Parity state

K. Kassner, A. Valance, C. Misbah, D. Temkin. New broken-parity state and a transition to anomalous lamellae in eutectic growth. Phys Rev E 4S 1091, 1993. 

The induced absorption band at 3 eV does not have any corresponding spectral feature in a(co), indicating that it is most probably due to an even parity state. Such a state would not show up in a(co) since the optical transition IAK - mAg is dipole forbidden. We relate the induced absorption bands to transfer of oscillator strength from the allowed 1AS-+1 (absorption band 1) to the forbidden 1 Ak - mAg transition, caused by the symmetry-breaking external electric field. A similar, smaller band is seen in EA at 3.5 eV, which is attributed to the kAg state. The kAg state has a weaker polarizability than the mAg, related to a weaker coupling to the lower 1 Bu state. 

Figure 3. In (a) the potential curve is unsymmetric with respect to the equilibrium position 0 of the nucleus. The crystal field in this case causes mixing of the even and odd parity states. In (b) there is symmetry with respect to the nucleus when it is at 0, but vibration carries the ion to the unsymmetric point P [from Ref. (25)].

Fig. 9.8 Fourier transforms of H spectra obtained in a magnetic field of 5.96 T with resolution 0.07 cm-1 (a) initial state 2p m = 0, final state m = 0 even parity states (b) initial state 2p m = — 1 final state m = — 1 even parity states. The squared value of the absolute value is plotted in both cases. The circled numbers correspond to the classical orbits depicted in Fig. 9.9 (from ref. 23).

Here a complete model space (P-space), defined on eigenfunctions of Ho, representing all possible distributions of electrons between open shells, is utilized. In our case the model space consists of the ls22s22p4 and ls22p6 configurations for the even parity states and of the ls22s2p5 configuration for odd parity states. The wave-operator may be written as... 

The representations here are labelled by the group theoretical notation [13] A/, A2, By, B2, E. The first four are one dimensional, while the representation E is two dimensional. For 3, some representations are contained twice and the situation is slightly more complicated. In condensed matter physics, it has become customary to label the representations with the letter T [14]. When both positive and negative parity states are considered also the parity label is added, r and V. The conversion between the two notations is Aj — Ti, A2 — T2, Bi — r3, B2 —> T4, and E —> Ts. 

Table 5.4 The total binding energy and autoionization half width (r/2) for the helium doubly excited even parity states below He+ (n = 2), where autoionization is nonrelativistically allowed...

N = 2 ionization threshold by roughly the energy of three and one IR photons, respectively. Since the absorption of an odd number of photons by a 1P° state results in an even parity state, the 2p multiphoton ionization amplitude, created by the IR pulse, should have odd parity right above the threshold and change to even parity for photoelectron energies around 1.4 eV (corresponding to absorption of four IR photons from the spj resonance and two from... 

Figure 2a,b. Calculations on 134xe and 130sn showing results with the bare KK potential and the KK with core polarization corrections. Only the positive parity states with even angular momentum are shown. 

Ex(9i+) > Bx(101+) as is observed experimentally. The spectrum of negative parity states is compressed relative to experiment. 

Fig. 1. Systematics of positive parity states in even Cd and Te isotopes.

From a microscopic point of view, octupole deformation in even-even nuclides is signalled by (r and 0 bands that have the same properties. This implies a ground state rotational band with alternating even and odd parity states, i.e. 0+, 1, 2+,. Such ground state bands have not been found in any nuclides to date. In Fig. 2, we show the results of a microscopic calculation of octupole correlation energies in the 0+ and the 1 states of Ra... 

Fig. 3 The moment of intertia and B(E1)/B(E2) ratios for negative parity states in 218Ra. Note the changes above the 11 state.

The 1=34, 35, 36, 40 and 42 states essentially exhaust the possibilities to form low-lying positive parity states with 1 30 within the ten valence particles of 15 Er. The most low-lying fully aligned negative parity states are calculated for I = 38 , 39 corresponding to the rearrangements V(i13 2 7/2 13/2 h9/2 relative to the 42+ state. This seems consistent... 

In Fig. 5. The structure of the negative parity states is as follows. The low lying 3 and 5 states appear to be rather complicated as their population does not follow the (2J+1) population expected for a simple multiplet. In contrast, the 7 , 9 and 10 appear to have equivalent f7/2 il3/2 strength and thus have rather simple structure. On the %other hand, no evidence is found for the 4 or 8 states and only weak evidence that the state at 3.3 MeV is a 6 state. Configuration mixing is a possible, though not a certain, reason for the absence of these states. In any case, there does not appear to be a simple vf7/2 v13/2 multiplet. 

For the positive parity states, the population of the 0+ 6+ states follows (2J+1) which indicates that these states are consistent with being an (f7/2)2 multiplet. As can be seen in Fig. 1, the spectrum of the (12C,11C) reaction leading to Nd enhances h9/2 transfer. Comparison of the (16q,15o) and (12C,nC) spectra clearly shows that the 8+ state at 2.709 MeV is primarily an f7/2 h9/2 configuration. Unfortunately, there are no extensive shell model calculations with..which to compare these results. 

The positive parity states are interesting because two 4+ states are seen with about equal strength and the previously unobserved decay of the higher one at 2.436 MeV is almost exclusively via a transition to the lower 4+ state. The positive parity of the higher 4+ state is determined from the L-2 character of the (3He,d) stripping reaction. 

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