Recent Articles

Heavy systems at intermediate energies in the Boltzmann-Uehling-Uhlenbeck approach

J. Aichelin

Phys. Rev. C 33, 537 (1986) - Published 1 February, 1986

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The Boltzmann-Uehling-Uhlenbeck equation is applied to nucleus-nucleus collisions with heavy targets, extending previous work on light systems. The model exhibits a hot source of nonequilibrated particles, giving single-particle spectra that are in reasonable agreement with experiment for the case studied, 84A MeV ${}^{12}C$ $+^{197}$ Au. However, the source is not localized in space, which questions the validity of models using global or local thermal equilibrium. The equilibration of the heavy remnant is not completed by 180 fm/c and turns out to be a complicated interplay between the mean field and collisions. The projectile transfers nearly all of its linear momentum to the target for energies up to 30A MeV. At higher energies the linear momentum transfer is incomplete, even for central collisions.

Nuclear interferometry and thermal freeze out

David H. Boal and Julian C. Shillcock

Phys. Rev. C 33, 549 (1986) - Published 1 February, 1986

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The technique of nuclear interferometry is applied to proton and light fragment emission in intermediate energy heavy ion reactions. It is shown that the source radii extracted by the technique are consistently larger for correlations involving two deuterons than for those with two protons. The time scale involved in particle emission is investigated with the technique and places a rough upper bound of a few times $10^{- 22}$ sec on the time scale associated with the source. A cascade model is formulated to predict the source parameters, and these are found to be in at least qualitative agreement with experiment. The implications of these results for the emission of heavier fragments are discussed.

Cross sections for the production of ${}^{11}C$ in C targets by ${}^{20}{Ne}$ and ${}^{56}{Fe}$ at relativistic energies

John C. Hill, J. A. Winger, C. M. McCullough, A. R. Smith, J. B. McCaslin, and P. J. Karol

Phys. Rev. C 33, 557 (1986) - Published 1 February, 1986

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Cross sections for the reactions ${}^{12}{Ne}$ ,X $)^{11}$ C and ${}^{12}{Fe}$ ,X $)^{11}$ C were measured using 1.05 GeV/nucleon ${}^{20}{Ne}$ and 1.7 GeV/nucleon ${}^{56}{Fe}$ ions. Annihilation radiation from ${}^{11}C$ was counted using a large volume NaI(Tl) detector. Values of 80.4±1.9 mb and 99.5±1.1 mb were obtained for ${}^{20}{Ne}$ and ${}^{56}{Fe}$ , respectively. The results are compared with earlier measurements of ${}^{11}C$ production from C targets using relativistic p, ${}^{4}{He}$ , and ${}^{12}C$ projectiles. The ${}^{12}C$ (RHI,X $)^{11}$ C cross sections are well described by a linear transport model, but are not in agreement with the predictions of strong factorization.

Fission fragment angular distributions

H. Rossner, J. R. Huizenga, and W. U. Schröder

Phys. Rev. C 33, 560 (1986) - Published 1 February, 1986

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A statistical scission model is developed and applied to fragment angular distributions from alpha- and heavy-ion-induced fission. Although the formal equations for fragment angular distributions in the statistical scission and transition-state models are of the same structure, the variances in the distribution of angular momentum projections on the fission direction are established at very different stages of the fission process in the two models. The statistical scission model predicts angular distributions in reasonable agreement with those measured for heavy-ion-induced fission of some reaction systems where the fission barrier has vanished or is very small relative to the nuclear temperature. For a number of these systems, the transition state model is inapplicable. The statistical scission model, however, predicts the variance to have too weak an energy dependence, possibly indicating dynamical effects. Inclusion of pre- and post-scission particle emission and asymmetric fission does not completely remove this discrepancy. The transition state model gives a better representation of fragment angular distributions from alpha-particle-induced fission of several targets (low-spin systems) as a function of fissility parameter. The large effective variances, deduced for systems with large spin and no fission barrier, are inconsistent with the concepts of ‘‘fast’’ or ‘‘pre-equilibrium’’ fission, occurring on a time scale too short for relaxation of the tilting mode. Some of the present discrepancies between the effective variances deduced from fragment angular distributions and those calculated with the statistical scission model may be due to small contributions of incomplete fusion followed by fission or due to sequential fission. Fragment spins deduced from γ-ray multiplicities are compared with predictions of the above two models.

