A method is presented for obtaining centroids of the effective nucleon-nucleon interaction directly from measured single-particle energies. An application to nuclei in the mass region A=28 to 56 is provided to illustrate the technique. Uncertainties in the centroids are estimated at 100 keV or less, except in cases of exceptional fragmentation of the single-particle strength. Methods such as the one proposed here can be used to place constraints on realistic interactions calculated from bare nucleon-nucleon potentials, which are known to possess defective centroids in many cases.

The role of trajectory fluctuations on the first and second moments obtained in the mean trajectory approximation for the proton and neutron distributions of the projectile-like fragments produced in deep inelastic heavy ion collisions has been studied in the framework of stochastic transfer of single nucleons. At each instant of time the neutron and proton numbers of the colliding nuclei are considered to be given by dynamically evolving Gaussian distributions generating trajectory fluctuations. The first moments calculated in this method differ considerably from those obtained in the mean trajectory approximation for the systems with strong gradient in the driving force around the point of injection. The second moments, however, do not change appreciably for all the systems studied.

Strutinsky’s shell correction prescription is analyzed from a thermodynamic viewpoint. The working of ‘‘entropy force’’ against the ‘‘shell force’’ is clearly established. The behavior of nuclear level density at low excitation is also discussed.

Recently Adhikari and Tomio have claimed that our W-matrix representation of the T matrix is a special case of previous results proposed by these authors. However, the early papers to which they refer do not go beyond the well-known Kowalski representation, and the more recent publication, which was the first of their papers to sketch the decisive modifications characteristic for the W-matrix representation, was submitted years after the first presentation of our approach. The priority claims by Adhikari and Tomio, therefore, are incorrect.

We argue that the emission rate of dipole γ rays in the preequilibrium hybrid model is not affected by the parity constraint that the dipole operator imposes on single-particle radiative transitions. Consequently, parity can be neglected when calculating preequilibrium spectra of medium-energy γ rays. The emission rate by Reffo et al. should be scaled down by a factor of 4.

We reply to the preceding Comment.

The production of protons from the ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(d,p${)}^3$H reaction was investigated using an electrolytic cell and a proportional counter. The cathode, consisting of a 30.5-mg/${\mathrm{cm}}^2$-thick Pd foil, separated the gas in the counter from the electrolyte (0.1M LiOD in ${\mathrm{D}}_2$O). The efficiency for proton detection was 28%. The electrolytic cell was operated with current densities up to 650 mA/${\mathrm{cm}}^2$. Several runs with the current switched on and off and with different Pd foils have been performed with the longest run lasting more than 10 days. No difference in the count rate was observed when the electrolytic cell was on or off. From the high-energy part of the particle spectrum we obtain an upper limit for the proton production from the fusion reaction ${}_{}{}^2{}_{}{}^{}\mathrm{H}$(d,p${)}^3$H of 4×${10}^{\mathrm{-}23}$ fusion/(dd pair/sec).

Polarization observables for the scattering of two spin-(1/2 particles are organized into different classes based on the difficulty of their measurement. The large or significantly varying ones are noted. A microscopic, momentum space optical potential is used to predict all polarization observables for 250–650 MeV proton scattering from the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ nucleus, and the observables are presented in three-dimensional plots.

The low-energy ${}_{}{}^{36}{}_{}{}^{}(\mathit{\alpha }$,α) elastic scattering data of Gaul et al. are analyzed within the frame of the optical model, using energy-independent Woods-Saxon squared or model-independent geometries for the real part of the potential. The optical-model scattering amplitude is decomposed into its barrier and internal wave components to understand the rapid and complicated evolution of the angular distributions with incident energy. The properties of the low-energy bound and quasibound states supported by this potential are compared with those of the states of the deformed 4p-4h rotational band in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, built on the $J^{\pi }$${=0\mathrm{}}^{+}$, $E_x$=3.35 MeV state. The possibility of extending this local potential model approach to neighboring nuclei near the sd-shell closure is discussed. A negative-parity band of states with appreciable α-cluster character, starting around the α-particle threshold, is expected to be systematically present in this mass region.

We show that in the plane-wave impulse approximation an incident proton cannot, in the case of elastic forward (q=0) scattering, change the polarization state (J,M) of a J=1 target nucleus from (1,+1) to (1,-1), where the direction of polarization is normal to the scattering plane. We then show that this double spin-flip process can take place when the effects of double scattering are taken into account. As a corollary, the spin-quadrupole moment of the deuteron must be zero.

Spectra, angular distributions, and cross sections have been measured for Z=3–12 fragments produced in the reaction of 161-MeV protons with a silver target. Nonequilibrium mechanisms dominate the fragment yields at forward angles and for low-Z ejectiles. Equilibrated emission is primarily responsible for fragments observed at backward angles, an effect which grows in importance with increasing fragment Z value. A power-law fit to the elemental cross section distributions yields an exponent τ=4.7, significantly larger than observed for higher-energy protons. These data are compared with the predictions of statistical decay, accreting source, and preequilibrium calculations.

