Recent Articles

Isospin mixing in ${}^{16}O$ by use of pion and deuteron probes

R. Y. Cusson and B. Castel

Phys. Rev. C 23, 1279 (1981) - Published 1 March, 1981

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The theoretical analysis necessary to isolate the effects of nuclear and Coulomb interactions in admixing the three $4^{-}$ states at 17.79, 18.98, and 19.80 MeV in ${}^{16}O$ is presented. An isospin mixing matrix element of 110±10 keV is determined to be compatible with the recent pion and deuteron induced reaction cross sections.

NUCLEAR REACTIONS Isospin Mixing; Pion and deuteron induced reactions.

Entropy generation and hydrodynamic flow in relativistic heavy ion collisions

J. I. Kapusta and D. Strottman

Phys. Rev. C 23, 1282 (1981) - Published 1 March, 1981

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The spectra of pions, protons, and deuterons from collisions of Ar on KCl at a beam energy of 800 MeV per nucleon have been computed in a conventional hydrodynamic approach. Extreme softening of the finite temperature form of the nuclear equation of state leads to significant differences in the number of emitted particles of each species, although there is still too little entropy and too few pions produced as compared with experiment.

NUCLEAR REACTIONS Hydrodynamic calculations, spectra of $π$ , $p$ , $d$ ; Ar + KCl, 800 MeV/A; entropy, equation of state.

$S$ -matrix approach to hadronic atom level shifts

A. Deloff

Phys. Rev. C 23, 1286 (1981) - Published 1 March, 1981

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It is shown that once the hadron-nucleus scattering problem has been solved, the hadronic atom level shifts and widths can be extracted by continuing the $S$ matrix below threshold.

NUCLEAR REACTIONS $S$ -matrix theory, hadronic atom complex level shift calculated and correlated with scattering parameters.

Comment on "Failure of the connected-kernel method"

Ian H. Sloan

Phys. Rev. C 23, 1289 (1981) - Published 1 March, 1981

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In a recent paper by Komarov et al., the claim is made that the coupled Faddeev-type equations for a system of two noninteracting particles in a fixed potential do not have a unique solution. It is shown here that the claim is not justified. Moreover, it is shown that the phenomenon on which the claim is based occurs even in a true three-body system of three finite-mass particles. Therefore, the property is not, as has been asserted, a consequence of the total Hamiltonian being the sum of commuting sub-Hamiltonians.

NUCLEAR REACTIONS Previously claimed nonuniqueness of Faddeev-type equations shown unjustified.

RAPID COMMUNICATION

Low energy angular distributions for the ${}^{12}C (e, π^{+} e^{'})$ reaction

R. M. Sealock, H. S. Caplan, G. J. Lolos, and W. C. Haxton

Phys. Rev. C 23, 1293(R) (1981) - Published 1 March, 1981

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Angular distributions for near threshold electroproduction of positive pions from ${}^{12}C$ are reported and compared to theory. These data provide tests of recently developed second-order optical potentials and of the nuclear response to electroproduction in the giant resonance region.

NUCLEAR REACTIONS ${}^{12}C (e, π^{+} e^{'})$ ; measured $σ (E_{π}, θ)$ , $E_{e} = 200$ MeV, $E_{π} = 6 - 13$ MeV; calculated $σ$ distorted wave Born approximation; giant resonances.

RAPID COMMUNICATION

Exact and approximate aspects of the boson expansion theories

T. Tamura, K. J. Weeks, and V. G. Pedrocchi

Phys. Rev. C 23, 1297(R) (1981) - Published 1 March, 1981

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It is shown that a boson expansion theory of the Kishimoto-Tamura type not only maps the operators exactly but also the space, and, consequently, the matrix elements of the fermion system onto those of the bosons. Significance of approximations made in calculations is also discussed.

NUCLEAR STRUCTURE Boson expansion theories, Pauli principles, pair representation, Tamm-Dancoff representation, exact mapping, collective approximation, ideal boson states.

Electroexcitation of giant multipole resonances in ${}^{24}{Mg}$

K. Itoh, S. Ohsawa, Y. Torizuka, T. Saito, and T. Terasawa

Phys. Rev. C 23, 945 (1981) - Published 1 March, 1981

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Highly excited multipole resonances of ${}^{24}{Mg}$ between 9 and 34 MeV excitation energy have been investigated by inelastic electron scattering for incident energies in the 102 and 200 MeV range. Prominent giant dipole resonances were observed at 18.9 and 20 MeV excitation energy, with a shape which is very similar to the shape of the photoneutron cross section. Over twenty-five quadrupole and twenty octupole resonances were identified and separated by means of the multipole expansion method. The giant dipole strength exhausts ( $85_{- 17}^{+ 9}$ )% of the isovector dipole energy-weighted sum rule. The quadrupole and the octupole strength exhaust (117±23)% and (115±23)% of the corresponding isoscalar energy-weighted sum rule, respectively. Evidence for the excitation of higher multipole states such as hexadecapole transitions was also found in the excitation energy region studied.