Fitting scenarios in a simple theoretical approach to $1 s$ level shifts in pionic atoms

R. Rockmore and B. Saghai

Phys. Rev. C 33, 576 (1986) - Published 1 February, 1986

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The Klein-Gordon version of a simple analytic model of the pionic atom due to M. Ericson is derived. The expected precision of the resulting expression for pionic atom $1 s$ level shifts is about 10%. The model is well-suited for the qualitative comparison of theory, especially with regard to various parametric fitting strategies, and experiment in this case. It is found that a repulsive $Re B_{0}$ , comparable with $Im B_{0}$ in magnitude, is required to fit the experimental ( $T = 0$ ) data in the low $A$ region.

$π^{+}$ d→ $π^{+}$ pn reaction as a test of relativistic Faddeev theories: Differential cross section

W. Gyles, E. T. Boschitz, H. Garcilazo, W. List, E. L. Mathie, C. R. Ottermann, G. R. Smith, R. Tacik, and R. R. Johnson

Phys. Rev. C 33, 583 (1986) - Published 1 February, 1986

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Three-fold differential cross sections σ( ${theta}_{π}$ , ${theta}_{p}$ , $P_{p}$ ) have been measured in a kinematically complete experiment over a large region of phase space at 228 and 294 MeV incident pion energy. The data are compared with predictions from a relativistic Faddeev calculation. Excellent agreement is found over most of the phase space. From this good agreement between theory and experiment there appears to be no need for the inclusion of nonconventional dynamics, such as the excitation of dibaryon resonances.

$π^{+}$ d→ $π^{+}$ pn reaction as a test of relativistic Faddeev theories: Vector analyzing power

W. Gyles, E. T. Boschitz, H. Garcilazo, E. L. Mathie, C. R. Ottermann, G. R. Smith, S. Mango, J. A. Konter, and R. R. Johnson

Phys. Rev. C 33, 595 (1986) - Published 1 February, 1986

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The vector analyzing power, ${iT}_{11}$ , has been measured for the $π^{+}$ d→ $π^{+}$ pn reaction in a kinematically complete experiment. The dependence of ${iT}_{11}$ on the momentum of the proton has been obtained for 35 pion-proton angle pairs at pion bombarding energies of 180, 228, and 294 MeV. The data are compared with a relativistic Faddeev calculation. The theoretical prediction that there is a single universal shape for ${iT}_{11}$ , which is positive at low proton momenta and negative at large proton momenta, independent of the final pion and proton angles or of the incident pion energy is confirmed by the experiment.

$π^{0}$ η and $π^{0}$ η’ mixing and the reaction d+d→ $π^{0}$ $+^{4}$ He

Sidney A. Coon and B. M. Preedom

Phys. Rev. C 33, 605 (1986) - Published 1 February, 1986

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The isospin-forbidden reaction d+d→ $π^{0}$ $+^{4}$ He provides a very good test of the validity of charge symmetry. The forward differential cross section dσ/dΩ is estimated to be ≊0.12 pb/sr at a deuteron laboratory energy of 1.95 GeV. The assumed reaction mechanism is virtual η and η’ production and $π^{0}$ η and $π^{0}$ η’ mixing.

Hybrid quark-hadron model of Λ nonmesonic decay: Finite nuclei

D. P. Heddle and L. S. Kisslinger

Phys. Rev. C 33, 608 (1986) - Published 1 February, 1986

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Λ hypernuclear nonmesonic lifetimes are calculated in the framework of the hybrid quark-hadron model, for both infinite nuclear matter and for a finite nucleus ${}_{Λ}^{12}C$ . For nuclear matter, an approximate solution of the Bethe-Goldstone equation is used for the initial state ΛN cluster wave function. For ${}_{Λ}^{12}C$ a shell model wave function is used. An eikonal approximation is used to represent final state interactions. It is shown that with an effective weak quark Hamiltonian explicitly constructed to be consistent with the ΔI=1/2 rule the ${}_{Λ}^{12}C$ nonmesonic width is about 1.3 times the free Λ width, which is consistent with a recent experimental measurement.