Excitation functions for the reactions ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$(α,xn${)}^{73\mathrm{-}x}$As, ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$(α,p3n${)}^{69}$Ge, ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$(α,2p4n${)}^{67}$Ga, ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$(α,xn${)}^{75\mathrm{-}x}$As, ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$(α,xn${)}^{125\mathrm{-}x}$I, ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$(α,p3n${)}^{121}$Te, and ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sb}$(α,xn${)}^{127\mathrm{-}x}$I were obtained from the measurements of the residual activity of stacked foils from threshold to 65 MeV. The excitation functions for the production of ${}_{}{}^{74}{}_{}{}^{}\mathrm{As}$, ${}_{}{}^{72}{}_{}{}^{}\mathrm{As}$, ${}_{}{}^{71}{}_{}{}^{}\mathrm{As}$, ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ge}$, and ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ga}$ from α-induced reactions on Ga and ${}_{}{}^{126}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{124}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{123}{}_{}{}^{}\mathrm{I}$, ${}_{}{}^{121}{}_{}{}^{}\mathrm{I}$, and ${}_{}{}^{121}{}_{}{}^{}\mathrm{Te}$ from α-induced reactions on Sb are presented.

The experimental data are compared with calculations considering equilibrium as well as preequilibrium reaction mechanisms according to the hybrid model of Blann. The high-energy part of the excitation functions are dominated by the preequilibrium reaction mechanism. Calculations were done using the a priori calculational method of Blann. From the reactions ${}_{}{}^{71}{}_{}{}^{}\mathrm{Ga}$(α,3n${)}^{72}$As and ${}_{}{}^{123}{}_{}{}^{}\mathrm{Sb}$(α,3n${)}^{124}$I, an initial exciton number $n_0$=4 ($n_n$=2, $n_p$=2, $n_h$=0) with the mean-free-path multiplier parameter k set to 2 has been deduced for both the targets. However, there are a few exceptions. The theory overestimates the cross section for the ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$(α,2p4n${)}^{67}$Ga reaction whereas it underestimates the cross section for the ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$(α,p3n${)}^{121}$Te reaction and the high-energy tail of ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$(α,2n${)}^{123}$I excitation function. For the (α,2p4n) reactions on Ga the discrepancy between theory and experiment may be attributed partly to a breakup of the α particle and partly to much more complex reaction mechanisms, whereas for the ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$(α,p3n${)}^{121}$Te reaction two different reaction mechanisms may be attributed.

The large discrepancy between theory and experiment for the reaction ${}_{}{}^{121}{}_{}{}^{}\mathrm{Sb}$(α,2n${)}^{123}$I at the high-energy tail of the excitation function may be attributed to emission of more than one preequilibrium nucleon which the theory cannot account for at present. Barring these reactions we have found that the overall agreement between theory and experiment is reasonably good, taking the limitations of the theory into account.

The dynamic deformation model has been used to examine collective features of tungsten isotopes. The magnitudes and signs of calculated Q values as well as the ratios Q${(2\mathrm{}}_{\gamma }^{+}$)/Q${(2\mathrm{}}_g^{+}$) agree well with recent experimental results. The amount of K=0 component in the $2_{\gamma }^{+}$ state is found to be about 10%, but the K=2 component in $2_{\beta }^{+}$ state ranges from 9 to 47 % for the tungsten isotopes A=180–186. A significant K=0, K=2, and K=4 mixing occurs for I≥4 states. Results are supported by published data and also by the X(E0/E2) value for the 792 keV transition between $2_{\gamma }^{+}$ and $2_g^{+}$ states in ${}_{}{}^{18}{}_{}{}^{}\mathrm{W}$.

The observation of a superdeformed band in the nucleus ${}_{}{}^{192}{}_{}{}^{}\mathrm{Hg}$ is reported. The band has sixteen transitions with an average energy spacing of 36 keV and an average dynamic moment of inertia ${\mathrm{scrI}}^{\mathrm{}\left(2\right)\mathrm{}}$ of 112 ${ħ}^2$ ${\mathrm{MeV}}^{\mathrm{-}1}$. This band persists to rather low rotational frequency (ħω∼0.125 MeV) and is proposed to extend in spin from ${10}^{+}$ to ${42}^{+}$. No transitions linking the superdeformed states and the low deformation yrast levels were found and the decay out of the superdeformed band appears to be statistical. This is the second case of superdeformation in the A∼190 region.

We have derived a new useful analytic formula for the T matrix in the quantum-mechanical perturbation approach within the two-state problem with finite-range coupling which is appropriate for the discussion of the Landau-Zener transition. The resonancelike behaviors were predicted by classical or semiclassical approach in which constant coupling between two adiabatic states was assumed. In the quantum-mechanical approach, inclusion of the effect of reasonable finite-range coupling would not destroy the pattern of the resonancelike structures so much, while the magnitude of the calculated cross section is merely about 10% of that calculated by the semiclassical approach.

The advantages of kaon versus pion interferometry as a probe of quark-gluon plasma formation in high energy nuclear collisions are studied by comparing predictions of Lund resonance gas and plasma hydrodynamic models.

The interpretation of the nucleon spectral function P(k,E) in terms of two parts, associated with one- and many-particle emission processes, is discussed in connection with the analytical structure of the nucleon momentum distribution n(k). The integrals over E of the one-particle emission part of P(k,E) yield the one-hole strengths. The estimated strengths in the lead region agree fairly well with recent (e,e’p) data.

The widths of the residue-mass distributions are used as a measure of the excitation energy of hot nuclei. They increase with the recoil velocity but saturate much below the calculated velocity $v_{\mathrm{CN}}$ for complete fusion. Above these critical excitations energies (4.5–6.4 MeV/nucleon) derived from the recoil velocity, the normal evaporation of nucleons and small clusters disappears, if a hot and equilibrated compoundlike nucleus is formed at all.