Symmetry Background of the Stability of the Second 0 + State of 4 He

It was found in this paper that the dominant component of the wave function of the second 0 + state of 4 He and the corresponding component of the 3 H+p channel have different spatial permutation symmetries and different parities. This fact will hinder the wave function to extend from the interior region to the outgoing channel and will results in having a narrower width. The few-nucleon systems usually have very few bound states but they might have a few resonances [1,2]. The investigation of the resonances is an important way to understand the underlying physics of these systems. An important feature of a resonance is its width. Some of them are very narrow, some are broad. Usually, the broadness is attributed to the dynamics. Of course this is true, because if the dynamical parameters vary, the resultant widths would vary in accord. However, in addition to the dynamics, the symmetry might be also important. In this paper, it is demonstrated how the stability of an excited state and thereby its width is affected by symmetry. Specifically, four-nucleon systems are involved in the discussion. 1 Based on an R-matrix analysis, a number of resonances of 4 He have been suggested. The existence of the second 0 + state as a resonance with a width about 390 keV is well recognized. However, the other suggested resonances have not yet been widely accepted. Evidently, if the width of a resonance is very broad, the discrimination of the resonance would be very difficult or even impossible. In what follows we shall discuss this problem in coordinate space. It is noted that in a region where all the norms of the Jacobi vectors are smaller than a given reasonable value, then this region is called the interior region; whereas in a region where the norm of one and only one Jacobi vector is unlimited, then the region is called a 2-body channel, and so on. On the other hand, the wave function of a state is in general composed of different components (as we shall see). If all the components are confined in the interior region, then the state is obvious a bound state. However, if some components extend outward along a channel, then it is a resonance. When the major components are confined in the interior region while some minor components leak into the channel, then the state is nearly bound and the …