Recent Articles

Nuclear disintegration of some complex nuclei by 60-MeV muons

C. J. Orth, J. D. Knight, K. Wolfsberg, and M. W. Johnson

Phys. Rev. C 21, 1967 (1980) - Published 1 May, 1980

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Cross sections for muodisintegration reactions (( $μ^{\pm}$ , $μ^{\pm} xN$ )) at $T_{μ} = 60$ MeV on eight nuclei from ${}^{12}C$ to ${}^{203}{Tl}$ have been measured by activation techniques. The cross sections, like those for comparable electron reactions, increase with target mass number. An additional measurement with 30-MeV $μ^{+}$ on ${}^{12}C$ shows a positive energy dependence. The observation that $σ (μ^{+}, μ^{+} x n) < σ (μ^{-}, μ^{-} x n)$ for heavy nuclei implies the presence of Coulomb distortion of the muon trajectories. Calculations employing the virtual photon method in the plane-wave Born approximation, together with reported photonuclear cross sections, give good agreement with the ${}^{12}C$ ( $μ$ , $μ^{'} n$ ) ${}^{11}C$ results, but not with those for higher- $Z$ nuclei.

NUCLEAR REACTIONS Muon scattering, 60-MeV ( $μ^{+}$ , $μ^{+'} xN$ ) cross sections in ${}^{12}C$ , ${}^{46, 48}{Ti}$ , ${}^{58}{Ni}$ , ${}^{63}{Cu}$ , ${}^{174}{Yb}$ , ${}^{197}{Au}$ , ${}^{203}{Tl}$ ; 30-MeV $μ^{+}$ on ${}^{12}C$ ; 60-MeV $μ^{-}$ on ${}^{12}C$ , ${}^{63}{Cu}$ , ${}^{197}{Au}$ , and ${}^{203}{Tl}$ . Activation method, natural targets, enriched ${}^{203}{Tl}$ . Comparison with plane-wave Born approximation (PWBA) virtual photon calculations.

Interpretation of quasielastic pion scattering coincidence experiments

Morton M. Sternheim and Richard R. Silbar

Phys. Rev. C 21, 1974 (1980) - Published 1 May, 1980

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The energy dependence of the $np$ charge exchange cross section, the angular dependence of the free $π^{\pm} p$ cross section ratio, and nucleon "absorption" due to quasielastic scattering are significant in predicting ( $π^{\pm}$ , $π^{\pm} N$ ) ratios. When these effects are taken into account, recent ( $π$ , $π N$ ) coincidence data can be understood in the impulse approximation picture, with the recoil nucleon subject to charge exchange on leaving the nucleus.

NUCLEAR REACTIONS Ratios of $σ (π, π N)$ when final $π$ and/or $N$ observed: ${}^{12}C$ , ${}^{27}{Al}$ , ${}^{208}{Pb}$ at $T_{π} = 180, 190, 255$ MeV. Differences from radiochemical experiments.

Analysis of quasi-free scattering data in the impulse approximation

Albert W. Stetz

Phys. Rev. C 21, 1979 (1980) - Published 1 May, 1980

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We propose a set of variables to be used in place of the customary energies and angles in the analysis of quasi-free scattering data. In terms of these variables one can reduce the usual fivefold differential cross section to a threefold differential including the effects of experimental acceptance without resorting to Monte Carlo techniques. In this form the dependence of the data on nuclear and two-particle variables is clearly separated. Finally, two simple tests of the impulse approximation, the Treiman-Yang test and the Chew-Low extrapolation, can be applied directly to the data in particularly simple form.

NUCLEAR REACTIONS Impulse approximation, relativistic analysis.

Proton-proton correlations, the fireball model, and inclusive pion spectrum

E. Forest, S. Das Gupta, and C. S. Lam

Phys. Rev. C 21, 1989 (1980) - Published 1 May, 1980

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Two proton correlations seen in the reaction ${}^{12}C$ on ${}^{12}C$ are calculated in the framework of the two fireball model. Substantial correlation is obtained. It is necessary to do the calculation in phase space, i.e., to use the microcanonical ensemble rather than the grand canonical ensemble. A model calculation shows that the latter will also overestimate pion production in the high energy tail compared to an energy and momentum conserving phase space calculation.

