The article by Bauer and Botvina criticizes on the basis of an intranuclear cascade-percolation calculation our previously published determination of the critical exponents associated with the multifragmentation of $1A$ GeV Au+C. Some questions are raised concerning the validity of their analysis.

We reply to the preceding comment.

Motivated by the success of models based on chiral symmetry in $\mathrm{NN}$ interactions, we investigate self-interacting scalar, pseudoscalar, and vector meson fields and their impact for $\mathrm{NN}$ forces. We parametrize the corresponding nonlinear field equations and get analytic wavelike solutions. A probability amplitude for the propagation of particle states is calculated and applied in the framework of a boson-exchange $\mathrm{NN}$ potential. Using a proper normalization of the meson fields makes all self-scattering amplitudes finite. The same normalization is able to substitute for the phenomenological form factors used in conventional boson-exchange potentials and thus yields a phenomenological understanding of this part of the $\mathrm{NN}$ interaction. We find an empirical scaling law which relates the meson self-interaction couplings to the pion mass and self-interaction coupling constant. Our model yields $\mathrm{np}$ phase shifts comparable to the Bonn B potential results and deuteron properties, in excellent agreement with experimental data.

Regularization and renormalization is discussed in the context of low energy effective field theory treatments of two or more heavy particles (such as nucleons). It is desirable to regulate the contact interactions from the outset by treating them as having a finite range. The low energy physical observables should be insensitive to this range provided that the range is of a similar or greater scale than that of the interaction. Alternative schemes, such as dimensional regularization, lead to paradoxical conclusions such as the impossibility of repulsive interactions for truly low energy effective theories where all of the exchange particles are integrated out. This difficulty arises because a nonrelativistic field theory with repulsive contact interactions is trivial in the sense that the $S$ matrix is unity and the renormalized coupling constant zero. Possible consequences of low energy attraction are also discussed. It is argued that in the case of large or small scattering lengths, the region of validity of effective field theory expansion is much larger if the contact interactions are given a finite range from the beginning.

Cascade calculations of hadronic hydrogen atoms are performed to obtain the x-ray yields as a function of the target density. An extension of Leon-Bethe’s Stark mixing rates to $m\ne 0$ states is made without the introduction of the parameter $k_{\mathrm{STK}},$ which is necessary in the Borie-Leon model to enhance the Stark mixing rates. Although the energies of their L x rays are too low to observe, we can roughly estimate the 2p absorption width of pionic and kaonic hydrogen atoms from the measured K x-ray yields.

Pion elastic scattering on deuterium is studied in the Kerman-McManus-Thaler multiple scattering approach developed in momentum space. Using a Paris wave function and the same methods and approximations as commonly used in pion scattering on heavier nuclei excellent agreement with differential cross section data is obtained for pion energies $100<\mathrm{}{T}_{\pi }<250\mathrm{}$ MeV. At higher energies and very backward angles, discrepancies appear that are reminiscent of disagreements in pion scattering on ${}^3$He, ${}^3$H, and ${}^4$He. At low energies $T_{\pi }<~65$ MeV the model fails to reproduce experimental data at forward direction. In this kinematical region the coupling with the breakup channels has to be included. Polarization observables are studied in detail. While tensor analyzing powers are well reproduced, vector analyzing powers exhibit dramatic discrepancies.

Coherent pion photoproduction, $d(\gamma ,{\pi }^0)d$, is calculated in a coupled channels approach in momentum space using an elementary production operator that includes Born terms, vector meson exchange, and $M1/E2\mathrm{}$ $\Delta$-resonance excitation. The final state interaction is treated in the Kerman-McManus-Thaler multiple scattering approach that describes $\pi d$ elastic scattering well. Differential cross sections are found to agree well with existing $(\gamma ,{\pi }^0)$ data. The polarization observables $\Sigma {,iT}_{11}$ and the tensor analyzing powers are predicted for forthcoming experiments. A number of transparent relationships between polarization observables and the elementary production operator is derived. Finally, calculations are performed for coherent $\eta$ photoproduction, $d(\gamma ,\eta )d$, in the threshold region which agree well with a very recent Mainz experiment.

The structure of ${}^{105}$Sn has been investigated through the ${}^{50}$Cr${(}^{58}$Ni,2pn) reaction at a beam energy of 210 MeV. In addition to an extension of the spherical level scheme a regular sequence of dipole transitions has been found. The states of the dipole band are suggested to be built on a neutron $h_{11/2}^2$ excitation coupled to proton particle-hole states, which polarize the core to a slightly prolate shape. The experimental results are in agreement with the prediction of tilted axis cranking calculations, which satisfactorily explain the properties of the band.

Spin asymmetries for the ${}^{16}\mathrm{O}(\overrightarrow{\gamma },p{\pi }^{-})$ reaction are reported for incident photon energies of 293 $\pm$ 20 MeV, proton angles ranging from 28$°$ to 140$°$ (lab), and pion angles of 35$°$ to 115$°$. The data are compared with calculations in a quasifree plane-wave impulse approximation model. This model is in good agreement with the data at small momentum transfer $q$, but does not follow the trend of the data at large $q$. Sensitivity to the $\Delta$-nucleus potential and to modification of the $\Delta$ lifetime from nuclear medium effects are explored using a simple modification of the $\Delta$ propagator in the calculations.