NUCLEAR REACTIONS ${}^{24}{Mg} (e, e^{'})$ , $E = 102, 125, 150, 200$ MeV, $q = 0.37 - 1.3$ ${fm}^{- 1}$ , measured $σ (E^{'}, θ)$ up to 34 MeV in excitation energy; deduced dipole, quadrupole, and octupole strengths in giant resonance region. Enriched targets.

Kinematically incomplete three-nucleon breakup reaction ${}^{1}H (\vec{d}, p) p n$ at 16 MeV

F. D. Correll, G. G. Ohlsen, Ronald E. Brown, R. A. Hardekopf, Nelson Jarmie, and P. Doleschall

Phys. Rev. C 23, 960 (1981) - Published 1 March, 1981

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We have measured the analyzing powers $A_{y}$ , $A_{xx}$ , $A_{yy}$ , and $A_{xz}$ for the kinematically incomplete three-nucleon breakup reaction ${}^{1}H (\vec{d}, p) p n$ at a deuteron bombarding energy of 16.0 MeV. Similar data for the elastic channel were obtained at the same time. Data were acquired at laboratory angles from 15.0° to 42.5°. The detected proton continua extended over a range in excitation energy $E^{*}$ for the residual $pn$ system, and this range varied from $E^{*} = 0 - 2.6$ MeV at 15.0° to $E^{*} = 0 - 0.2$ MeV at 42.5°. The experimental energy resolution was about 150 keV (lab). The breakup tensor analyzing powers attain magnitudes as large as about 0.2 at the lowest excitation energies. Faddeev calculations have been performed for a variety of final-state configurations having $E^{*} = 0 and 200$ keV and indicate that a full kinematically incomplete calculation would probably show no major disagreement with the data.

NUCLEAR REACTIONS ${}^{1}H (\vec{d}, p) p n$ , $E = 16$ MeV; measured $A_{y} (θ, E_{p})$ , $A_{xx} (θ, E_{p})$ , $A_{yy} (θ, E_{p})$ , $A_{xz} (θ, E_{p})$ . Faddeev calculations for $E_{p} = 0 and 200$ keV.

Possible bound states of repulsive potentials

Henry Brysk and P. F. Zweifel

Phys. Rev. C 23, 968 (1981) - Published 1 March, 1981

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The Dirac equation predicts the existence of deeply bound states in the field of a repulsive potential. We discuss some of the implications of these states, especially with regard to the possible existence of the "charged vacuum." We also suggest an experiment to detect the $V^{+ +} - a$ bound state of a proton and a positron.

NUCLEAR REACTIONS Relativistic wave equations. Bound states. Predict bound state of $p - e^{+}$ . $T_{\frac{1}{2}} \sim 10^{- 8}$ sec. Suggest experiment to detect in bending magnetic field.

Mass of ${}^{6}{Li}$ and the excitation energy of its 3.56-MeV state

R. G. H. Robertson, J. A. Nolen, Jr., T. Chapuran, and R. Vodhanel

Phys. Rev. C 23, 973 (1981) - Published 1 March, 1981

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The excitation energy of the second excited state of ${}^{6}{Li}$ has been measured to be 3562.88±0.10 keV by comparing the energy of resonance fluorescence radiation from this state to calibration lines from a ${}^{56}{Co}$ source. Also the $Q$ value of the ${}^{6}{Li} (p, α) {}^{3}{He}$ reaction has been determined relative to the ${}^{19}F (p, α) {}^{16}O$ reaction, giving a result for the ground state mass excess of ${}^{6}{Li}$ of 14 085.5±1.1 keV, somewhat below the tabulated value of 14 087.3±0.8 keV. These measurements improve the sensitivity of experiments searching for isovector parity violation in ${}^{6}{Li}$ .

NUCLEAR REACTIONS ${}^{6}{Li} (γ, γ) {}^{6}{Li}$ , bremsstrahlung source, $E_{x} = 3.56$ MeV, measured $E_{x}$ . Ge(Li) detector. ${}^{6}{Li} (p, α) {}^{3}{He}$ , $E_{p} = 10.5$ MeV, measured $Q$ . Magnetic spectrograph.

