Energy Averages over Regular and Chaotic States in the Decay Out of Superdeformed Bands

Abstract

We describe the decay out of a superdeformed band using the methods of reaction theory. Assuming that decay-out occurs due to equal coupling (on average) to a sea of equivalent chaotic normally deformed (ND) states, we calculate the average intraband decay intensity and show that it can be written as an "optical" background term plus a fluctuation term, in total analogy with average nuclear cross sections. We also calculate the variance in closed form. We investigate how these objects are modified when the decay to the ND states occurs via an ND doorway and the ND states' statistical properties are changed from chaotic to regular. We show that the average decay intensity depends on two dimensionless variables in the first case while in the second case, four variables enter the picture. §1. IntroductionThe first superdeformed (SD) rotational band to be observed was that identified in the nucleus 152 66 Dy 86 by Twin et al. 1) A sequence of nineteen γ-rays of nearly constant spacing was observed which permitted the attribution of the moment of inertia of a symmetric prolate rigid rotor with elliptic axes in the proportion 1:1:2. Since then 320 SD bands have been observed in various mass regions extending from A∼20 to A∼240. 2) The stability of nuclei at any deformation can be related to the existence of energy gaps between shells of independent particle states. The shell gaps which appear for certain nuclear deformations give origin to non-spherical configurations of special stability. 3), 4)As explained by Lopez-Martens et al., 5) the γ-spectrum of a compound nucleus whose decay path includes an SD band typically contains γ-rays which result from four distinct stages: I Statistical γ-rays which populate the SD band after formation of the nucleus under consideration by particle evaporation following a fusion evaporation or fragmentation reaction. II Collective E2 γ-rays from decay along the SD band. III Statistical γ-rays from excited normally deformed (ND) configurations. IV Collective E2 γ-rays from decay along the yrast ND band. In cases where this kind of decay scheme applies, stages I and III correspond to the cooling of a hot and chaotic system while stages II and IV correspond to the decay of a cold and regular system. Other decay schemes which include SD bands are typeset using PTPT E X.cls Ver.0.89

How large is the spreading width of a superdeformed band?

“…The motivation behind the SB model may be thought of as similar to the calculation of a "doorway-doorway" interaction in the GW/SH approach, for which a fluctuation contribution could also be calculated [8]. It seems unlikely, given the relatively low ND level density, that a fully statistical mixing process occurs in the decay of SD 192 Pb, and thus this type of doorway approach may be more suitable than the present statistical models.…”

“…The possible causes of this rapid loss of flux have been the subject of much discussion, but despite more than a decade of theoretical and experimental work, no complete theory of the decay mechanism has been arrived at. Indeed, it is as yet not clear whether the sudden enhancement of the decay probability is due to the dependence on angular momentum of the height of the bar-rier separating the SD and normal potential wells, to the increasing effect of pairing correlations with decreasing spin, or to the onset of chaos in the structure of the normal-deformed (ND) states [8]. One of the obstacles to progress in the attempt to understand the decay mechanism has been the difficulty in arriving at a consistent, broadly-applicable and reliable means of characterizing the size of the interaction between the SD and ND states involved in the decay-out.…”