Recent Articles

Pion reactions in deuterium and the muon-capture rate and weak form factors

S. L. Mintz

Phys. Rev. C 22, 2507 (1980) - Published 1 December, 1980

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The muon-capture rate for the reaction $μ^{-} + {}^{2}H \to n + n + ν_{μ}$ is calculated by the use of the elementary particle model. The form factors describing the axial current matrix element are determined from the pion photoproduction reaction $γ + {}^{2}H \to n + n + π^{+}$ via the partially conserved axial vector current hypothesis. The form factors describing the vector current matrix element are obtained from the reactions $γ + {}^{2}H \to p + n$ and $e + {}^{2}H \to p + n + e$ . A result of $Γ = 155$ $\sec^{- 1}$ is obtained. In addition a capture rate for the reaction $π^{-} + d \to n + n + γ$ of $Γ = 3.41 \times 10^{14}$ $\sec^{- 1}$ is obtained.

NUCLEAR REACTIONS Muon-capture ${}^{2}H (μ^{-}, ν_{μ}) n n$ and pion-capture ${}^{2}H (π^{-}, γ) n n$ rates are calculated using the elementary particle model.

Proton-proton bremsstrahlung at 200 MeV

J. G. Rogers, J. L. Beveridge, D. P. Gurd, H. W. Fearing, A. N. Anderson, J. M. Cameron, L. G. Greeniaus, C. A. Goulding, C. A. Smith, A. W. Stetz, J. R. Richardson, and R. Frascaria

Phys. Rev. C 22, 2512 (1980) - Published 1 December, 1980

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The coplanar symmetric proton-proton bremsstrahlung cross section at 16.4° and 200 MeV incident proton energy has been measured. The data are compared with four theoretical calculations, and sizable discrepancies are found. The data are in better agreement with a soft photon calculation than with predictions based on the Hamada-Johnston or the Reid soft-core potential models. The differences between the realistic potential model calculations and the data do not seem to be entirely explained by reasonable variations of the off-shell behavior of the model potentials.

NUCLEAR REACTIONS $pp \to pp γ$ $σ (θ_{γ})$ measured; compared to several model calculations.

Inelastic production of deuteron bag states

C. W. Wong, K. F. Liu, and Y. Tzeng

Phys. Rev. C 22, 2523 (1980) - Published 1 December, 1980

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The relevance of quark degrees of freedom in intermediate-energy nuclear structure is discussed. Besides the appearance of mesons and isobars, there may also appear dinucleon "color resonances" of six quarks each. The inelastic production of these "bag" states by electron and proton scattering from deuterons is suggested as one way of studying them. Formulas are given for the form factors or cross sections of these inelastic processes. The calculated results suggest that the size and rough composition of these dinucleon bag resonances can be deduced under favorable circumstances.

NUCLEAR REACTIONS Calculated inelastic $ed$ form factors and $pd$ cross sections for dinucleon bag productions.

Angular momentum selection rule and the ${}^{9}{Be} (π^{+}, p) {}^{8}{Be}$ reaction at 50 MeV

D. Bachelier, J. L. Boyard, T. Hennino, J. C. Jourdain, P. Radvanyi, and M. Roy-Stéphan

Phys. Rev. C 22, 2531 (1980) - Published 1 December, 1980

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Angular distributions have been measured at 50 MeV for the ${}^{9}{Be} (π^{+}, p) {}^{8}{Be}$ reaction leading to the $0^{+}$ , $2^{+}$ , and $4^{+}$ states of ${}^{8}{Be}$ . An angular momentum selection rule is considered in order to account for the preferential excitation of high spin states. Two-step processes in the framework of the distorted-wave Born approximation and momentum sharing in the two-nucleon model are also discussed.

NUCLEAR REACTIONS ${}^{9}{Be} (π^{+}, p) {}^{8}{Be}$ , $E_{π} = 50$ MeV; measured $σ (θ)$ ; reaction mechanism discussed.

