COLLISIONS OF A - MESONS WITH DEUTERONS

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Document Number (FOIA) /ESDN (CREST): 
CIA-RDP82-00039R000100230010-5
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RIPPUB
Original Classification: 
R
Document Page Count: 
6
Document Creation Date: 
December 22, 2016
Document Release Date: 
May 10, 2012
Sequence Number: 
10
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Publication Date: 
March 4, 1952
Content Type: 
REPORT
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PDF icon CIA-RDP82-00039R000100230010-5.pdf1.67 MB
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Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 Collisions of n - Mesons with Deuterons V. B. BerestetskiY and I. ya. Pomeranchuk Doklady Akademii Nauk SSSR, Volume LXXXI, No. b, PP? 1019?1021. MoscOW-Leningrad: 21 Dec 1951. STAT STAT Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 coalsioNS Q !L- MESONS WITH DEUTERONS V. B. Berestetskiy and I. Ya. Pomeranchuk. he following is an article that appeared in the regular Physics section of the thrice monthly Doklady Akad:emii Nauk SSSR, Volume 81, No, 6 (21 December 1951), pages 1019-1021. The article was submitted by academician L. D. Landau, 2~ October 1951,E r During collision of -n -mesons with deuterons, their scattering and also their conversion into neutron mesons can occur, The cross-sections of scattering and conversions into a neutral meson were calculated (1) with the aid of the theory of perturbations for various possible types of bond between n-mesons and nucleons. A series of data concerning the character of the interaction of mesons with nucleons, in particular the dependence upon spin, can be analyzed by comparison of the data on scattering (and on conversion into a neutral meson) in hydrogen and deuterium, Theretidal considerations here do not re- quire any assumptions concerning the smallness of the interaction. Let us apply the semiphenomenological method, employed earlier (2) to the problem of the scattering of fast neutrons by deuterons and to the problem of the capture of ,mesons by deuterons. Let a n-meson collide with a proton. s We shall calculate the familar amplitude of the scattered meson (charged or neutral) for a given angle of scattering. If the meson possesses the spin 0, then the amplitude of scattering must be scalar; the amplitude, however, corresponding to the flight of the neutral meson must be scalar if the internal "count" of the charged and neutral mesons are the same, and must be pseudo- scalar if they are opposite. . -1- STAT Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 From this requirement we can determine the character of the possible dependence of amplitude upon the nucleon's spin. Namely: 1) amplitude of scattering: -4J ? =a+b_O It where a is a scalar (which is generally a function of the angles), sigma Q is the spin operator, and b is a pseudovector; here (1) ~ ?-* lock , (1a) 1 where b0 is a scalar function of the angles, and k and kare the initial and final impulses (momenta) of the meson. The same structure is possessed by the expression for the amplitude of conversion of a n~meson into a neutral ?np for the same "count" >-_ h_ In the case, however, of different "count" we have; m) A IL ?R CO" no where t is a vector (also depending upon the angles). Corresponding cross sections for collisions with hydrogen, averaged over the orientations of the nucleon's spin, equal: o- _ /a/2 + /b/2 = c - + c' TI a b Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 /;o*?.. i' /','' ' 4? . (2) (3) Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 Let us now consider the collision of negative a meson with a deuterons which collision leads to its conversion to a neutral meson. In so far as the process proceeds only because of the interaction with the proton, the amp- litude of scattering will then be ?D = f*(p).e ~n D toQ ()) M where ?/2 is the radius-vector of the proton (in the system of the deuteron's of inertia); '(p) is the wave function of the deuteron; ~.'() is the center o ~ D F wave function of the two neutrons forming as a result of the collision. Let us derive the expression for the cross section averaged over the spin states of the nucleons and summed over the states of the neutrons (the expres- sion is effected by the same method as in (1)): 0 Ito 1 (ak + a, cr)F +1( ~? - 1B)F- 2 A 3 g 2 A 3 where (k , Y /*( ik k ' ~ikk')p/2 )~/2 ( ) If we use for D the following expression D 4) where2 2/M is the deuteron's energy of bond, then we have / k-k / dD + ~. ? (+ i.) ..~ arc tan ? f47. 2 .k ~ no A B A 3 ?B -~ i(k-k')p/2 yApAp~Y{QI~ (5) (6) Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 Similarly in the case of different 'counts" of mesons, we have no or no 3 /krc'/ arc tan - 2 ---..) a~ (7) (8) We note the essential absence of cases of similar or different "counts' of it and n -mesons. For k' close to k, then D (6) tends to 0 because (la) B B kxk', but we have (arc tan x/x) 0 x=o 1, at the same time as r D 2rr no If there exists a connected state of the system of two neutrons (deuterons), then its formation as a result of collision is possible. Here the system of nitc3: onssmust pass from the triplet to the singlet state in order that, in correspondence with Pauli's principle, the two neutrons might be found in the S-state. The corresponding cross-sections are: / e ~ D-> ~s~ _ I. d' --..~ ~ arc tan 1k-k' ..,~ no 3 n0 kelp 2 ( 2 (9 ) where O is or 6 , and 3~2 3 2/M is the dineutron's energy of bond, There no B no fore the amplitude of scattering is: - D m ei (k?k' )p/2 ' e?(1)/2) ' jad .. It (p) Y (10) Here is the amplitude of scattering on neutron, and E' () i th ' final state n P of the neutron and proton. The scattering cross section summed over the neutron and proton's states of motion possesses the following form: ~- D +0 +- + cr + ? arc tan k- - -- tt a b a b /k-"k' / 2o. u Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 1 ( fT a(T a ? COS a a-, ? cos " ), b b where a-at + c b are the cross-section of scattering on neutron, and Oa is the phase difference of the quantities a and a1; similarly for b In the work (3) devoted to a similar review of the scattering of a nrrneson on deutron, the presence of two types of scattering by nucleons (the types corresponding to amplitudes a and b) was not taken into consideration. For elastic scattering we have: ~ D ~ 16c~2 ~~ (arc tan ?-i'/ -a.) 2 La n _ ~/2 ~ a, a (db + 3 +2 o-~ o a ? cos + a + 2 bb ? cos tb )1 Literature Cited 1. V. Berestetskiy and I. Pomeranchuk. Ibidem /Eok1ady7,9, ~olurne 77, page 803 (19f.1). V. Berestetskiy and I. Shmushkevich. Zhurnal Eksper i teoret Fiziki, Volume 21, No. 12 (1951). 2. I. Porrieranehuk. Ibidern ~okladil, Volume 78, page 249 (1951); Zhurnal Eksper i teoret Fiziki, Volwne 21, page 1113 (1951); ibidera ok1ad7, Volume 80, pages 47 (1951). G. F. Chew. Physical Review, Volume 80, page 196 (1950). 3. S. Fernbach, T. A. Green, and K. M. Watson. Physical Review, Volume 82, page 980 (1951). -END - w 5 r Declassified in Part - Sanitized Copy Approved for Release 2012/05/10 : CIA-RDP82-00039R000100230010-5 (12)