States in ${}^{20}O$ by use of ${}^{18}O (t, p γ)$ measurements

K. C. Young, Jr., D. P. Balamuth, J. M. Lind, and R. W. Zurmühle

Phys. Rev. C 23, 980 (1981) - Published 1 March, 1981

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Levels in ${}^{20}O$ populated in the ${}^{18}O (t, p) {}^{20}O$ reaction have been studied at bombarding energies of 10 and 12 MeV using proton-γ angular correlation measurements in an axially symmetric geometry. Spin assignments have been made to levels at 1.67 MeV ( $J^{π} = 2^{+}$ ) and 4.06 MeV ( $J^{π} = 2^{+}$ ). The angular correlations measured for levels at $E_{x} = 4.45 and 5.38$ MeV are consistent with $J^{π} = 0^{+}$ for both. The $\frac{E 2}{M 1}$ mixing ratio for the 4.06 → 1.67 MeV transition is measured as $δ = - 0.18 \pm 0.08$ . Comparison of relative electromagnetic matrix elements (obtained from mixing ratio and branching ratio measurements) with the predictions of shell model calculations suggests that excitations out of the $1 p$ shell play a role in describing these transitions. The population parameters measured for the ( $t, p$ ) reaction leading to the first excited states of ${}^{18}O$ and ${}^{20}O$ show that at $E_{t} = 12$ MeV the reaction mechanism is predominantly direct.

NUCLEAR REACTIONS ${}^{18}O (t, p γ) {}^{20}O$ , ${}^{16}O (t, p γ) {}^{18}O$ , $E = 10, 12$ MeV, measured $σ (E_{p})$ , $p γ (θ)$ , $E_{γ}$ . ${}^{2}O$ deduced levels, $J$ , $π$ , $δ$ , branching ratios.

Gamma-ray widths in ${}^{15}N$

R. Moreh, W. C. Sellyey, and R. Vodhanel

Phys. Rev. C 23, 988 (1981) - Published 1 March, 1981

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The ground-state radiative widths of nine levels below 10.2 MeV in ${}^{15}N$ were measured using resonance fluorescence. The results are compared with various theoretical predictions and are found to best agree with very recent unpublished calculations in which the full $1 ℏ ω$ configurational basis is included in constructing the wave functions of the ${}^{15}N$ levels.

NUCLEAR REACTIONS ${}^{15}N (γ, γ^{'})$ , $E = 10.3, 11.4$ MeV bremsstrahlung. Deduced $E_{x}$ , $Γ_{0}$ . Li ${}^{15}{NO}_{3}$ enriched target.

Two-body effects in deuteron photoabsorption sum rules

A. Cambi, B. Mosconi, and P. Ricci

Phys. Rev. C 23, 992 (1981) - Published 1 March, 1981

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The effect of the two-body charge and current densities is considered in the deuteron photoabsorption sum rules. The modifications induced in the Siegert form of the $E 1$ operator give rise to an enhancement factor $k_{2} ≃ 0.2$ over the Thomas-Reiche-Kuhn value of the integrated cross section $σ_{0}$ . The bremsstrahlung-weighted cross section $σ_{- 1} (E 1)$ is found practically unchanged with respect to its value in impulse approximation, while $σ_{- 1} (M 1)$ shows a 30% increase. The calculations are performed with hard-core, soft-core, and super-soft-core potentials. The dependence on the potential model is small for $σ_{0}$ and quite negligible for $σ_{- 1}$ .

NUCLEAR REACTIONS Two-body charge and current densities, deuteron photoabsorption sum rules.

Adiabatic approximation for deuteron breakup effect

H. Amakawa, A. Mori, H. Nishioka, K. Yazaki, and S. Yamaji

Phys. Rev. C 23, 583 (1981) - Published 1 February, 1981

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The adiabatic treatment of the deuteron breakup effect is examined by comparing the calculated breakup cross sections and the partial-wave amplitudes for elastic scattering with those of the more accurate coupled-channel or variational calculations. The three-body scattering system used in the coupled-channel calculation by Austern et al. is employed as an example. It is shown that the adiabatic approximation for the $s$ -wave breakup effect is acceptable event at $E_{d} = 22.9$ MeV and becomes quite good for $E_{d} \geq 40$ MeV.

NUCLEAR REACTIONS Adiabatic approximation in deuteron-nucleus scattering. Comparison with other methods.