Triple-differential cross sections of the ( $π^{+}$ ,pp) reaction on lithium isotopes

R. Rieder, P. D. Barnes, B. Bassalleck, R. A. Eisenstein, G. Franklin, R. Grace, C. Maher, P. Pile, J. Szymanski, W. R. Wharton, F. Takeutchi, J. F. Amann, S. A. Dytman, and K. G. R. Doss

Phys. Rev. C 33, 614 (1986) - Published 1 February, 1986

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The ( $π^{+}$ ,pp) reactions on ${}^{6}{Li}$ and ${}^{7}{Li}$ have been studied at $T_{π}$ =59.4 MeV with high resolution. The first triple-differential cross sections for these reactions are presented. The data are fitted to a T matrix and compared to the $π^{+}$ d→pp reaction. A model in which the pion is absorbed on a ${}^{3}S_{1}$ (pn) pair in the lithium nucleus describes many features of the data very well. An extrapolation of our data into unmeasured regions of phase space suggests that about 60% of the pion absorption cross section on ${}^{6}{Li}$ at 59.4 MeV goes into the ( $π^{+}$ ,pp) channel. One surprising feature of the data is that the ${}^{6}{Li}$ ( $π^{+}$ ,pp $)^{4}$ He ( $2^{-}$ ) transition at 22.1 MeV excitation is strongly populated, similar to what is observed in the ${}^{6}{Li}$ (d,α $)^{4}$ He reaction. This transition involves removing one nucleon from the 1p shell and one from the 1s shell.

Calculation of the (Δ-h, p-h) Landau parameter $g_{Δ}^{’}$ from a many-body Hamiltonian including π and Δ degrees of freedom

H. Sagawa, T.-S. H. Lee, and K. Ohta

Phys. Rev. C 33, 629 (1986) - Published 1 February, 1986

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The (Δ-h, p-h) Landau parameter $g_{Δ}^{’}$ has been calculated in the reaction matrix theory using a model Hamiltonian for π, N, and Δ. The main feature of the calculation is that the chosen NN→NΔ transition potential is consistent with the NN scattering data up to the energy region where NN→NΔ→πNN pion production can take place. Our result, $g_{Δ}$ ’=0.36, agrees qualitatively with a previous calculation based on the meson-exchange potential and simple hard-core correlations.

Relativistic plane-wave impulse approximation for nuclear inelastic scattering of protons and electrons

J. R. Shepard, E. Rost, and J. A. McNeil

Phys. Rev. C 33, 634 (1986) - Published 1 February, 1986

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We establish the general form of inelastic scattering amplitudes based on invariance principles and derive simple relations between these amplitudes and spin-transfer observables. We then examine a plane-wave relativistic impulse approximation for (p,p’) which is a simple extension of the relativistic impulse approximation for elastic scattering. We show under what approximations this amplitude reduces to the standard (nonrelativistic) impulse approximation and then examine the novel features of the free relativistic impulse approximation which results from less restrictive assumptions. We also derive free relativistic impulse approximation inelastic electron scattering form factors and then use our (p,p’) and (e,e’) formulations to extract nuclear structure information for the first two $1^{+}$ levels in ${}^{12}C$ . We consider possible experimental signatures of the strong scalar and timelike vector potentials of modern relativistic theories.

Pion-induced pion production on the deuteron

J. Lichtenstadt, D. Ashery, S. A. Wood, E. Piasetzky, P. A. M. Gram, D. W. MacArthur, R. S. Bhalerao, L. C. Liu, G. A. Rebka, Jr., and D. Roberts

Phys. Rev. C 33, 655 (1986) - Published 1 February, 1986

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Pion-induced pion production on the deuteron was studied via the reactions $π^{+}$ d→ $π^{-}$ $π^{+}$ pp and $π^{-}$ d→ $π^{+}$ $π^{-}$ nn. The doubly differential cross sections for these reactions were measured, covering the center-of-mass phase space at incident pion energies of 256, 331, and 450 MeV. Calculations of the quasifree production process on one nucleon were performed in a plane-wave approximation using a phenomenological, on-shell $π^{-}$ p→ $π^{+}$ $π^{-}$ n amplitude. Comparison of the data with the calculations indicates that the quasifree mechanism dominates these production reactions on the deuteron. Upper limits for bound $π^{-}$ nn and $π^{+}$ pp systems with small binding energies were also measured. The possible existence of a resonance in these systems near the production threshold was investigated.

