Carr, Bloom, Petrovich, and Philpott reply

Abstract

Carr, Bloom, Petrovich, and Philpott Reply: Geesaman and Zeidman l have pointed out a deficiency in the double ratio (R-Rz/Rs) of isoscalar to isovector inelastic scattering strengths (Rz^Zo/Z?) and proton stripping spectroscopic strengths (Rs~Sp/Sp) predicted in our recent large-basis shell-model study 2 of stretched 6~ states in 28 Si as compared with experiment. This is a valid point which was inadequately discussed in our Letter; however, Geesaman and Zeidman also make comparisons with an earlier, more restricted shell-model study 3 and introduce an "experimental" spectroscopic strength ratio 4 in a manner that obscures the improvement in our extended-basis calculation and exaggerates the problem with the double ratio.Specifically, the theoretical calculation of Ref. 3 predicts more than one "observable" 6 ~, !T-0 excitation as was emphasized in Fig. 1 of our Letter. This additional r-0 strength should be included when comparing the results of Ref. 3 with our work. Further, the experimental ratio (R ,wm Rs/R<j) of the spectroscopic factor ratio Rs to the transfer cross-section ratio (i? a -<7p/<7p), R' = 1.25/0.9-1.4, provides a measure of the influence of finite-well considerations on the interpretation of the transfer reactions 4 (see Fig. 7 in Ref. 4). Since the theoretical calculations of Refs. 2 and 3 were carried out in an oscillator basis, the theoretical Sj should be suitably corrected before comparing with Rs 1 " 1.25. Clausen 5 has shown that finite-well considerations are much less important for inelastic scattering from 28 Si.On the basis of these remarks, we have reconstructed Table I of the Comment by Geesaman and Zeidman below. Under "Amusa" we include all of the observable 6~, r-0 strength that was predicted to fall below the observed 6~, T-1 state. In short, we include two additional low-lying T-0 states that are quite strong in the spectrum (cf. Fig. 1 in Ref. 2). Further, we have increased (reduced) all theoretical Sp (Sp) by Vh4 to reflect finite-well effects included in the analysis of Ref. 4. The main effect of this correction is to increase (decrease) the theoretical Rs (R), improving agreement with experiment. The division of the effect between isoscalar and isovector levels is admittedly arbitrary, but does not affect the final ratio considerations.In this form the table properly reflects the significant improvement that is obtained in the spectrum of 6~ states by extending the basis used in the theoretical calculations. The ZT, Sp, Rz, and Rs all move toward experiment as the basis is expanded with the Sp and Rs tending to overshoot somewhat. The Zr closely follow the Sp, so the double ratio R changes only slowly and remains above the data. This slow variation of R is the signature of "fragmentation" and is to be expected in our calculation. Although our results are almost within experimental errors for specific observables, there is a systematic deviation which is amplified in the double ratio R. This indicates the need for additional mechanisms which reduce the ZT faster than th...

Nucleon Charge-Exchange Reactions at Intermediate Energy

“…Measurements for the excitations however provide only a limited extension of the inelastic scattering results. At present, the most interesting aspect of the study of stretched configurations is the fragmentation of the strength [206]. Charge-exchange measurements have not contributed to such studies though, because of the relatively poor energy resolution available, about 300 keV for (p,n) measurements and 1 MeV for (n,p).…”

“…It was shown that although the 1p-1h configuration was unique, this was not an eigenstate of the nuclear Hamiltonian, so that the strength of the excitation was spread over other states by residual interactions. The cross section for excitation of a particular state however was proportional to the strength of the stretched configuration in the wave function of that state [206]. Thus the (e, e') reaction, involving the well understood electromagnetic interaction, may be used to determine the 1p-1h transition density; this may then be used in the analysis of (p,p') results to study the effective N-N interaction.…”

Pion scattering to6−stretched states inMg24<

“…14) of the total (f7/2d&iz) strength [7], the T = O, J = 6 state in Mg represents only 4.4% (Zo =0.044) of the total (f7/2d5/z) strength (see Table I). Recent large basis shell model calculations predict that the T=O, J =6 strength concentrated in the yrast state should be Z0=0.…”

“…The theoretical Z coefficients are from the sum rules of Ref. [6] for the extreme-single-particle model (ESPM) and from the large basis shell model (LBSM) calculations of Carr [7,8]. The ratio between experiment and theory is defined as Mg, which is in strong disagreement with that from ana1ysis of recent proton scattering measurements [10].…”

“…However, previous proton scattering measure-44 2413 TABLE I. The Z coefFicients for the pure isoscalar and pure isovector 6 states in Mg, Mg, and ' Si observed by pion and electron scattering [7,19]. The theoretical Z coefficients are from the sum rules of Ref.…”