Recent Articles

( $π^{\pm}$ , $π^{\pm} p$ ) reaction at 245 MeV

E. Piasetzky, D. Ashery, A. Altman, A. I. Yavin, F. W. Schlepütz, R. J. Powers, W. Bertl, L. Felawka, H. K. Walter, R. G. Winter, and J. v. d. Pluym

Phys. Rev. C 25, 2687 (1982) - Published 1 May, 1982

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The inclusive ( $π^{\pm}$ , $π^{\pm} p$ ) reactions on C, Fe, and Bi were studied at 245 MeV in a broad kinematic range by means of coincidence measurement of the outgoing particles. The $π - p$ angular correlations and proton-energy spectra show features consistent with those expected from quasifree scattering. It is observed that about 80% of the inclusive inelastic scattering cross section at backward pion angles may be attributed to nucleon knockout mechanisms. The results allow identification of the direct quasifree process, unperturbed by higher order effects, which accounts for 30%, 20%, and 15% of the C, Fe, and Bi inclusive ( $π^{+}$ , $π^{+}$ ) differential cross sections, respectively. The ratio of positive to negative pion cross sections for quasifree scattering, integrated over the proton energy and angle, are in agreement with the ratio for free $π - p$ scattering. Such is not the case for various proton angles. The deviation of the positive to negative ratio at the peak of the proton angular correlation from the free scattering ratio is most pronounced for more forward pion angles.

NUCLEAR REACTIONS ( $π^{\pm}$ , $π^{\pm} p$ ) coin. measurements on C, Fe, Bi, $E = 245$ MeV; deduced $σ_{knockout}$ decomposition of $σ_{inelastic}$ .

Inelastic scattering of kaons on ${}^{12}C$

Y. Sakamoto, Y. Hatsuda, and F. M. Toyama

Phys. Rev. C 25, 2695 (1982) - Published 1 May, 1982

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The cross sections for the reactions ${}^{12}C$ ( $K^{\pm}$ , $K^{\pm'}$ ) ${}^{12}C$ * ( $J^{π} = 2^{+}$ , $E_{x} = 4.44$ MeV; $J^{π} = 0^{+}$ , $E_{x} = 7.65$ MeV, and $J^{π} = 3^{-}$ , $E_{x} = 9.64$ MeV) at incident momentum $p_{lab} = 800$ MeV/c are calculated in the distorted wave impulse approximation. Multiple scattering effects are taken into account by means of the $K^{\pm}$ -nucleus elastic scattering amplitudes. The results are compared with recent data for the reactions leading to the $2^{+}$ and $3^{-}$ states. The difference between the angular patterns of the cross sections for the $K^{-}$ and $K^{+}$ scattering is mainly due to the fact that the $K^{-} N$ scattering amplitude depends strongly on the momentum transfer compared with the $K^{+} N$ amplitude.

NUCLEAR REACTIONS ${}^{12}C$ ( $K^{\pm}$ , $K^{\pm'}$ ) ${}^{12}C$ * ( $2^{+}$ , 4.44 MeV; $0^{+}$ , 7.65 MeV; $3^{-}$ , 9.64 MeV), $p_{lab} = 800$ MeV/c, $\frac{d σ}{d Ω}$ calculated in DWIA, distortion effects through $K^{\pm}$ -nucleus elastic scattering amplitudes.

Lee model and mesic atoms

Michael G. Fuda

Phys. Rev. C 25, 2701 (1982) - Published 1 May, 1982

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An extension of the Lee model in quantum field theory is presented which has some of the features of mesic atoms. The model has three fermions $V$ , $N_{1}$ , and $N_{2}$ , and two bosons $θ_{1}$ and $θ_{2}$ , which interact according to $V ⇄ N_{α} + θ_{α}$ , $α = 1, 2$ . There is also a pair interaction between an $N_{α}$ and $θ_{α}$ particle which can produce atomic bound states whose energies are shifted and broadened by the interaction $V ⇆ N_{α} + θ_{α}$ , $α = 1, 2$ . The $T$ matrix for $N_{β} - θ_{α}$ scattering is obtained in closed form, and its bound state and decaying or resonant state poles are investigated.