Recent measurements of fission fragment anisotropies in the ${}^{12}$C+${}^{232}$Th reaction by Majumdar et al. [Phys. Rev. C 53, R544 (1996)] show a peaklike structure in the sub-barrier energy region. We present new measurements for this reaction at near- and sub-barrier energies. Our results are in dramatic disagreement with the work of Majumdar et al. We see no peaklike structure in the fragment anisotropy as a function of the projectile kinetic energy, but instead find an anomalous plateau in the anisotropy at $W$(180$°)$/$W$(90$°)$$\sim$1.5.

We have measured elastic scattering angular distributions for ${}^{58}$Ni+${}^{60}$Ni at $E_{{}^{58}\mathrm{Ni}}$ =204, 220, 236, and 250 MeV and for ${}^{62}$Ni+${}^{64}$Ni at $E_{{}^{64}\mathrm{Ni}}\hspace{0.5em}=250\mathrm{}$ MeV. The measured angular distributions show bell-shaped structures at backward angles for both systems at $E_{\mathrm{lab}}$=250 MeV which are due to the neutron pair exchange between identical cores for the projectile and target. The pair exchange has been analyzed by using the macroscopic form factor. For elastic scattering the coupled-channels analyses have been performed. The data are reproduced well. The possibility of a nuclear Josephson effect is discussed.

New values for the $\gamma$ ray intensities following the $\beta$ decay of ${}^{11}$Li are presented. Special emphasis is put on the determination of the Gamow-Teller transition ${}^{11}$Li $\to$ ${}^{11}$Be (1/2${}^{-}$, 320 keV) to the only bound excited state in ${}^{11}$Be. We show that a shell-model calculation can simultaneously reproduce the half-life of ${}^{11}$Li and the newly measured branching ratio to the ${1/2}^{-}$ state provided the ${}^{11}$Li ground state wave function contains about 50% of $s$-wave neutron components.

We have measured differential cross sections for pion elastic scattering from ${}_{}{}^3{}_{}{}^{}\mathrm{H}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in the angular region near the minimum in the non-spin-flip amplitude. Data were acquired for incident pion energies of 180, 220, 256, and 295 MeV. Nuclear charge symmetry is investigated with the aid of several charge-symmetric ratios formed from combinations of measured cross sections. A particularly intriguing result is obtained from the superratio R, which is defined as R=dσ(${\mathrm{\pi }}^{+\mathrm{}3}$H)dσ(${\mathrm{\pi }}^{\mathrm{-}\mathrm{}3}$H)/dσ(${\mathrm{\pi }}^{+\mathrm{}3}$He)dσ(${\mathrm{\pi }}^{\mathrm{-}\mathrm{}3}$He). R is found to be greater than unity at 180 MeV and significantly smaller than unity at 256 MeV, with the transition occurring at around 210 MeV. The charge-symmetry prediction for this ratio (after allowance for the Coulomb force) is one, and is independent of energy and angle. © 1996 The American Physical Society.

Interest in the production of hyperon-antihyperon pairs following antiproton-proton annihilation stems largely from attempts to understand the nature of flavor production. To date the major focus of both the experimental and the theoretical effort has been on the p¯p→Λ¯Λ reaction. In this paper, we present data on the complementary channels p¯p→Σ¯${\mathrm{}}^0$Λ and p¯p→Λ¯${\mathrm{\Sigma }}^0$. Events from the kinematically similar p¯p→Λ¯Λ reaction were obtained in parallel. The procedure to distinguish these three separate reactions is described and results for all channels are presented. These include the total and differential cross sections, hyperon polarizations, and spin correlation coefficients. Data were obtained at incident antiproton lab momenta of 1.726 and 1.771 GeV/c which correspond to excess kinetic energies in the p¯p→Λ¯${\mathrm{\Sigma }}^0$+c.c. reaction of 26 and 40 MeV, respectively, above threshold. Comparisons are made to earlier work at similar excess energies in the p¯p→Λ¯Λ channel. The low-energy regime has been highlighted in this experiment to reduce the complexity in the theoretical analysis. © 1996 The American Physical Society.

Pionic-decay spectra are discussed in A=4 and 5 Λ hypernuclei by using wave functions obtained by the resonating group method. For ${}_{\mathrm{\Lambda }}{}^5{}_{}{}^{}\mathrm{He}$, the ${\mathrm{\pi }}^{\mathrm{-}}$ spectrum shows a sharp peak at 171 MeV with 1.5 MeV FWHM in the total pion energy. For ${}_{\mathrm{\Lambda }}{}^4{}_{}{}^{}\mathrm{H}$ and ${}_{\mathrm{\Lambda }}{}^4{}_{}{}^{}\mathrm{He}$, the spectra have broad peaks around 170 MeV with 6–7 MeV FWHM. This difference is caused by resonance structures of the final-state nuclei under the spin-nonflip dominance in the pionic decay. Partial decay widths are calculated to check the normalization of the spectra, and are in systematically good agreement with all available experimental data. © 1996 The American Physical Society.