NUCLEAR REACTIONS Relativistic ion-ion collisions; fireball model; phase space; pion spectrum; two proton correlations.

Local field corrections in $π$ -nucleus scattering

M. K. Banerjee and S. J. Wallace

Phys. Rev. C 21, 1996 (1980) - Published 1 May, 1980

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The local field correction to the $π$ -nucleus optical potential is calculated taking recoil into account. The correction arises from the triple scattering matrix element $〈 0; \vec{k} | τ_{1} G τ_{2} G τ_{1} | 0; {\vec{k}}^{'} 〉$ , where $τ_{i}$ are $π N$ amplitudes. The recoil energy of nucleon 1 affects the pion Green's function $G$ and the intermediate scattering amplitude $τ_{2}$ . The recoil of nucleon 2 affects only $τ_{2}$ and has not been included to save computational time. Effects of antisymmetry of the two nucleons, spin flip, and charge exchange have been included, but not those of pair correlation and Pauli blocking. Inclusion of recoil is found to reduce the local field correction by a factor of 7 from the result of fixed scatterer calculations. Nevertheless, the local field correction remains sizable. In the $π$ - ${}^{16}O$ case it represents a correction $\frac{2}{3}$ as large as the first order optical potential near the $π N$ resonant energy. Nucleon 1 typically recoils through × 1 fm while in terms of the internucleon separation $r_{12}$ the effect is very long ranged. Thus the $P$ -wave nature of the $π N$ interaction which enhances the reflection of the pion from nucleon 2 back to nucleon 1 is the main reason why the local field correction is so important in $π$ -nucleus scattering. The imaginary part of the local field correction part of the optical potential is analyzed and its reactive content is shown to arise from two competing mechanisms. The first, and dominant, mechanism is a reduction of the single nucleon knockout contribution that is overestimated in the first order optical potential while the second mechanism is the two-nucleon knockout. The analysis suggests very slow convergence of multiple scattering expansions near the $π N$ resonance energy.

NUCLEAR REACTIONS Pion optical potential, local field corrections, reactive content of optical potential.

Photoproduction of pions from deuterons at medium energies

J. D. Anand, V. S. Bhasin, and V. K. Gupta

Phys. Rev. C 21, 2010 (1980) - Published 1 May, 1980

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We study, within the framework of impulse approximation, photoproduction of pions by deuterons leading to two final protons at incident photon energy varying from 210 to about 700 MeV. Employing for the two-body processes $γ N \to π N$ a dispersion theoretic model by Chew et al. and taking spin, isospin, and the identity of the two outgoing particles explicitly into account, the present investigation is primarily directed towards studying (i) the effect of the deuteron wave functions used (including the tensor force and hard core), and (ii) the effect of inserting the $γ N \to π N$ amplitude in different reference frames thereby introducing off-shell corrections to the physical amplitude. We find that the tensor force and hard core terms play only a marginal role in improving the agreement with experimental data. On the other hand, different forms of the wave function, e.g., Yamaguchi versus Gaussian, involving relatively small momentum components do affect the results considerably. The effect of off-shell corrections to the two-body amplitude is found to be significant at medium energies and large angles. The results obtained for the total cross section as well as the differential cross section for the produced pions in the entire angular region are compared with the experimental data.

NUCLEAR REACTIONS Photopion production, total and differential cross sections, impulse approximation, effect of reference frames, deuteron wave functions.

Actinide muonic atom lifetimes deduced from muon-induced fission

W. W. Wilcke, M. W. Johnson, W. U. Schröder, D. Hilscher, J. R. Birkelund, J. R. Huizenga, J. C. Browne, and D. G. Perry

Phys. Rev. C 21, 2019 (1980) - Published 1 May, 1980

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Time distributions of fragments from delayed fission after muon capture have been measured for muonic ${}^{235}U$ , ${}^{238}U$ , ${}^{237}{Np}$ , ${}^{239}{Pu}$ , and ${}^{242}{Pu}$ . Comparison of these data with previously measured lifetimes using muon decay electrons, neutrons, and $γ$ rays emitted after muon capture indicates that the observed systematic discrepancies are due to atomic muon capture by fission fragments after prompt fission induced by radiationless muonic transitions. The deduced capture rates are compared with theoretical models, and very good agreement is found with a giant-resonance excitation model.