Hole states in the tin isotopes observed by the ( $p, t$ ) reaction

G. M. Crawley, W. Benenson, G. Bertsch, S. Gales, D. Weber, and B. Zwieglinski

Phys. Rev. C 23, 589 (1981) - Published 1 February, 1981

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A broad structure has been observed in ( $p, t$ ) reactions on the tin isotopes ${}^{112}{Sn}$ , ${}^{116}{Sn}$ , ${}^{118}{Sn}$ , ${}^{120}{Sn}$ , ${}^{122}{Sn}$ , and ${}^{124}{Sn}$ between 7 and 9 MeV of excitation energy. The width of the peak has a minimum of around 1.9 MeV for the reaction ${}^{116}{Sn} (p, t)$ and increases for both the ${}^{112}{Sn} (p, t)$ reaction and for the heavier tin targets, but the excitation energy of the structure increases with mass number. The measured angular distributions of the bump in ${}^{110}{Sn}$ , ${}^{114}{Sn}$ , and ${}^{120}{Sn}$ agree reasonably well with single-step, distorted-wave Born approximation calculations. The widths of the peaks observed in two neutron transfer show the same trends with mass number as the widths of the single hole states observed in one neutron transfer reactions. It appears that the peak contains components which arise from the pickup of one particle from a deep orbit and one particle from a valence orbit, plus possibly some contribution from pickup of two particles from deep orbits.

NUCLEAR REACTIONS ${}^{112, 116, 118, 120, 122, 124}{Sn} (p, t)$ , ${}^{117, 119}{Sn} (p, d)$ ; $E = 42$ MeV; ${}^{110, 114, 116, 118, 120, 122}{Sn}$ measured $E_{x}$ , $Γ$ ; ${}^{110, 114, 120}{Sn}$ measured $σ (θ)$ . DWBA analysis; enriched targets, resolution 40 keV.

Dynamical equations for the optical potential

K. L. Kowalski

Phys. Rev. C 23, 597 (1981) - Published 1 February, 1981

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Dynamical equations for the optical potential are obtained starting from a wide class of $N$ -particle equations. This is done with arbitrary multiparticle interactions to allow adaptation to few-body models of nuclear reactions and including all effects of nucleon identity. Earlier forms of the optical potential equations are obtained as special cases. Particular emphasis is placed upon obtaining dynamical equations for the optical potential from the equations of Kouri, Levin, and Tobocman including all effects of particle identity.

NUCLEAR REACTIONS Optical potential equations from many-particle scattering theory. Inclusion of effects of nucleon identity and many-body forces in the optical potential.

Energy levels in ${}^{23}{Mg}$ from the ${}^{25}{Mg} (p, t) {}^{23}{Mg}$ reaction

H. Nann, A. Saha, and B. H. Wildenthal

Phys. Rev. C 23, 606 (1981) - Published 1 February, 1981

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Angular distributions of the ${}^{25}{Mg} (p, t) {}^{23}{Mg}$ reaction have been measured at 40 MeV bombarding energy. An energy resolution of 10-15 keV permitted the observation of about 40 new levels in ${}^{23}{Mg}$ up to 9.72 MeV of excitation. Unambiguous spin and parity assignments of ${5 / 2}^{+}$ are made to the levels at 0.045(3), 5.662(8), 6.566(8), 6.899(5), 6.982(5), 7.582(6), 7.795(6), and 8.155(6) MeV on the basis of an $L = 0$ admixture in the angular distributions. Values of the orbital angular momentum $L$ transferred to several states have been deduced. Microscopic distorted-wave Born approximation calculations for the transitions to the first eight ${5 / 2}^{+}$ states have been performed using spectroscopic amplitudes from recent shell model calculations and are compared to the experimental data.

[NUCLEAR REACTIONS ${}^{25}{Mg} (p, t)$ , $E_{P}$ MeV; measured $σ (E_{t}, θ)$ . ${}^{23}{Mg}$ deduced levels, $L$ , $J^{π}$ . DWBA analysis. Enriched target.]

Elastic scattering of 200 MeV polarized protons from ${}^{12, 13}C$ and the optical potential

H. O. Meyer, G. L. Moake, and P. P. Singh

Phys. Rev. C 23, 616 (1981) - Published 1 February, 1981

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The differential cross sections and analyzing powers for 200 MeV protons elastically scattered from ${}^{12}C$ and ${}^{13}C$ have been measured in the angular region 6-115°. The ${}^{12}C$ data were analyzed in terms of a local, complex, spindependent optical potential. The potentials were defined phenomenologically (simple or double Woods-Saxon forms) or derived from the impulse approximation in the Kerman-McManus-Thaler approach with and without a semiempirical correction for Pauli blocking. Acceptable fits to the data over the whole angular range were obtained only for a real central potential which exhibits a pronounced depression inside the nuclear surface, a feature also suggested by some theoretical models for medium-energy optical potentials.

