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B. Rak6in, N. Maltar-Strmecˇki / Spectrochimica Acta Part A 56 (2000) 399–408
lattice dynamics. Indeed, ~n (~ꢀ=0.09 ps, DE/
k=2710 T) corresponding to the methyl group
motion measured by proton NMR on the un-
damaged crystal [12] can be employed in relation
(Eq. (3)). In order to better describe the ENDOR
linewidths, the relation (Eq. (3)) is employed and
besides b, ~B and ~n only one constant was ad-
justed in jn (b/33) leading to a solid line in Fig. 6
(bottom line). The employed constant (b/33) leads
to a small proton hyperfine coupling (((b/2y)/
33):2.1 MHz) which is expected for a next
neighbor group. This agreement indicates that for
the ENDOR line intensities a similar pseudo-
scalar term ( jn(~nꢀn)) should be added to relation
(Eq. (2)). In this case ~B, ~n, and two coupling
constants (b, b/27)) are applied and the continu-
ous line with fairly good agreement is obtained as
a sum of the two processes. Here, the temperature
dependence of we was neglected as in the original
model [9]. It can be noted that the ratios between
coupling constants in both processes (33, 27) are
comparable supporting the same origin of these
pseudo-secular relaxation mechanisms. As was
demonstrated here, besides that small hyperfine
coupling, the contribution of the pseudo-secular
mechanism (especially around the maximum of
relaxation rate, ~nꢀn:1) to the integral relax-
ation rate can be significant. The obtained quali-
tative fit of the ENDOR experimental data also
supports the origin of the high potential barrier
detected for quadrature signals in the low temper-
ature region.
decrease in the energy barrier [16]. Therefore, it is
more probable that an oversimplified description
of the relaxation mechanism leads to this
discrepancy.
An additional checking of the obtained ~B can
be provided by analyzing multi-frequency data for
T1 relaxation times of the SAR1 center measured
at room temperature [5]. Two different T1 relax-
ation times are detected by the pulse saturation
transfer method measured at various microwave
frequencies. The possible origin of these relax-
ation mechanisms was discussed but there was no
conclusive suggestion for it. In study [5], it was
pointed out that the faster relaxing component in
the recovery curves decreased with increased mi-
crowave frequency and the ratios of the weight-
ings between this component and the slower
component were evaluated for each frequency.
One can suppose that the faster component corre-
sponds to the cross-relaxation mechanism, domi-
nant around room temperature. The ratio of the
weightings of the short and long components
(which were extrapolated at t=0 in the pulse
experiment) is proportional to the ratio of the
corresponding transition probabilities. On the
other hand, the ratio of the transition probabili-
ties for the forbidden and allowed transitions is
proportional to 1/ꢀ2e. Therefore, one can expect
that the ratio of weightings for these components
is also proportional to 1/ꢀ2e if the faster relaxation
component is proportional to a cross-relaxation.
Fig. 7a shows the experimentally obtained [5]
ratios of weighting components as a function of
frequency, and the fitted solid line on the 1/ꢀe2
dependence. This leads to a functional depen-
dence of the short component and supports the
electron-nuclear-cross-relaxation as a relaxation
mechanism. For a further check of the relaxation
mechanism, one can expect that the relaxation
rate for the cross-relaxation mechanism is propor-
tional to j(ꢀe) and the relaxation time Te1f is
proportional to:
Another alternative to the described ENDOR
intensities is to assume that only a single ~ is
present. The obtained parameters for the unique ~
(~ꢀ:0.005 ps, DE/k:2050 K) [9] lead to a large
decrease in the pre-exponential factor and an
increase in the energy barrier in comparison to ~B.
It should be mentioned that according to proton
NMR measurements of non-irradiated L-alanine,
the pre-exponential factor is not shorter than 0.09
ps. The increase of ~ꢀ can only reach ꢁ1 ps for
methyl groups in various amino acids with the
variation of hydrogen-bond densities. One cannot
expect that a local potential in the vicinity of
SAR1 center will change so drastically that the
pre-exponential factor decreases with nearly two
orders in magnitude with a simultaneous small
1 1
ꢁ ꢂ
Te1f8
+~ꢀ2
(4)
b2
~
Indeed, a good proportionality between the
data for the relaxation times obtained in [5] and
relation (Eq. (4)) (Fig. 7b) can be seen. From the