RADIOACTIVITY Muonic atoms ${}^{235}U$ , ${}^{238}U$ , ${}^{237}{Np}$ , ${}^{239}{Pu}$ , and ${}^{242}{Pu}$ . Measured fission fragment time distributions, deduced total muon-capture rates and isotopic effect, present data compared to lifetimes based on all other decay channels.

$L_{2, 3}$ -subshell x-ray fluorescence and Coster-Kronig yields at $Z = 64 and 67$

B. E. Gnade, R. A. Braga, and R. W. Fink

Phys. Rev. C 21, 2025 (1980) - Published 1 May, 1980

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The total Coster-Kronig transition probability $f_{23}$ for the $L_{2} - L_{3}$ transition and the $L_{2}$ and $L_{3}$ subshell x-ray fluorescence yields $ω_{2}$ and $ω_{3}$ were measured utilizing resolved $L - K$ x-ray coincidence techniques for $Z = 64 and 67$ with radioactive sources of 4.68 yr ${}^{155}{Eu}$ and 10.4 h ${}^{165}{Er}$ , respectively. Improved accuracy in the results is achieved by advances in the experimental method. The values of $f_{23}$ are 0.130±0.012 and 0.115±0.011 at $Z = 64 and 67$ , respectively, and of $ω_{2}$ and $ω_{3}$ are 0.165±0.022 and 0.161±0.019 at $Z = 64$ , and 0.186±0.023 and 0.180±0.020 at $Z = 67$ , respectively. The quoted uncertainties are twice the average deviation from the mean of 12 values of $f_{23}$ and two values each of $ω_{2}$ and $ω_{3}$ , and arise predominantly from systematic errors.

RADIOACTIVITY ${}^{155}{Eu}$ ; ${}^{165}{Er}$ ; measured $ω_{2}$ , $ω_{3}$ , $f_{23}$ in $L_{2, 3}$ subshells; $XX \cdot t$ coin; Ge(HP)-Si(Li) detectors.

Half-life of ${}^{241}{Pu}$

S. K. Aggarwal and H. C. Jain

Phys. Rev. C 21, 2033 (1980) - Published 1 May, 1980

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The half-life of ${}^{241}{Pu}$ was determined by studying the ingrowth of ${}^{241}{Am}$ by $α$ spectrometry. A synthetic mixture was prepared by mixing was prepared by mixing different isotopes of plutonium so as to obtain a ${}^{238}{Pu}$ /( ${}^{239}{Pu}$ + ${}^{240}{Pu}$ ) $α$ activity ratio of nearly 0.1 and an increase in the $α$ activity ratio due to the ingrowth of ${}^{241}{Am}$ of about 0.1 after a period of 30 days. This was done to get a desired change periodically in the $α$ activity ratio and to measure this change with high precision and accuracy. The initial values of ${}^{239}{Pu}$ / ${}^{241}{Pu}$ and ${}^{240}{Pu}$ / ${}^{241}{Pu}$ atom ratios in the mixture were obtained by mass spectrometry. The ingrowth of ${}^{241}{Am}$ was measured periodically by $α$ spectrometry on electrodeposited sources using a silicon surface barrier detector. From the 80 $α$ spectrometric measurements carried out on five electrodeposited sources over a period of 457 days, a value of 14.42±0.09 yr is obtained for the half-life of ${}^{241}{Pu}$ using a value of 432.6 yr for the half-life of ${}^{241}{Am}$ . The uncertainty quoted on the value is a combination of one standard deviation on the average value and the error evaluated from the estimate on various error components. The half-life obtained in this work is in good agreement with the preliminary results reported recently by CBNM (Geel), NBS (Washington), and AERE (Harwell) using different methods.

RADIOACTIVITY ${}^{241}{Pu}$ half-life; measured: ${}^{241}{Am}$ ingrowth by $α$ spectrometry, ${}^{239}{Pu}$ / ${}^{241}{Pu}$ and ${}^{240}{Pu}$ / ${}^{241}{Pu}$ atom ratios by mass spectrometry.