NUCLEAR REACTIONS Model quantum field theory for mesic atoms.

Decays of ${}^{194, 195, 196}{Pb}$

K. H. Hicks, T. E. Ward, J. Wiggins, C. A. Fields, and F. W. N. de Boer

Phys. Rev. C 25, 2710 (1982) - Published 1 May, 1982

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Decay properties of ${}^{194, 195, 196}{Pb}$ were studied using singles and coincident $γ$ -ray spectroscopy. Sources were produced by the 95 MeV ${}^{197}{Au}$ ( ${}^{6}{Li}$ , $xn$ ) reactions. No direct evidence for the decay of a low-spin isomer of ${}^{195}{Pb}$ was observed. Several new levels were observed in ${}^{195, 196}{Tl}$ , and are interpreted in terms of a rotational model.

RADIOACTIVITY ${}^{194, 195, 196}{Pb}$ [from ${}^{197}{Au}$ ( ${}^{6}{Li}$ , $xn$ ), $E = 95$ MeV]. Measured $E_{γ}$ , $I_{γ}$ , $γ - γ$ coin; deduced $log ft$ . ${}^{194, 195, 196}{Pb}^{m}$ deduced $t_{\frac{1}{2}}$ . ${}^{194, 195, 196}{Tl}$ deduced levels, $J$ , $π$ , Nilsson configurations. Ge(Li) detectors.

Electron capture shakeoff

Akira Suzuki and J. Law

Phys. Rev. C 25, 2722 (1982) - Published 1 May, 1982

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$K$ -electron shakeoff probabilities during $K$ capture have been calculated using Dirac-Fock-Slater wave functions, and by direct calculation of the ejected-electron continuum wave functions. The results indicate an overall better agreement with experimental results, but leave room for some residual electron-electron correlation effects.

RADIOACTIVITY $K$ -vacancy creation calculations in electron capture.

Meson fields with vanishing expectation values

M. Bolsterli

Phys. Rev. C 25, 2728 (1982) - Published 1 May, 1982

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A method for treating meson fields whose expectation values must vanish because of symmetry is presented in terms of a simplified model of pions, nucleons, and deltas constituting a model alpha particle. Self-consistent equations for the wave functions are derived from the variational principle. The relation to the mean-field procedure, which can be used for fields with expectation values, is discussed.

NUCLEAR STRUCTURE Self-consistent pion field.

Relationship between the Bohr-Mottelson model and the interacting boson model

Abraham Klein, Ching-Teh Li, and Michel Vallieres

Phys. Rev. C 25, 2733 (1982) - Published 1 May, 1982

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The interacting boson model was invented in two independent modes: The Schwinger mode using six bosons ( $s$ and five $d$ bosons) and the Holstein-Primakoff mode using five quadrupole quasibosons. We show that the mathematical equivalence of the two modes can be used to define a number conserving quadrupole boson (the $b$ boson). Two equivalent bases, the usual $s - d$ basis and a new $s - b$ basis, are exhibited. By an exercise of (possibly objectionable) physical license, the result can be interpreted as a proof of equivalence of interacting boson model I with the Bohr-Mottelson model. In the $s - b$ basis, the Hamiltonian and other operators depend only on the $b$ boson. In this form, all the topics usually associated with the Bohr-Mottleson model can be discussed: potential energy surface, shape parameters, vibrations vs rotations, etc. The precise relationship of our method to that employed in previous work is exposed. The latter is shown to correspond to the use of the Dyson generators of SU(6).

NUCLEAR STRUCTURE Interacting bosons, Bohr-Mottelson form of IBM, potential energy surface from IBM, generator coordinates and IBM.

