Missing and quenched Gamow-Teller strength.

Gamow-Teller strength functions in full (pf) spaces are calculated with sufficient accuracy to ensure that all the states in the resonance region have been populated. Many of the resulting peaks are weak enough to become unobservable. The quenching factor necessary to bring into agreement the low lying observed states with shell model predictions is shown to be due to nuclear correlations. To within experimental uncertainties it is the same that is found in one particle transfer and (e,e’) reactions. Perfect consistency between the observed Ca(p, n)Sc peaks and the calculation is achieved by assuming an observation threshold of 0.75% of the total strength, a value that seems typical in several experiments Typeset using REVTEX Centre de Recherches Nucléaires, IN2P3-CNRS/Université Louis Pasteur, Division de Physique Théorique, BP 20, F-6037 Strasbourg Cedex, France Departamento de F́ısica Teórica, Universidad Autónoma de Madrid, 28049 Madrid (Spain) 1 Since the time of the pioneering (p,n) experiments [1], [2], and the more recent (n,p) ones [3], [4] it has been possible to know the full Gamow Teller strength functions of many nuclei. The most striking result is that a large fraction of the theoretically expected sum rules for the στ operators, S+ and S−, is not visible. The precise amount may be difficult to asses, in particular because calibration discrepancies with beta decay measures [5], [6], but there is no doubt that it is substantial and a reduction by a factor 0.6 of S+ and S− is currently accepted as standard. This number is obtained through two different channels. One is the Ikeda sum rule S+ S−= 3(N-Z), which is model independent provided we do not introduce non-nucleonic degrees of freedom -and we will not. Therefore the strength difference cannot be quenched, i.e. suppresed. It is missing but it must be somewhere [7]. The other indication comes from the well defined, isolated peaks seen in β decays which are about a factor 0.6 weaker than predicted by the most accurate shell model calculations available [8], [9]. Here we can speak of quenching because the data demand it. In section I we will calculate complete strength functions that suggest that many states must be unobservable. In section II we decompose the model independent sum rule in a way that makes apparent that quenching originates in nuclear correlations. In section III we give the reasons to expect that only about 50% of the S− sum rule for Ca is observed [10]. I. To understand how the strength distributes among daugther states we rely on the method propossed by Whitehead [11] and now quite popular [12], [13], [14]. We work in the full pf shell with the KB3 interaction [15], [16], and obtain an exact eigenstate of the target | i > in this model space. Then we define states |S± >= στ | i > whose norms are the sum rules S±, and we use them as pivots (i.e. starting states) in a Lanczos tridiagonal construction. After I iterations we obtain I+1 eigensolutions and the amplitudes of the pivot in each of them determine their share of strength. The situation at I=50 is shown in fig. 1 for Ca(p, n)Sc, i.e. | i > is the (pf) T=4 ground state and the pivot is projected to keep only T=3 states. The first 4 spikes correspond to converged eigenstates whose position