SCIENTIFIC ABSTRACT VALIYEV, K.A. - VALKA, O.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001858510005-8
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: August 31, 2001
• Sequence Number: 5
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

28756 9/056J61/041/003/009/020
Theory of spin-lattios relaxation... B125/BI02
terms in the series expansion of the spin energy, which are linear with
respect to QJ, The terms in the expansion of %(2), which are quadratic
with respeatto Qp excite a more efficient relaxation. rndepeniently of
the present authors, r. V. Aleksandrov and 0. M. Zhidomirov arrived at the
same conclusion (ZhETY, ~Ll, 127, 1961). The relaxation-transition
probability between sublevels of the spin energy is calculated from the
perturbation-theoretical formula
w ~;-2 Z f 1/2), another relaxation
-1 2 02 2
mechanism is possible, which leads to Ti ~alh (ttj/2kT)-rr/('+ M 'MITP.
2+ 1
The reeonance-line vi th of Cu ions in aqueous solution: The orbital
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28756 S/056 '61/041/003/009/020
,Theory of spin-lattice relaxation... B1257B102
levels are described bythe wave functions -Y2 + 'F
-Ta - ( -2)/rZ ' 'Pb - V.'
'Po - (12 - V-2)/F21 Yd - (VI + V-1 )/ F21 'f6 - OYI -:1-1 )/f 2. A 104 and 6 '103cm7~
The width of the resonance line observed during the transitions
at M - -1/2 - a, M - + 1/2 is due to relaxation transitions etween the orbital
sublevels a and b which are excited tinder the action of WM alone (without
participation of the interaction ArS ). The direct transitions a-b are
much more probable than transitions with spin re-orientation. The matrix
element of a direct transition reads
941-1b =a(Q:7-q,,)+bQsQs+cQ6Q,;
a (A, ~5- A.). b=- 18 A, 375 A, 1!5 IL3 As, (17i
8 ( WO 8
A, eea?R-5, A, et'~74R-I, a 3P 2/21.
and the probabilities of the transitions a-*b reid
2 [a2 (--T -T 'j -3 -7 2--772 -6/2kT
w + Ib' - 0 e (20)-
a,b 5155 Q6~66) Q2 Q3f23 +
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28756
S/056J61/041/003/009/020
Theory of spin-lattice relaxation... 3125/B102
The temperature dependence of (20) is given by
V -exp(-6/2kT) a th2 (A W/2kT)Xio where X jexp(-E/RT)j the parameter E
a,b i j
has the significance of a "viscosity barrier" of ~he liquid. The
1.8-fold broadening of the line in the same temperature range, obser7ed
by Kozyrev, is close to the calculated value. There are 1 figure and
12 references: 5 Soviet and 7 non-Soviet. The three most recent
references to English-language publications read as follows:
J. R. Senitzky. Phys. Rev., 119, 670, 1960; H. J. Mc Connell. J. Chem.
Phys., 25, 709, 1956; B. R. Mc Garvey. J. Phys. Chem., 61, 1232, 1957.
ASSOCIATION: Kazanskiy pedagogicheskiy institut (Kazan' Pedagogical
Institute)
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0 (1,6 fply
AUTHORS: Timerovo R. Kh., Valiyev, K
TITLE: Theoryof nuclear resonance
PERIODICAL: Zhurnal eksperimentalinoy i
no. 501), 1961, 1566-1575
26708
5/056/61/041/005/023/038
B102/B138
A.
in paramagnetic media
teoreticheskoy fiziki, v. 41,
TEXT: The influence of paramagnetic atoms on nuclear resonance results in
the reduction of the relaxation times of the components of nucle 'ar
magnetization and in a shift 6 of the nuclear resonance frequency tiI.
Where there is low concentration of paramagnetic atoms their effect can be
described by an additive law which has been verified theoretically as well
as experimentally. In the case of high concentrations, which is that
investigated in the present paper, exchange interactiea between para-
magnetic ions-,has to be taken into account. This determines the exchange
of electron spin orientations reduces the effect of the paramagnetic atoms
on relaxation times TH and T.L of the nuclear magnetization components.