Alpha-deuteron structure of ${}^{6}{Li}$ as predicted by three-body models

D. R. Lehman and Mamta Rajan

Phys. Rev. C 25, 2743 (1982) - Published 1 May, 1982

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Three-body ( $α NN$ ) models of the ${}^{6}{Li}$ ground state are used to examine its alpha-deuteron structure. Three models of the ${}^{6}{Li}$ ground-state wave function are considered: simple, full (0%), and full (4%). The full (4%) model is derived by solving the Schrödinger equation with the ${}^{3}S_{1} - {}^{3}D_{1}$ $n - p$ interaction (4% $D$ state in the deuteron) plus the $S_{\frac{1}{2}}$ , $P_{\frac{1}{2}}$ , and $P_{\frac{3}{2}}$ $α - N$ interactions, whereas the full (0%) and simple models truncate the $n - p$ interaction to only the ${}^{3}S_{1}$ component and the simple model also drops the $S_{\frac{1}{2}}$ and $P_{\frac{1}{2}}$ components of the $α - N$ interaction. These models are used to calculate the $s$ - and $d$ -wave ${}^{6}{Li} \to α + d$ momentum distributions, the percentage of $s$ - and $d$ -wave $α - d$ components in the ${}^{6}{Li}$ wave functions, the effective $s$ - and $d$ -wave configuration-space wave functions, and the $S$ - and $D$ -wave ${}^{6}{Li} \to α + d$ asymptotic normalization constants. The most sophisticated of the models, full (4%), predicts a ${}^{6}{Li} \to α + d$ momentum distribution in agreement at low momentum transfers ( $q ≲ 0.3$ ${fm}^{- 1}$ ) with the latest momentum distribution extracted from a 670 MeV ${}^{6}{Li} (p, p d) α$ experiment; a 65.4% $α - d$ component in the ${}^{6}{Li}$ wave function with only 0.049% coming from the $d$ -wave contribution; that both the $s$ - and $d$ -wave effective $α - d$ wave functions have nodes at ∼1.6 and ∼1.65 fm, respectively, though they differ in shape; and the values of the ${}^{6}{Li} \to α + d$ , $S$ - and $D$ -wave asymptotic normalization constants to be 2.182 and 0.0178, respectively, consistent with present experimental values. Detailed comparison between the models is made, especially with respect to the role of the $n - p$ tensor force and repulsive $S_{\frac{1}{2}}$ $α - N$ interaction. The character of the $α - d$ $d$ -wave component is thoroughly examined.

NUCLEAR STRUCTURE ${}^{6}{Li}$ , three-body models, asymptotic norms, spectroscopic factors, momentum distributions.

Electric quadrupole moments and isotope shifts of radioactive sodium isotopes

F. Touchard, J. M. Serre, S. Büttgenbach, P. Guimbal, R. Klapisch, M. de Saint Simon, C. Thibault, H. T. Duong, P. Juncar, S. Liberman, J. Pinard, and J. L. Vialle

Phys. Rev. C 25, 2756 (1982) - Published 1 May, 1982

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On-line high resolution laser spectroscopy has been performed on radioactive ${}^{20 - 31}{Na}$ . New values for the isotope shift of the $D_{1}$ line of ${}^{20 - 24, 31}{Na}$ relative to ${}^{23}{Na}$ have been obtained. The spectroscopic quadrupole moments of ${}^{21, 25 - 29}{Na}$ have been determined using a double resonance method. The $D_{2}$ line hyperfine structure of ${}^{21, 25 - 27}{Na}$ has also been studied by laser optical spectroscopy. Results are in agreement with those obtained by rf double resonance. No evidence of the sudden onset of a deformation expected at $N = 20$ has been found. A strong shell effect in the change in the mean-square charge radius is exhibited at $N = 14$ .

