Excitation with PIPs

As in the phase coherence in RF pulses, the phase coherence in PIPs - 

Under such circumstances, the evolution of a spin system has to be calculated in different rotating frames defined by the corresponding PIPs and a special case may arise, where a spin experiences an on-resonance excitation but off-resonance evolution in the conventional rotating frame. Unpredictable results may occur if the phase coherence in PIPs fails. Unfortunately, to date, no 

NMR instruments take care of this phase coherence in PIPs and therefore human intervention becomes inevitable. 

To understand the concept of phase coherence in PIPs it is quite helpful to define an Eigenframe of a PIP as shown in Fig. 18. For a frequency-shifted 

The phase coherence in RF pulses is maintained through a reference signal that provides a phase reference for all the pulses applied at any time as shown in Fig. 19. For example, if the first pulse, described by 4maxsin( )rft), is applied at a time t = 0, the second pulse, applied at a time ts from the beginning of the pulse sequence, must have the form of 

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Due to the large number of steps in a PIP, each with a phase increment, it is quite discouraging to calculate directly the response of a PIP. This obstacle, however, can be lifted largely by introducing a new or the second rotating frame (in contrast to the conventional rotating frame), in which the phase of the PIP is periodic. As a result, all the strengths and phases of the effective RF fields, which are responsible to the excitation profile of multiple bands, can be derived analytically as discussed in Section 2.25... 

The excitation profile of multiple bands was also known for periodic RF pulses, such as the DANTE (delays alternating with nutation for tailored excitation) sequence.26 Similar to the PIP, all the phases and strengths of the effective RF fields can be obtained by expanding the periodic pulse into a Fourier series and properly rearranging the terms afterwards.27 Detailed calculation, comparison with the PIP, and the excitation profiles by a periodic pulse of fix sin(7tt/T) Ix and a DANTE sequence are presented in Section 3. 

This result is expected and in agreement with the energy conservation law in PIPs since under the above condition, the PIP reduces to a normal RF pulse with no phase increment. Consequently, the sideband excitations vanish and there is no scaling and UPS for the centre band. 

Table 3. The frequencies / , phases 9n of the effective RF fields and the amplitudes A of the excitation bands created by a Gaussian shaped PIP with the same parameters as that in Table 2, except for a A0 = O.82jt and 27rA/r = (2m + 0.5)jr...

Fig. 18. The relationship between the excitations in the rotating frame by a RF pulse and in the Eigenframe by a PIP. The offset in the Eigenframe S is measured from the effective carrier fr( = A/+/rr, where the frequency shift is A/= Atp/lnAr. Reprinted from Ref. 49 with permission from Elsevier.

As shown in Fig. 21a, the simulated broadband inversion profile by the three PIPs resembles the profile by the composite pulse 90°180°90° except for a different excitation region. The inversion profile is severely distorted (Fig. 21b) if the three initial phases, phase relationship in the rotating frame is the wrong one in the Eigenframe. The phase coherence in PIPs needs to be considered even for PIPs with the same frequency shift, A/ = 50 kHz in this case. 

Electron configuration of Bp" is (6s) (6p) yielding a Pip ground state and a crystal field split Pap excited state (Hamstra et al. 1994). Because the emission is a 6p inter-configurational transition Pap- Pip. which is confirmed by the yellow excitation band presence, it is formally parity forbidden. Since the uneven crystal-field terms mix with the (65) (75) Si/2 and the Pap and Pip states, the parity selection rule becomes partly lifted. The excitation transition -Pl/2- S 1/2 is the allowed one and it demands photons with higher energy. 

Let us consider (within the RHF scheme) the simplest closed-shell qrstem with both electrons occupying the same orbital (p. The Slater determinant, called (G from the ground state) is built from two spinorbitals d> =

2 = virtual orbital (p2, corresponding to orbital energy S2, and we may form two other spinorbitals from it. We are now interested in the energies of all the possible excited states which can be formed from this pair of orbitals. These states will be represented as Slater determinants, built from (pi and (p2 orbitals with the appropriate electron occupancy. We will also assume that excitations do not deform the q> orbitals (which is, of course, only partially true). Now all possible states may be listed by occupation of the ej and S2 orbital levels, see Table 8.2. 

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