The authors have developed a theory of the shape and width (T.Cl) Of a
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26708
8/056J61/041/005/023/038
Theory.of nuclear resonance in... B102/B138
nuclear resonance line which allows for the exchange interactions between
paramagnetic atoms, which are in their turn modulated by the thermal
motion in the system. The system contain-i NI magnetic nuclei and ff.
paramagnetic atoms per unit volume. The shape of the absorption line IM.
is represented as a Fourier transform of the autocorrelation function G(t)
of the projection of the magnetic moment in the diroation x of the variable,
magnetic field: IM +00 G(t)q- i(4 dt; G(t) (0)J> - In order
f Nx
-00
to find the parts of the Hamiltonian the first terms of the series
G(t) Y-Gn(t) are determined (G,(t). 0):
Go (f) NiT211 V + 1) lel'f 1 + K - c. (7)
62 (1) -LN/T2/1 Q + 11[el"t a'~d-r (t - T) e"('f, (T) + x, c], (8)
T
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267 08
S/056J61/041/005/023/038
Theory of nuclear resonance in ... B102/B138
h-2 1 ,
with G.
+ Y 4- Ti (9)
R < J A71'+O), AF, (r) (0). MT) J>,
it' (T) ~- YJ S'wl% Yf' , (T) I C CXP (iTX-2/h) .7?, exp PrYt,lh). (11)
2 - - ---I M i V-- --
0 is the contribution fro to the second moment of the resonance line
(in frequency units), f (-r) the correlation function of the Yl(-r) values,
Y A Y.
which vary with time due to the effect of 7C2, and N is R formal operator:
NA(t) -A(t)/.A(O)l the prime denotes the perturbation terms, +X C. means:
+ complex conjugates. Por Go (t) +02(t)
a' dc (t -r) e("l +'q'As) T X
CL 1. 2 Y. 0 .0
X ex p + K. C., (21)
or, approximately, --------
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26708
S10561611041100510231038
Theory of nuclear resonance invas B102/B136
exp li(olt - 0711-2 d-r(t-T)e~("I'"ws X
a 1.2 Y.0 0
x exp I --- 71 ~ I v.-' - I c 17-01 - OF (T))1 + K. C. (22)
is found; In the expression (21) only a constant factor is omitted.' Then'
the line shape is calculated for two limiting cases: fast (fluid) and slow
(viscous liquid or solid) motion of the molecules of the system. In the
first case, TO ~>Te, from (22) oranother formula the half-width of a
Lorentz line with its center at ej + 6 Is found to be
S (S + KO-11
+ 1)(111S I I S
2 K-12 + to 4 V,, +
V
+ (.s + ;1), 4* 12,jiT,
oa/ (0.02
K12'
+ S (S + 1) K. + )2 (23)
3 T~~Caj - WS
The shift (in rad/sec) is determined by
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26708
8/056/61/041/005/023/038
Theory of nuclear resonance in... B102/B138
t C.)i + WS
6 = S P + 1) (is ~ 2 K,-12 + w21 + 2 K',, + (w, +
+ C01 - (OS _WS (24)
" I + S (S + 1)
KI-2
12 K-1 + ((01 - (OS) 2 + (_I - (OS)l
-1 2 (25)
T;I + TV + + T, + >1
The reciprocal relaxation times T 1 and T 2 are, for paramagnetic ions of
the Cu 2+ 'VO 2+ type, of the order of 108 eec -1 , for others much shorter
-1 '* 11 -1
still; -ri -10 sec . Estimations show that very different situations
may arise. For large W e the half-width can be approximated by
A& S(S+l)F20 2 + L I /Te&)e
71 B(S+1)62 K +j-S(8+1)K For slow thermal motion,
(A'JI/2)h-f ' 22 is P'I 3 P,2'
TO