Pion-meson-exchange nucleon-nucleon potentials are derived for two nucleons in the intermediate states. The mesons we include are (i) pseudoscalar mesons π,η, and ${\mathrm{\eta }}^{\prime }$, (ii) vector mesons ρ, ω, and φ, (iii) scalar mesons ${\mathit{a}}_0$(980), ɛ(760), and ${\mathit{f}}_0$(975), and (iv) the J=0 contribution from the Pomeron. Strong dynamical pair suppression is assumed, and at the nucleon-nucleon-meson vertices Gaussian form factors are incorporated into the relativistic two-body framework using a dispersion representation for the pion- and meson-exchange amplitudes. The Fourier transformations are performed using factorization techniques for the energy denominators. The potentials are first calculated in the adiabatic approximation to all planar and crossed three-dimensional momentum-space π-meson diagrams. Next, we calculate the 1/M corrections. © 1996 The American Physical Society.

Two-meson-exchange nucleon-nucleon potentials are derived where either one or both nucleons contains a pair vertex. Physically, the meson-pair vertices are meant to describe in an effective way (part of) the effects of heavy-meson exchange and meson-nucleon resonances. From the point of view of ‘‘duality,’’ these two kinds of contribution are roughly equivalent. The various possibilities for meson pairs coupling to the nucleon are inspired by the chiral-invariant phenomenological Lagrangians that have appeared in the literature. The coupling constants are fixed using the linear σ model. We show that the inclusion of these two-meson exchanges gives a significant improvement over a potential model including only the standard one-boson exchanges. © 1996 The American Physical Society.

Ohta proposed a solution for the well-known difficulty of satisfying the Ward-Takahashi identity for a photo-meson-baryon-baryon amplitude (γMBB) when a dressed meson-baryon-baryon (MBB) vertex function is present. He obtained a form for the γMBB amplitude which contained, in addition to the usual pole terms, longitudinal seagull terms which were determined entirely by the MBB vertex function. He arrived at his result by using a Lagrangian which yields the MBB vertex function at tree level. We show that such a Lagrangian can be neither Hermitian nor charge conjugation invariant. We have been able to reproduce Ohta’s result for the γMBB amplitude using the Ward-Takahashi identity and no other assumption, dynamical or otherwise, and the most general form for the MBB and γMBB vertices. However, contrary to Ohta’s finding, we find that the seagull terms are not robust. The seagull terms extracted from the γMBB vertex occur unchanged in tree graphs, such as in an exchange current amplitude. But the seagull terms which appear in a loop graph, as in the calculation of an electromagnetic form factor, are, in general, different. The whole procedure says nothing about the transverse part of the (γMBB) vertex and its contributions to the amplitudes in question. © 1996 The American Physical Society.

The neutron-rich isotopes ${}_{}{}^{54\mathrm{-}57}{}_{}{}^{}\mathrm{Ti}$ and ${}_{}{}^{58\mathrm{-}60}{}_{}{}^{}\mathrm{Cr}$ are produced by fragmentation of a 64.5 MeV/nucleon ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}_{}^{26+}{}_{}{}^{}$ beam in a 90 mg/${\mathrm{cm}}^2$ ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$ target. Following particle identification by energy loss and time of flight, the radioactive decay was observed by β singles and βγ-coincidence measurements. The results obtained for ${}_{}{}^{58\mathrm{-}60}{}_{}{}^{}\mathrm{Cr}$ are compared to previous results, whereas the decay of the ${}_{}{}^{54\mathrm{-}57}{}_{}{}^{}\mathrm{Ti}$ isotopes is studied here. γ-ray intensities and energies are estimated. The new experimental results are compared to quasi-random-phase-approximation predictions. © 1996 The American Physical Society.

The half-life (${\mathit{T}}_{1/2}$) and g factor of the 2002 keV ${11}^{\mathrm{-}}$ isomer in the odd-odd nucleus ${}_{}{}^{92}{}_{}{}^{}\mathrm{Tc}$ produced by the pulsed heavy-ion reaction ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}$${(}^{28}$Si,p3n${)}^{92}$Tc have been measured using time differential perturbed angular distribution method. The measured ${\mathit{T}}_{1/2}$ value is 3.15(20) ns. From the observed spin precession frequency ${\mathrm{\omega }}_{\mathit{L}}$ of a ${}_{}{}^{92}{}_{}{}^{}\mathrm{Tc}$ recoil implanted into a ferromagnetic Ni host, we obtain the g factor to be 0.806(20). The measured value of the g factor is in good agreement with a shell model analysis carried out using π(${\mathit{p}}_{1/2}$${\mathit{g}}_{9/2}$) and ν(${\mathit{p}}_{1/2}$${\mathit{g}}_{9/2}$) orbitals for the proton particles and neutron holes outside the ${}_{}{}^{88}{}_{}{}^{}\mathrm{Sr}$ core. © 1996 The American Physical Society.