Hyperfine state

During the collision of atoms which have unfilled electron shells, a spin exchange is possible [30]. The spin exchange substantially perturbs the hyperfine states of the colliding atoms and thus plays an important role in... 

Since the leakage factor can be easily calculated from Ti relaxation data, and ys/y is constant, that only leaves the determination of smax before the coupling factor can be directly accessed. For solutions of radicals where Heisenberg exchange is prominent, Emax must be measured as a function of concentration and extrapolated to infinite concentration where smax 26,50 pQr jmmobilized or tethered radicals, nitrogen nuclear spin relaxation effectively mixes the hyperfine states in virtually all cases (small peptides may be an exception) and smax 1 can safely be assumed. 56 Alternately, the determination of smax can be avoided... 

The laser beam is introduced parallel to the axis of the trap and retro-rellected by a mirror at the bottom of the trapping cell (Fig. 2.) A mechanical chopper pulses the laser at typically 1 kHz. The 2S atoms are in the same hyperfine state d and therefore remain trapped. After excitation for a brief period, the population of the 2S level is measured by detecting the Lyman-a fluorescence in an applied electric field. A microchannel plate detector is used to permit single photon detection. Due to the small optical collection efficiency for our geometry, the detection efficiency is limited to 10-5. Nevertheless, signal rates as high a few hundred thousand counts per second laser time have been observed. 

Fig. 1. Resonant molecular formation rate in /it + Do collisions calculated for a 3 K target [7,8,9]. The rates are normalized to the liquid hydrogen density and averaged over fit hyperfine states. Also shown is the /it elastic scattering rate on the d nucleus [12]...

About 20000 Ka events were recorded, which did not allow to determine unbiased the individual hyperfine components with an accuracy comparable to the one of the spin-averaged values. The errors for the 3S hyperfine state are of the order of 10% for the shift and 15% for the broadening and are consistent with the values given in [12] (Table 4). Parameters for the less intense bS o state could be obtained if the 3Si/1 So intensity ratio was fixed for the fit in accordance with reasonable assumptions for the different 2p-level widths [22]. An unbiased fit yields errors of the order of at least 50%. 

Table 4. Hadronic parameters of individual hyperfine states in pH...

The spin-averaged hadronic shifts and widths of the Is and the 2p state have been measured both for antiprotonic hydrogen and deuterium. Furthermore, information on individual hyperfine states was obtained for pH. Here, the strong-interaction parameters of the 23Po hyperfine state could be determined using a crystal spectrometer. The hadronic effects in the lx5o and 13,S i hyperfine ground states were derived with the help of a few assumptions. 

The experimental results support the meson-exchange model, which is used to derive the real part of the long- and medium-range NN potential. There is no need for exotic pp bound states close to threshold. The poor accuracy concerning the individual hyperfine states idiSo and 13.S i of pH in an unbiased analysis... 

To carry out this scheme, a fast atomic beam (v/c = 0.01) is used to translate the required nanosecond time intervals into convenient laboratory distances. To avoid complications due to motional electric fields, the entire experiment is performed in zero magnetic field and the resonance is tuned through directly by changing the frequency of the applied rf field. Other rf fields are used to select one hyperfine state so as to simplify the line shape. 

To select one hyperfine state the preparation quench plates are driven at 1110 MHz and the detection quenching plates are driven at 910 MHz. Figure 3 shows the microwave system used to produce the two separated oscillatory fields. A high precision coaxial magic Tee drives the two rf regions so that they have relative phases of 0° or 180°. Figure 4 shows the hyperfine state selection. 

Fig. 4 A series of plots of the average quench and interference signals showing the hyperfine state selection due to the continuous rf fields in the state selection region and in the quench region.

The temperature for Bose-Einstein condensation varies with density as n20. Because density is limited by three-body recombination, the search for the transition leads naturally to lower temperatures. Unfortunately, at temperatures below 0.1 K, adsorption rapidly becomes prohibitive. To avoid this problem, Hess [4] suggested confinirig the atoms in a magnetic trap without any surfaces. The states confined are the "low-field seeking" states, (HT, electron spin "up"). These are the hyperfine states (F-l,m-l) and (F=l,m=0). 

The trapped hydrogen is in the hyperfine state F=l, m=l. The gas can decay by dipole relaxation to a lower-lying hyperfine state and escape from the trap. The decay rate is given by Td = nG, where n is the total density and the factor G is approximately temperature independent. Lagendijk, Silvera and Verhaar [9] have calculated G = 1 x 10-15 cm3-s-1, which is in agreement with the observed value [7] G= (1.2 0.5) xlO-15 cm3 S 1. With a density of 1012cm-3, the lifetime is 103 s-1. Dipole decay imposes a requirement on the supply rate of hydrogen to maintain the density, but does not limit the spectral resolution. 

To study the relaxation of Ht to the high field seeking hyperfine states we plot our data as V tl/N2 versus time as shown in Fig.4. W(t) is the total number of atoms in the trap at a given time t, obtained by integrating the observed flux from t to . Vy is the effective volume of the sample defined by V 0/V2e,... 

It is well known from the Bom-Oppenheimer separation [1] that the pattern of energy levels for a typical diatomic molecule consists first of widely separated electronic states (A eiec 20000 cm-1). Each of these states then supports a set of more closely spaced vibrational levels (AEvib 1000 cm-1). Each of these vibrational levels in turn is spanned by closely spaced rotational levels ( A Emt 1 cm-1) and, in the case of open shell molecules, by fine and hyperfine states (A Efs 100 cm-1 and AEhts 0.01 cm-1). The objective is to construct an effective Hamiltonian which is capable of describing the detailed energy levels of the molecule in a single vibrational level of a particular electronic state. It is usual to derive this Hamiltonian in two stages because of the different nature of the electronic and nuclear coordinates. In the first step, which we describe in the present section, we derive a Hamiltonian which acts on all the vibrational states of a single electronic state. The operators thus remain explicitly dependent on the vibrational coordinate R (the intemuclear separation). In the second step, described in section 7.55, we remove the effects of terms in this intermediate Hamiltonian which couple different vibrational levels. The result is an effective Hamiltonian for each vibronic state. 

Figure 8.22. Schematic energy level diagram for the first four rotational levels of N2 in its A 3E+ state, showing the nuclear hyperfine states which are allowed to combine with each N level. Relative vertical spacings are not drawn to scale [43].

Turning now to ortho-Hj in N = 1, the situation is considerably more complicated because all four interaction terms contribute, and more states are involved specifically the appropriate five allowed hyperfine states are ... 

In their experiment, Rabi, Nafe, and Nelson used a beam of hydrogen atoms and measured the transition frequencies between the two hyperfine states. The measured values were as follows ... 

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