NUCLEAR REACTIONS ${}^{20 - 24, 31}{Na}$ ; measured isotope shift. ${}^{20 - 22, 24, 31}{Na}$ ; measured hyperfine constants $A (3 s {}^{2}S_{\frac{1}{2}})$ , $A (3 p {}^{2}P_{\frac{1}{2}})$ ; deduced $μ$ . ${}^{21, 25 - 29}{Na}$ ; measured hyperfine constants $A (3 p {}^{2}P_{\frac{3}{2}})$ , $B (3 p {}^{2}P_{\frac{3}{2}})$ ; deduced $Q$ . Atomic beam laser spectroscopy and laser rf double-resonance spectroscopy.

Isoscalar giant-resonance energies and long-mean-free path nuclear fluid dynamics

Rainer W. Hasse, Gautam Ghosh, Joachim Winter, and Albert Lumbroso

Phys. Rev. C 25, 2771 (1982) - Published 1 May, 1982

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The collisionless Vlasov equation is solved by a moment expansion and truncated after the fourth moments. This scheme yields fluid dynamical equations for the eigenvibrations of a nucleus which are beyond the usual elastic equations. These Euler equations are solved exactly and also approximately for the normal parity (electric, surface) modes $2^{+}$ , first excited $2^{+}$ , $3^{-}$ , $4^{+}$ , the abnormal parity (magnetic, twist) modes $1^{+}$ , $2^{-}$ , and the compression (breathing and squeezing) modes $0^{+}$ , $1^{-}$ . Without adjustable parameters, agreement of the resulting giant resonance energies with experimental data, where available, is reasonably good. Since the corrections due to the inclusion of the third and fourth moments enhance the energies by up to 35%, the moment expansion coverges only slowly.

NUCLEAR STRUCTURE Giant resonances; electric, magnetic, and compression modes; elastic vibrations; calculated energies.

Collective transitions at high level density

G. Leander

Phys. Rev. C 25, 2780 (1982) - Published 1 May, 1982

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It has been assumed that highly excited collective bands, more or less parallel to the yrast line, are important for the gamma deexcitation of rotational nuclei formed in heavy-ion reactions. This paper draws attention to the possibility that the in-band decay of any given state may be spread over a broad spectrum and discusses the implications for the cascade process. A simple model, where bands are generated by coherent matrix motion in the Gaussian orthogonal ensemble, indicates how the spreading width may depend on the fundamental nature of nuclear level structure.

NUCLEAR STRUCTURE Model for collective bands at high level density. Spreading of in-band transitions and consequences for quasicontinuum gamma cascades at very high spin.

Dynamics of nuclear fluid. VII. Isovector, spin-vector, and spin-isovector giant multipole resonances as elastic vibrations

Cheuk-Yin Wong

Phys. Rev. C 25, 2787 (1982) - Published 1 May, 1982

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Previously, we studied the isoscalar giant resonances as the elastic vibration of a nucleus, the peculiar properties of elasticity being a manifestation of the quantum stress tensor. We examine here the other types of collective vibrations involving elastic spin and isospin waves. Relevant electric and magnetic multipole states for the isovector, the spin vector, and the spin-isovector modes are determined. We find that for a given electric or magnetic state with multipolarity $l$ different from zero, the lowest eigenenergies for the different modes of giant resonances (isoscalar, isovector, spin-vector, and spin-isovector) are approximately degenerate. On the other hand, the $l^{π} = 0^{+}$ states depend on the nuclear incompressibility and the symmetry energy coefficients. Their eigenenergies can be quite different. The theoretical eigenenergies for the giant isovector electric multipole states compare well with experimental data.

NUCLEAR STRUCTURE Elastic vibration of a nucleus. Giant isovector, spin-vector, and spin-isovector resonances of electric and magnetic multipolarities.