Levels of ${}^{230}{Ac}$ and ${}^{230}{Th}$ populated by decay of ${}^{230}{Ra}$ and ${}^{230}{Ac}$

J. Gilat, S. Katcoff, and L. K. Peker

Phys. Rev. C 21, 2041 (1980) - Published 1 May, 1980

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Decay schemes, based on $γ$ -ray and $β$ -ray spectroscopy, are proposed for 93-min ${}^{230}{Ra}$ and 122-sec ${}^{230}{Ac}$ . Of 48 observed $γ$ transitions following decay of ${}^{230}{Ra}$ , 39 are accommodated among 19 levels in ${}^{230}{Ac}$ . For decay of the ${}^{230}{Ac}$ , 135 $γ$ transitions were observed and 98 are accounted for among 46 levels (22 known previously) in ${}^{230}{Th}$ . The ground state of ${}_{89}^{230}{Ac}_{141}$ is assigned $I^{π} = K^{π} = 1^{+}$ . A number of levels are discussed in terms of Nilsson orbital assignments. $Q_{β^{-}} \approx 0.71$ MeV for ${}^{230}{Ra}$ and $Q_{β^{-}} = 2.70$ MeV for ${}^{230}{Ac}$ .

RADIOACTIVITY ${}^{230}{Ra}$ , ${}^{230}{Ac}$ from ${}^{232}{Th}$ ( $n$ , $2 p n$ ) ${}^{230}{Ra} \overset{β^{-}}{\to} {}^{230}{Ac}$ ; radiochemistry, Ge(Li) and plastic detectors. Measured $T_{\frac{1}{2}}$ , $E_{γ}$ , $I_{γ}$ , $I_{β^{-}}$ ; deduced $I_{β^{-}}$ , $log ft$ , decay schemes, $J$ , $π$ , Nilsson assignments.

Sturmian expansion method for bound state problems

A. Deloff and J. Law

Phys. Rev. C 21, 2048 (1980) - Published 1 May, 1980

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A novel precision method is developed to solve a two-body bound state problem where the interaction may be an arbitrary relativistic, complex, nonlocal operator and, in particular, may contain also the Coulomb potential. The method is based on the expansion of the Green's function (free or Coulomb modified) in terms of a discrete set of Coulomb Sturm functions which have equally simple forms in $x$ or $p$ space representation. The method should be particularly useful for hadronic atom problems. Other applications are also suggested.

NUCLEAR STRUCTURE Sturmain expansion, bound states.

Alternative methods for the solution of static Hartree-Fock and related problems

M. Di Toro, G. Russo, and F. Duggan

Phys. Rev. C 21, 2054 (1980) - Published 1 May, 1980

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Alternative ways to the usual diagonalization procedures to solve the self-consistent nuclear Hartree-Fock problem are discussed. It is shown that they are much faster than the conventional approach and computationally much simpler. It is shown how they can be further improved. Finally all these new methods are unified within the framework of a direct minimization of the total energy in the subspace of Slater determinants. Results are given for medium-light deformed nuclei.

NUCLEAR STRUCTURE Alternative Hartree-Fock solutions.

Mass parameters in the adiabatic time-dependent Hartree-Fock approximation. I. Theoretical aspects; the case of a single collective variable

M. J. Giannoni and P. Quentin

Phys. Rev. C 21, 2060 (1980) - Published 1 May, 1980

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A self-consistent method for evaluation of mass parameters is presented in the framework of the adiabatic limit of the time-dependent Hartree-Fock approximation, reduced to a single collective variable. The corresponding collective path is assumed to be given either by solving a constrained Hartree-Fock problem with a given time-even constraining operator $Q$ , or by scaling a static Hartree-Fock equilibrium solution. In the former case, once the path is given, a method for solving the equation of motion (of the Hamilton type) is provided, which reduces to a double-constrained Hartree-Fock problem with the time-even constraint $Q$ and with a time-odd constraining operator $P$ . In the case of the scaling path, an analytical solution of the Hamilton equation is discussed and the adiabatic mass for the particular case of an isoscalar quadrupole $Q_{20}$ mode is given. The operator $P$ , which is uniquely determined from the knowledge of $Q$ , has the physical meaning of a momentum operator; it satisfies, together with $Q$ , a weak quantal conjugation relation. Finally, the connection between the two paths is discussed in terms of generalized random-phase approximation sum rules.