NUCLEAR REACTIONS ${}^{12, 13}C (\vec{p}, p)$ , $E_{p} = 200$ MeV; measured $σ (θ)$ and $A (θ)$ ; phenomenological optical-model analysis, deduced best-fit potentials for ${}^{12}C$ , comparison with impulse-approximation calculations.

Formulation in terms of hyperspherical harmonics of the effect of breakup in deuteron-nucleus collisions

G. H. Rawitscher and W. Zickendraht

Phys. Rev. C 23, 623 (1981) - Published 1 February, 1981

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The overall two-nucleon-nucleus wave function is decomposed into two parts $ψ_{1}$ and $ψ_{2}$ . The coordinates of the latter are the hyperspherical ones, suitable for the description of breakup, while the former, which contains both the scattered deuteron channel and additional breakup components, is given in terms of the conventional coordinates $\vec{r}$ and $\vec{R}$ . A basis set of functions in $ψ_{1}$ are the (continuum) eigenstates of $H_{np}$ and the basis set for $ψ_{2}$ are the discrete hyperspherical harmonics. Coupled equations for the coefficients of each basis set are derived. The inhomogeneous source terms which couple $ψ_{1}$ to $ψ_{2}$ are evaluated for a numerical example, and the coupling terms within $ψ_{2}$ space are discussed in a separate publication. It appears feasible to calculate the effect of $ψ_{2}$ upon $ψ_{1}$ and vice versa in an iterative sequence, but the calculation within $ψ_{2}$ space requires the noniterative solution of coupled equations. Such a calculation appears possible with the computer power currently available, but has not been carried out.

NUCLEAR REACTIONS Formulation of three body scattering in terms of hyperspherical harmonics. Application to deuteron-nucleus scattering.

Breakup coupling potentials for deuteron-nucleus collisions in the space of hyperspherical harmonics

W. Zickendraht and G. H. Rawitscher

Phys. Rev. C 23, 633 (1981) - Published 1 February, 1981

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Formulas are derived for expressing the sum of neutron-nucleus and proton-nucleus optical potentials in terms of a series of hyperspherical harmonic functions and Legendre polynomials. Matrix elements of this expansion between two hyperspherical harmonics are obtained analytically and given in terms of triple sums of finite number of terms. The results are evaluated numerically for the breakup space associated with 21.6 MeV deuterons scattering on the nucleus of nickel. Conclusions are drawn regarding the feasibility of solving the corresponding coupled equations which describe breakup space in the hyperspherical basis.

NUCLEAR REACTIONS Mathematical techniques for expanding three-body wave functions in terms of hyperspherical harmonics. Numerical examples.

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Physical Review C

Recent Articles

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Recent Issues

Isospin mixing in ${}^{16}O$ by use of pion and deuteron probes

Entropy generation and hydrodynamic flow in relativistic heavy ion collisions

$S$ -matrix approach to hadronic atom level shifts

Comment on "Failure of the connected-kernel method"

Low energy angular distributions for the ${}^{12}C (e, π^{+} e^{'})$ reaction

Exact and approximate aspects of the boson expansion theories

Electroexcitation of giant multipole resonances in ${}^{24}{Mg}$

Kinematically incomplete three-nucleon breakup reaction ${}^{1}H (\vec{d}, p) p n$ at 16 MeV

Possible bound states of repulsive potentials

Mass of ${}^{6}{Li}$ and the excitation energy of its 3.56-MeV state

States in ${}^{20}O$ by use of ${}^{18}O (t, p γ)$ measurements

Gamma-ray widths in ${}^{15}N$

Two-body effects in deuteron photoabsorption sum rules

Adiabatic approximation for deuteron breakup effect

Hole states in the tin isotopes observed by the ( $p, t$ ) reaction

Dynamical equations for the optical potential

Energy levels in ${}^{23}{Mg}$ from the ${}^{25}{Mg} (p, t) {}^{23}{Mg}$ reaction

Elastic scattering of 200 MeV polarized protons from ${}^{12, 13}C$ and the optical potential

Formulation in terms of hyperspherical harmonics of the effect of breakup in deuteron-nucleus collisions

Breakup coupling potentials for deuteron-nucleus collisions in the space of hyperspherical harmonics

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