Model-independent error analysis of $K^{+}$ -nucleus elastic scattering

J. D. Lumpe and L. Ray

Phys. Rev. C 33, 665 (1986) - Published 1 February, 1986

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Recent studies have demonstrated the enhanced sensitivity of $K^{+}$ mesons to interior nuclear matter distributions compared to that of protons at similar momenta. An approximately model-independent error analysis technique, similar to that used in analyses of electron scattering data, has been applied to $K^{+}$ -nucleus elastic scattering at 442 and 991 MeV. The primary result of this work is that the momentum transfer range and statistical quality of data necessary to provide meaningful new constraints on the distribution of nuclear matter in the interior of large nuclei is specified. The model dependence of this approach for hadron-nucleus scattering is considered and shown to be negligible.

Nonmesonic nucleon decay in nuclei

Leonard S. Kisslinger and Carl B. Dover

Phys. Rev. C 33, 673 (1986) - Published 1 February, 1986

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Shape coexistence and level structure of ${}^{100}{Zr}$ from decay of the low-spin isomer of ${}^{100}Y$

F. K. Wohn, John C. Hill, C. B. Howard, K. Sistemich, R. F. Petry, R. L. Gill, H. Mach, and A. Piotrowski

Phys. Rev. C 33, 677 (1986) - Published 1 February, 1986

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The level structure of the N=60 isotone ${}^{100}{Zr}$ has been studied via the decay of the low-spin isomer of ${}^{100}Y$ . A half-life of 735±7 ms was determined from γ-ray multiscaling measurements. γ singles and γ-γ coincidence measurements have resulted in the placement of 64 γ transitions in a decay scheme with 20 levels up to 4288 keV. Angular correlation measurements were used to deduce a $J^{π}$ of $0^{+}$ for the 829-keV level. A simple band-mixing calculation is presented which supports a picture of the structure of the low-lying levels in ${}^{100}{Zr}$ as that of coexistence between an axially symmetric deformed yrast band and a nearly spherical excited band.

Summed strength and signature properties of magnetic multipole excitations in a single j shell

L. Zamick

Phys. Rev. C 33, 691 (1986) - Published 1 February, 1986

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Taking the titanium isotopes as an example, the magnetic multipole excitation strengths are calculated in the single j shell model ( $f_{7 / 2}$ ). Expressions are derived for the summed strength in this model for the modes with nonvanishing strength–M1, M3, M5, and M7. An approximate expression for this sum is obtained in which only the components of the wave function in which neutrons and protons couple to angular momentum L=0 and 2 (v=2) in the ground state are included. The signature selection rules for the nucleus ${}^{48}{Ti}$ are considered. It is noted that the M1 strength is mostly concentrated in the lowest state (at least 80%). The higher multipole modes are more strongly fragmented. For these modes, there is significant strength in the isobaric analog states, especially for M5. A closed expression for strength to the isobaric analog strength in ${}^{48}{Ti}$ is obtained.