NUCLEAR STRUCTURE Evaluation of mass parameters within time-dependent Hartree-Fock approximation in adiabatic limit for single collective variable motion. Discussion and comparison of constrained Hartree-Fock and scaling paths. Expression as a doubly constrained Hartree-Fock problem with momentum operator uniquely defined from coordinate operator. Connection with sum rule and Inglis cranking approaches.

Mass parameters in the adiabatic time-dependent Hartree-Fock approximation. II. Results for the isoscalar quadrupole mode

M. J. Giannoni and P. Quentin

Phys. Rev. C 21, 2076 (1980) - Published 1 May, 1980

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The formalism presented in the preceding paper is used to compute self-consistent adiabatic mass parameters for the isoscalar quadrupole modes. Skyrme-like effective forces have been used. A detailed study of the practical methods of calculation is made. A special attention is devoted to the problem of numerical accuracy. Results are presented for both scaling and constrained Hartree-Fock paths. A comparative discussion of the two corresponding sets of results is made. The method used to calculate self-consistent mass parameters for the constrained Hartree-Fock path provides, as a byproduct, the non-self-consistent cranking mass. This method (for self-consistent as well as cranking masses) is free of continuum problems inherent to the application of the usual cranking formula. The effect of self-consistency is extensively studied by use of a large set of Skyrme-like forces.

NUCLEAR STRUCTURE ${}^{12}C$ , ${}^{16}O$ , ${}^{40}{Ca}$ , ${}^{48}{Ca}$ , ${}^{56}{Ni}$ , ${}^{90}{Zr}$ , ${}^{140}{Ce}$ , ${}^{208}{Pb}$ ; mass parameters for isoscalar quadrupole collective motion calculated within time-dependent Hartree-Fock approximation in adiabatic limit. Skyrme-like forces used. Numerical accuracy discussed. Self-consistent results for both scaling and constrained Hartree-Fock paths discussed. Validity of Inglis cranking masses assessed. Influence of forces studied.

Pion-nucleus optical potential including the nuclear Hamiltonian

Humberto Garcilazo

Phys. Rev. C 21, 2094 (1980) - Published 1 May, 1980

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We use the fact that the mass of the pion is much smaller than the mass of the nucleon to derive an expression for the first-order pion-nucleus optical potential that includes the effect of the nuclear Hamiltonian through a single-particle model. We apply this potential to calculate the total and reaction cross sections of ${}^{12}C$ and the charge-exchange cross section to the isobaric analog state in ${}^{13}C$ for energies between 0 and 300 MeV, obtaining qualitative agreement with experiment.

NUCLEAR REACTIONS ${}^{13}C$ ( $π^{+}$ , $π^{0}$ ), ${}^{12}C$ ( $π^{+}$ , $π^{+}$ ), $E = 0 - 300$ MeV; calculated $σ_{tot} (E)$ , $σ_{reac} (E)$ , and $σ_{cex} (E)$ .

RAPID COMMUNICATION

Glauber theory and $N - N$ inelasticity

William A. Friedman and Alvin M. Saperstein

Phys. Rev. C 21, 2098(R) (1980) - Published 1 May, 1980

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RAPID COMMUNICATION

New isotope ${}^{199}{Rn}$ and evidence for an isomeric state ${}^{199}{Rn}^{m}$

A. C. DiRienzo, H. A. Enge, S. B. Gazes, M. K. Salomaa, A. Sperduto, W. Schier, and H. E. Wegner

Phys. Rev. C 21, 2101(R) (1980) - Published 1 May, 1980

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The nuclide ${}^{199}{Rn}$ has been produced in the ${}^{169}{Tm}$ ( ${}^{35}{Cl}$ , $5 n$ ) ${}^{199}{Rn}$ reaction. The recoiling ${}^{199}{Rn}$ nuclei were separated from the beam at zero degrees by a recoil-separator arrangement utilizing electric and magnetic fields, and detected by their alpha decay signatures in a surface-barrier detector. Two alpha lines were found with energies 6.990±0.015 MeV and 7.060±0.015 MeV. Alpha decay of the known daughter ${}^{195}{Po}$ was also observed.

RADIOACTIVITY ${}^{199}{Rn}$ and ${}^{199}{Rn}^{m}$ ; measured excitation functions ${}^{169}{Tm}$ ( ${}^{35}{Cl}$ , $5 n$ ) ${}^{199}{Rn}$ and $E_{α}$ 's.