Collective Hamiltonians in the generator coordinate method: A numerical procedure

D. Galetti and S. S. Mizrahi

Phys. Rev. C 25, 2795 (1982) - Published 1 May, 1982

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A numerical procedure is introduced which allows us to extract a collective Hamiltonian, expressed in terms of a collective canonical pair $\hat{p}$ and $\hat{q}$ . The starting point is a microscopic many-body approach, namely the generator coordinate method, and the Weyl formalism permits the description of the collective dynamics in the $p - q$ space. As an illustration we compare numerical calculations with exact results, obtained analytically, for the quadratic energy kernel with the Gaussian overlap approximation case and the Goldhaber-Teller dipole model applied to the ${}^{4}{He}$ nucleus.

NUCLEAR STRUCTURE Numerical derivation of collective Hamiltonians. Generator coordinate method, Weyl procedure. Comparison with analytical results.

${}^{218}{Po}$ half-life

James R. Van Hise, Dowell E. Martz, Richard A. Jackson, Dale Y. Kunihira, and Edward Bolton

Phys. Rev. C 25, 2802 (1982) - Published 1 May, 1982

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Electron scattering study of the 10.32 MeV transition in ${}^{40}{Ca}$

P. E. Burt, L. W. Fagg, H. Crannell, D. I. Sober, W. Stapor, J. T. O'Brien, X. K. Maruyama, J. W. Lightbody, and R. A. Lindgren

Phys. Rev. C 25, 2805 (1982) - Published 1 May, 1982

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Values of the form factor for the 10.32 MeV transition in ${}^{40}{Ca}$ have been measured at six different low momentum transfers corresponding to incident electron energies between 31 and 65 MeV and scattering angles of 127.8° and 162.4°. Analysis of the data shows that the transition is transverse and $M 1$ . Our data in conjunction with that of earlier workers yield a value of $Γ_{0} (M 1) = 4.82 \pm 0.26$ eV for the ground state transition width. It is shown that in the low momentum transfer range covered in this work, $q < 0.55$ ${fm}^{- 1}$ , this result is essentially model independent. Results for the transition at 9.86 MeV state are also discussed.

NUCLEAR REACTIONS ${}^{40}{Ca}$ ( $e$ , $e^{'}$ ), $E_{0} = 31 - 65$ MeV; measured $\frac{d σ}{d Ω}$ at $θ = 127.8 °, 162.4 °$ ; deduced mulipolarity and transition width, $Γ_{0}$ .

Thermal neutron capture cross section of deuterium

E. T. Jurney, P. J. Bendt, and J. C. Browne

Phys. Rev. C 25, 2810 (1982) - Published 1 May, 1982

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Shape coexistence and shape transitions in the even- $A$ Ge nuclei

R. Lecomte, G. Kajrys, S. Landsberger, P. Paradis, and S. Monaro

Phys. Rev. C 25, 2812 (1982) - Published 1 May, 1982

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A comparison of experimental data obtained in Coulomb excitation and two neutron transfer reaction measurements definitely assesses the existence of shape transitions and shape coexistence in the even- $A$ germanium nuclei.

NUCLEAR REACTIONS Comparison of two neutron transfer reactions and Coulomb excitation measurements. Shape coexistence and shape transitions in the Ge nuclei.

Cross-section fluctuations in the ${}^{24}{Mg}$ , ${}^{12}C$ scatterings at high incident energy

M. C. Mermaz, A. Greiner, M. LeVine, F. Jundt, J. -P. Coffin, and A. Adoun

Phys. Rev. C 25, 2815 (1982) - Published 1 May, 1982

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Statistical fluctuations are probably present in the 180° c.m. angle scattering cross sections for elastic and inelastic channels, between 24 and 43 MeV c.m. energy.

NUCLEAR REACTIONS 180° c.m. elastic and inelastic scattering data for 0-, 1.36-, 4.43 MeV states: $24 \leq E_{c . m .} \leq 43$ MeV; 0.26 MeV step. Statistical fluctuation analysis.