Microscopic calculations in the A=6 system

J. J. Bevelacqua

Phys. Rev. C 33, 699 (1986) - Published 1 February, 1986

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The A=6 structure problem is solved within the framework of the nuclear shell model. Model states are expanded upon a basis of properly symmetrized, translationally invariant harmonic oscillator eigenstates including states of up to 6ħω of excitation. The model interaction is based upon a modification of the two-body Sussex interaction. Eigenvalues and ( $J^{π}$ ,T) values are predicted for the ground states of the following systems: ${}^{6}n$ , ${}^{6}H$ , ${}^{6}{He}$ , ${}^{6}{Li}$ , ${}^{6}{Be}$ , ${}^{6}B$ , and ${}^{6}C$ . The ground state binding energies are within 4 percent of experiment for ${}^{6}{He}$ , ${}^{6}{Li}$ , and ${}^{6}{Be}$ . Excited states for the ${}^{6}{He}$ , ${}^{6}{Li}$ , and ${}^{6}{Be}$ systems are determined and compared to experiment and other calculations. The model spectra for the ${}^{6}{Li}$ system is similar to that proposed by Ajzenberg-Selove. However, the ${}^{6}{He}$ and ${}^{6}{Be}$ spectra contain levels in addition to those suggested by existing compilations. In particular, the ${}^{6}{He}$ and ${}^{6}{Be}$ level spectra have the following level ordering: ( $0^{+}$ ,1), ( $2^{+}$ , 1), ( $1^{+}$ ,0), ( $0^{+}$ ,1), ( $0^{+}$ ,1), ( $3^{+}$ ,0) ( $2^{+}$ ,1), ( $4^{-}$ ,1), ( $2^{-}$ ,1), ( $3^{-}$ ,1), and ( $4^{+}$ ,1).

Clustered quark matter

J. W. Clark, J. Cleymans, and J. Rafelski

Phys. Rev. C 33, 703 (1986) - Published 1 February, 1986

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In cold quark matter, quantum chromodynamic binding effects can favor clustering of three quarks into nucleon-like clusters. An equation of state of clustered quark matter is derived. It is estimated that the adiabatic transformation of nuclear matter to clustered quark matter sets in at about 1 baryon/ ${fm}^{3}$ , while at the minimum of the energy per baryon the excitation energy relative to ordinary nuclear matter is only 200 MeV/b.

Relativistic effects in three-body bound states

W. Glöckle, T.-S. H. Lee, and F. Coester

Phys. Rev. C 33, 709 (1986) - Published 1 February, 1986

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We formulate relativistic and nonrelativistic two-particle dynamics in such a manner that the two-body binding energies are the same for both. We then formulate and solve the relativistic Faddeev equations for a simple s-wave potential (Malfliet-Tjon V). The relativistic effects are small (about 3%) and reduce the three-body binding energy. The expectation value of the relativistic energy operator with the nonrelativistic wave function is a fairly good approximation, but approximate expressions involving expansions in powers of the momentum are shown to be quite unreliable.

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Heavy systems at intermediate energies in the Boltzmann-Uehling-Uhlenbeck approach

Nuclear interferometry and thermal freeze out

Cross sections for the production of ${}^{11}C$ in C targets by ${}^{20}{Ne}$ and ${}^{56}{Fe}$ at relativistic energies

Fission fragment angular distributions

Fitting scenarios in a simple theoretical approach to $1 s$ level shifts in pionic atoms

$π^{+}$ d→ $π^{+}$ pn reaction as a test of relativistic Faddeev theories: Differential cross section

$π^{+}$ d→ $π^{+}$ pn reaction as a test of relativistic Faddeev theories: Vector analyzing power

$π^{0}$ η and $π^{0}$ η’ mixing and the reaction d+d→ $π^{0}$ $+^{4}$ He

Hybrid quark-hadron model of Λ nonmesonic decay: Finite nuclei

Triple-differential cross sections of the ( $π^{+}$ ,pp) reaction on lithium isotopes

Calculation of the (Δ-h, p-h) Landau parameter $g_{Δ}^{’}$ from a many-body Hamiltonian including π and Δ degrees of freedom

Relativistic plane-wave impulse approximation for nuclear inelastic scattering of protons and electrons

Pion-induced pion production on the deuteron

Model-independent error analysis of $K^{+}$ -nucleus elastic scattering

Nonmesonic nucleon decay in nuclei

Shape coexistence and level structure of ${}^{100}{Zr}$ from decay of the low-spin isomer of ${}^{100}Y$

Summed strength and signature properties of magnetic multipole excitations in a single j shell

Microscopic calculations in the A=6 system

Clustered quark matter

Relativistic effects in three-body bound states

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