RAPID COMMUNICATION

Self-energy of the $Δ$ resonance in finite nuclei and Fermi broadening

R. S Bhalerao, L. C. Liu, and C. M. Shakin

Phys. Rev. C 21, 2103(R) (1980) - Published 1 May, 1980

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It is shown that because of the Fermi motion of the target nucleons the $Δ$ resonance exhibits a large kinematic broadening in nuclei. This broadening is unrelated to the coupling of the isobar to inelastic channels and is neglected in some of the calculations of pion-nucleus scattering based upon the isobar-hole model.

NUCLEAR REACTIONS Effects of Fermi motions; self-energy of the $Δ$ isobar; pion-nucleus optical potential.

RAPID COMMUNICATION

Relative importance of neutron and proton components of nuclear transitions and comparative $\frac{π^{-}}{π^{+}}$ inelastic scattering

B. A. Brown and B. H. Wildenthal

Phys. Rev. C 21, 2107(R) (1980) - Published 1 May, 1980

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Shell-model calculations for ${}^{18}O$ and ${}^{26}{Mg}$ yield predictions of strong state dependence of the isovector component of nuclear transition strengths, with results for ${}^{18}O$ being consistent with recent measurements of $\frac{π^{-}}{π^{+}}$ inelastic scattering ratios.

NUCLEAR STRUCTURE ${}^{18}O$ , ${}^{26}{Mg}$ ; calculated neutron and proton components of inelastic scattering excitations; estimates of $\frac{π^{-}}{π^{+}}$ cross section ratios; shell model.

RAPID COMMUNICATION

${}^{12}C$ + ${}^{12}C$ intermediate structures correlated among elastic and reaction channels

E. R. Cosman, R. Ledoux, and A. J. Lazzarini

Phys. Rev. C 21, 2111(R) (1980) - Published 1 May, 1980

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Prominent intermediate structure correlations are suggested between ${}^{12}C$ + ${}^{12}C$ elastic and reaction channel excitation functions over a wide range of energies above the Coulomb barrier. The associated resonant states in ${}^{24}{Mg}$ would have large partial widths to elastic, inelastic, and $α$ + ${}^{20}{Ne}$ * channels.

NUCLEAR REACTIONS Correlation analysis on ${}^{12}C$ + ${}^{12}C$ resonance channels. Deduced positions of intermediate structure states in ${}^{24}{Mg}$ and ${}^{12}C$ , $Γ ({}^{12}C + {}^{12}C)$ strength function.

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Nuclear disintegration of some complex nuclei by 60-MeV muons

Interpretation of quasielastic pion scattering coincidence experiments

Analysis of quasi-free scattering data in the impulse approximation

Proton-proton correlations, the fireball model, and inclusive pion spectrum

Local field corrections in $π$ -nucleus scattering

Photoproduction of pions from deuterons at medium energies

Actinide muonic atom lifetimes deduced from muon-induced fission

$L_{2, 3}$ -subshell x-ray fluorescence and Coster-Kronig yields at $Z = 64 and 67$

Half-life of ${}^{241}{Pu}$

Levels of ${}^{230}{Ac}$ and ${}^{230}{Th}$ populated by decay of ${}^{230}{Ra}$ and ${}^{230}{Ac}$

Sturmian expansion method for bound state problems

Alternative methods for the solution of static Hartree-Fock and related problems

Mass parameters in the adiabatic time-dependent Hartree-Fock approximation. I. Theoretical aspects; the case of a single collective variable

Mass parameters in the adiabatic time-dependent Hartree-Fock approximation. II. Results for the isoscalar quadrupole mode

Pion-nucleus optical potential including the nuclear Hamiltonian

Glauber theory and $N - N$ inelasticity

New isotope ${}^{199}{Rn}$ and evidence for an isomeric state ${}^{199}{Rn}^{m}$

Self-energy of the $Δ$ resonance in finite nuclei and Fermi broadening

Relative importance of neutron and proton components of nuclear transitions and comparative $\frac{π^{-}}{π^{+}}$ inelastic scattering

${}^{12}C$ + ${}^{12}C$ intermediate structures correlated among elastic and reaction channels

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