Energy dependence of the zero-range normalization constant for the ( $p$ , $t$ ) reaction at incident energies of 34.9, 45.1, 54.7, and 65.0 MeV

M. Matoba, K. Tsuji, K. Marubayashi, T. Shintake, K. Ohba, and T. Nomiyama

Phys. Rev. C 25, 2819 (1982) - Published 1 May, 1982

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Angular distributions of ${}^{124}{Sn}$ ( $p$ , $t$ ) reactions to low-lying states of ${}^{122}{Sn}$ were measured at $E_{p} = 34.9, 45.1, 54.7, and 65.0$ MeV and analyzed with zero-range distorted-wave Born approximation theory. It is found that the zero-range normalization constant $D_{0}^{2}$ is smoothly decreasing as a function of the incident proton energy in the several tens of MeV region of bombarding energy.

NUCLEAR REACTIONS ${}^{124}{Sn}$ ( $p$ , $t$ ), $E = 34.9, 45.1, 54.7, and 65.0$ MeV; measured ( $E_{t}$ , $θ_{t}$ ); DWBA analysis; deduced zero-range normalization factor.

Proton capture in the 19 MeV region of ${}^{12}C$

M. C. Wright, N. R. Roberson, H. R. Weller, D. R. Tilley, and Dean Halderson

Phys. Rev. C 25, 2823 (1982) - Published 1 May, 1982

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The 60° and 90° yield curves for the ${}^{11}B$ ( $p$ , $γ$ ) ${}^{12}C$ reaction have been measured for $E_{p} = 2.9 to 4.6$ MeV in 100 keV steps for $γ$ rays leading to the ground and first and third excited states. Recent ( $π$ , $π^{'}$ ) data suggest the existence of an isospin mixed doublet near 19.5 MeV in ${}^{12}C$ . A continuum shell model calculation which successfully describes the ( $π$ , $π^{'}$ ) data predicts an observable effect in the $γ_{3}$ channel. However, no evidence for these states is found in our $γ_{3}$ data.

NUCLEAR REACTIONS ${}^{11}B$ ( $p$ , $γ$ ) ${}^{12}C$ ; measured $σ (E_{p})$ , $E_{p} = 2.9 to 4.6$ MeV, $θ = 60 °, 90 °$ , for $γ_{0}$ , $γ_{1}$ , $γ_{3}$ . Compared $γ_{3}$ data to continuum shell model calculations. No evidence for 19.25 and/or 19.65 MeV states is found.

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Recent Issues

( $π^{\pm}$ , $π^{\pm} p$ ) reaction at 245 MeV

Inelastic scattering of kaons on ${}^{12}C$

Lee model and mesic atoms

Decays of ${}^{194, 195, 196}{Pb}$

Electron capture shakeoff

Meson fields with vanishing expectation values

Relationship between the Bohr-Mottelson model and the interacting boson model

Alpha-deuteron structure of ${}^{6}{Li}$ as predicted by three-body models

Electric quadrupole moments and isotope shifts of radioactive sodium isotopes

Isoscalar giant-resonance energies and long-mean-free path nuclear fluid dynamics

Collective transitions at high level density

Dynamics of nuclear fluid. VII. Isovector, spin-vector, and spin-isovector giant multipole resonances as elastic vibrations

Collective Hamiltonians in the generator coordinate method: A numerical procedure

${}^{218}{Po}$ half-life

Electron scattering study of the 10.32 MeV transition in ${}^{40}{Ca}$

Thermal neutron capture cross section of deuterium

Shape coexistence and shape transitions in the even- $A$ Ge nuclei

Cross-section fluctuations in the ${}^{24}{Mg}$ , ${}^{12}C$ scatterings at high incident energy

Energy dependence of the zero-range normalization constant for the ( $p$ , $t$ ) reaction at incident energies of 34.9, 45.1, 54.7, and 65.0 MeV

Proton capture in the 19 MeV region of ${}^{12}C$

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