Difference in population

The intensity of a non-degenerate n.m.r. transition between the nuclear Zeeman levels n and m is proportional to the difference in population of levels n and m as given by the Boltzmann distribution. This can be expressed by equation (35). 

When the pulse is applied to nucleus S, the population levels connected by S transitions are rapidly equalized, but there is no immediate change in the difference in population levels connected by the I transitions. Figure 4.2 shows that on application of the pulse, levels 2 and 4 acquire the same populations as levels 1 and 3, respectively, but the population difference... 

Factors such as assay variations, age, and prostate gland size are known to affect cutoff values. Also, free to total PSA cutoffs are influenced by the sensitivity and specificity values chosen, the reflex range for total PSA used, differences in free PSA assays, and differences in populations studied. Different PSA values are considered due to differences in cutoffs in different assays. Studies have shown that the comparison of a chemiluminescent free PSA showed a 25 percent difference in values. These types of variations suggest a need for standardization (9,29). 

One can calculate the ratio of populations of spin-up to spin-down electron orientations at room temperature (T = 300 K) from the Boltzmann formula finding that Nl / N is approximately equal to one (0.999), indicating that there is about a 0.1% net excess of spins in the more stable, spin-down orientation at room temperature. Using the same mathematical expression, this difference in populations can be shown to increase as the temperature is lowered. Actually, the EPR signal will be linearly dependent on 1/ T, and this linear dependence is called the Curie law. Because of the excited state population s temperature dependence, most EPR spectra are recorded at temperatures between 4 and 77 K. 

The number of nuclei in the upper energy state, N+, is less than that in the lower energy state, Nf, and the probabilities of upwards and downwards transitions are different. The spin transitions are caused by the spins S of a nucleus, and the influence of these occurs directly through space. The transitions and their relaxations may be between the same or different type of nucleus, but in either case they are chemically shifted from the spin 7. At equilibrium, some relative spin 7 populations exist and the fractional difference in populations between the two energy states can be written (remembering that e is approximated by 1 + x) as... 

The relaxation fits of the Mossbauer spectra of [Fe(HB(pz)3)2] yield [30] the temperature dependence of both the population of the iron(II) high-spin and low-spin states and the relaxation rate between these two states. The resulting population of the high-spin state has a striking resemblance to that of the magnetic moment shown in Fig. 1 and these populations provide clear support both for the spin-state crossover and for the difference in populations upon heating and cooling. 

Glabrous soybeans supported a higher population of fabae and had a higher Incidence of oviposition than pubescent varieties (25, 26). This same observation has been made on other pubescent host plants (17). The differences in populations of E. fabae... 

Because the coefficients of absorbance and emission are identical, a microwave photon of the appropriate frequency would be equally likely to cause emission of an identical photon from an excited molecule as to be absorbed by a molecule in the ground state if equal numbers of molecules were present in each state. Therefore, net absorbance of energy depends on the difference in populations between the ground state and the excited state. 

K f. U, + Ix2 tj) 2. (It might be thought necessary to consider also the effect of the relative populations of the levels on the transition intensities, but the separation between nuclear-spin energy levels is much less than kT, so that the very slight differences in population can be ignored here.)... 

The small difference in population among the Af/ or Ms levels allows the magnetic resonance experiments. From now on we will focus on the nuclear magnetic resonance experiment, but little would be changed if we dealt with EPR. 

When the paramagnetic site is the least populated, and the difference in population is very large, Eqs. (4.2)-(4.4) can be simplified [3-6]. For example, the chemical shift for the signal in the diamagnetic site evolves as follows as a... 

Understanding the factors controlling organic matter turnover is complicated by possible differences in population distributions of organisms responsible for enzyme production and product uptake. Although relationships between enzyme Vmax and bacterial productivity have been reported (Sinsabaugh et al., 1997), correlations between total bacterial numbers or bacterial production and enzyme activities are frequently found to be variable or weak (e.g., Mayer, 1989 Boetius et al., 1996, 2000). Vrba et al. (1992) observed that MUF-a-glucosidase activity correlated with bacterial biomass measured in a freshwater reservoir over the course of three seasons,... 

The population difference, Pa — Pp, is the most interesting thing for us because the magnetism of every up nuclear magnet cancels the magnetism of every down nuclear magnet, and it is only the difference in population that results in a net magnetization of the sample. 

Immediately after a 90° pulse the net magnetization vector is in the x-y plane. This means that the z component of the net magnetization is zero and that there is no difference in population between the upper (P) and lower (a) energy states. The net magnetization vector will rotate (precess) in the x-y plane at the Larmor frequency, v0- The phase coherence... 

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