Nearby Doorways, Parity Doublets and Parity Mixing in Compound Nuclear States

We discuss the implications of a doorway state model for parity mixing in compound nuclear states. We argue that in order to explain the tendency of parity violating asymmetries measured in 233Th to have a common sign, doorways that contribute to parity mixing must be found in the same energy neighbourhood of the measured resonance. The mechanism of parity mixing in this case of nearby doorways is closely related to the intermediate structure observed in nuclear reactions in which compound states are excited. We note that in the region of interest (233Th) nuclei exhibit octupole deformations which leads to the existence of nearby parity doublets. These parity doublets are then used as doorways in a model for parity mixing. The contribution of such mechanism is estimated in a simple model. 24.80.Dc, 24.60.Dr, 25.40.Ny, 25.85.Ec, 24.10.-i Typeset using REVTEX 1 Recent experiments on parity violation in compound nuclear (CN) states [1,2] are providing new information on the parity non-conserving (PNC) interaction. The experimental results for Th showed that measured PNC asymmetries fluctuated about non-zero average, in contradiction to the purely random behavior expected on the basis of the statistical model of the CN. The understanding of PNC phenomena challenges theory to treat simultaneously the chaotic and the regular aspects of the CN system. A number of attempts were made to explain the new results in the framework of statistical models [3] or in models that combine nuclear dynamics with the statistical aspects [4,5]. Among the latter the doorway state approach was used in several theoretical works [4,5]. In Ref. [4] the spin-dipole (SD) resonance was used as the doorway to describe the PNC spreading width of the compound resonances. Later the same model was applied [6] in the calculation of the average longitudinal asymmetry. In Ref. [5] the s1/2 and p1/2 single-particle states were used as the doorways in an attempt to explain the constancy of signs. The common feature of these models is that they deal with distant doorways and involve only the one-body part of the PNC interaction. The term “distant doorways” refers to the fact that the position of the doorways is removed by 1h̄ω ∼ 7 MeV from the CN resonances under consideration. The model in Ref. [4] which involved the collective effects of the spin-dipole resonance was able to account for the PNC spreading width when a reasonable [7] value for the one-body PNC matrix element was used. However, when the same size matrix element was used the average asymmetry was almost two orders of magnitude smaller than measured. Recently more extensive theoretical investigations characterized several terms that could contribute to PNC asymmetries in the CN [8,9]. Additional terms were derived and evaluated. However these theories did not identify new terms that were large enough to explain the large non-fluctuating asymmetry. The quantity measured in the experiments with polarized epithermal neutrons is the longitudinal asymmetry P (Er) = σ + (Er)− σ − (Er) σ+(Er) + σ −(Er) , (1) where σ + , σ − are the resonance part of the total cross sections for neutrons with positive 2 and negative helicities respectively. The index r designates the fact that the scattering is to a compound resonance |r〉 at energy Er, carrying the quantum numbers J = 12 − . We will refer to these resonances as p1/2. The leading term of the asymmetry P can be written [6,9] P (Er) = −2 ∑ s 〈s|V PNC|r〉 Er − Es γs γr , (2) where γr and γs denote the escape amplitudes from resonances |r〉 and |s〉 due to the strong interaction force and are given by: γr = 〈Φ (+) p |H|r〉 , γs = 〈Φ (−) s |H|s〉 , (3) where Φ (+) p and Φ (−) s denote the continuum p and s-wave functions in the elastic channels. The sum in Eq. (2) extends in principle over all states |s〉 that have the quantum numbers J = 1 2 + . To reduce the sum in the equation one often introduces the doorway state approximation [10,11]. One seeks a subspace of states |s〉, denoted by |d〉 such that the coupling between these states and the states |r〉 – 〈r|V PNC|d〉 is sizeable or that the coupling between |d〉 and the continuum is strong or that both conditions are fulfilled so that when the sum in Eq. (2) is replaced by the partial sum over states |d〉 the result will be a good approximation to Eq. (2). In a formal treatment [9,10,12] one divides the space of states |s〉 into: {s} = {d}+ {s′}. Assuming that the signs of the matrix elements 〈r|V PNC|s′〉 are randomly distributed one derives [9–12] the following expression: