated that the entropy of a crystal does not depend on the symmetry of its molecules. The relation Sliqu (T) = s0(T) - R in n is given for the entropy of a liquid; n denotes the so-called symmetry number of the molecules. T he melting temperature is given by &T = RT 2 &in n/Q., where Q is thle heat of fusion. A difference melt f f of 300C in the melting temperatures of para-chlorobenzene and meta- and Card 2/3 2 58 14 9 S7020/61/1 39/004/009/025 Molecular syrrmetryp melting, of ... -61002010 ortho-ohlorobenzene (the melting points of' the two last ara ausumed to be equal) is obtained by means of the above fro-,mula. 1-11 eXDerlimenLEI, a difference of 730C was determined, Morec,,.rer, the experiments proved triat T T r., it " F, -ortho " - 70C. The author poir~*~i ci~t t1hat thb in liquids does not permit a free rotation of thQ molecalos. The molecules rather perform rotational vibrations with rare Jumps from orte alignment to the other. A very weak effect of symmetry is possible in t,;,,o cases: 1)4hen the crystal is not completely retijilar. This is the case when physi- cally alightly different groups determining the crystal symmetr-yr are suii~ti- tuted (e.g. hydrogen by deuterium). The entropy In thia catie does riot van- ish at absolute zero but depends*on the syiametry of the molecules, 2) When the liquid retains -a certain orderliness of aliLnment at U6 melting point. The author thanks A. V. Shubnikov and A. I. K-itaygorodskiy for their rem arks. There is 1 figure. SUBLI'ITTED: April 26, 1961 Card 3/5 A 1 ~_2~ WE S/020/6-1/140/006/009/030 B104/B102 AUTHORSS Zelldovich Ya. B. Academician, Barenblatt., G; I., and TITLE: quasi-periodic precipitations during mutual diffusion of two substances (Lisegang rings) PERIODICAL: Akademiya nauk SSSR. Doklady, v. 140, no. 6, 1961, 1281 1284 TEXTs During mutual diffusion of two reacting substances insoluble pre- cipitates fall out in so-called Lisegang rings. The most probable forma- tion of Lisegang rings is described as follorst During diffusion the soluti6n is supersaturated as long as the product ab of the concentrations a and b of the substances A and B does not reach a critical value k (metastable limit). As ab exceeds k at a given point, one of the reaction comp:>nents is precipitated completely. Due to diffusion, a new portion of this component enters the impoverished region and the precipitation mecha- nism appears again. If the region of precipitations does not propagate too fast, the following precipitation is somewhat distant from the pre-., Card 1/0 3/02 611140100610091030 Quasi-periodic precipitations during ... B104YB102 vious one. In the present paper, an approximation of the formation.of Lisegang rings during diffusion of subs tances in a cylindrical tube is given. The authors derive a and b as functions of the reduced parameter. x/X ng where xis the coordinate of the axis of the tube, and x n is the coordinate of the n-th precipitation. For sufficiently high n the distributions, of a and b within the ranges oo and 141