Solvable model for pion-pion $S$ and $P$ waves derived from noncovariant perturbation theory

Walter Ferchländer and Dieter Schütte

Phys. Rev. C 22, 2536 (1980) - Published 1 December, 1980

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Motivated by Lagrangian field theory, we construct an effective Hamilton operator for $P$ - and $S$ -wave pion-pion interactions, which can be handled easily by noncovariant perturbation methods. The result is a factorable $T$ -matrix equation with unambiguous off-shell behavior, which includes the effects of intermediate states with $ε (1300)$ , $S^{*} (980)$ , and $ρ (770)$ mesons as well as with $K \bar{K}$ and $N \bar{N}$ pairs and describes the influence of inelastic pair effects on elastic scattering. The numerical calculations are in good agreement with the experimental $S_{00}$ and $P_{11}$ amplitudes up to a scattering energy of 2.5 GeV; a range of fundamental importance for nuclear physics.

NUCLEAR REACTIONS Pion-pion scattering; theory, $S$ and $P$ waves, field theoretical model, noncovariant perturbation theory.

$β$ decay of ${}^{51}{Ca}$

A. Huck, G. Klotz, A. Knipper, C. Miehé, C. Richard-Serre, G. Walter, and H. L. Ravn

Phys. Rev. C 22, 2544 (1980) - Published 1 December, 1980

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The new isotope ${}^{51}{Ca}$ has been observed in the decay of ${}^{51}K$ produced by fragmentation of a uranium target with 600-MeV protons. The half-life of ${}^{51}{Ca}$ was determined to be 10.0±0.8 s; the decay properties were established from $γ$ -ray singles and coincidence measurements. The deexcitation scheme accounts for twenty-two $γ$ transitions between eleven levels in ${}^{51}{Sc}$ . Two states, located at 3039 and 3195 keV, can be related to the excitation of the odd proton in the $2 p$ $\frac{3}{2}$ orbital.

RADIOACTIVITY ${}^{51}{Ca}$ from $p + U$ at 600 MeV ${}^{51}K (β^{-})$ , natural target, mass separated, measured delayed $E_{γ}$ , $I_{γ}$ , $γ - γ$ coincidences, $T_{\frac{1}{2}}$ , deduced decay scheme, $log ft$ , $J$ , $π$ .

Decay of mass-separated ${}^{78}{Zn}$

F. K. Wohn, John C. Hill, and D. A. Lewis

Phys. Rev. C 22, 2547 (1980) - Published 1 December, 1980

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The decay of neutron-rich ${}^{78}{Zn}$ produced by the thermal neutron fission of ${}^{235}U$ was studied with mass-separated sources. The decay scheme was deduced from $γ$ singles and coincidence measurements. The ${}^{78}{Zn}$ half-life was determined to be 1.47±0.15 s and 57 $γ$ transitions were placed in a level scheme for ${}^{78}{Ga}$ involving 19 excited states. The systematics of odd-odd Ga nuclides is discussed.

RADIOACTIVITY ${}^{78}{Zn}$ [from ${}^{235}U (n, f)$ ]: measured $T_{\frac{1}{2}}$ , $E_{γ}$ , $I_{γ}$ , $γ γ$ coin., Ge(Li) detectors; ${}^{78}{Ga}$ deduced levels, $J$ , $π$ , $log ft$ . Mass-separated ${}^{78}{Zn}$ activity.

Equations-of-motion method and pairing correlations in odd- $A$ nuclei

F. Andreozzi, A. Covello, and A. Porrino

Phys. Rev. C 22, 2555 (1980) - Published 1 December, 1980

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An equations-of-motion method is presented for treating pairing correlations in odd- $A$ nuclei. This method is the natural extension of a previous study of the pairing problem in doubly even nuclei, which provides the input data for the present work. It is shown that the spurious states arising from the use of an overcomplete set of basis vectors can be removed through a procedure analogous to that developed for the doubly even case. The energies, spectroscopic factors, and occupation probabilities of seniority-one states in the Ni isotopes are calculated in the first-order theory. By comparison with exact results, the accuracy of the method is seen to be very good.

NUCLEAR STRUCTURE Equations-of-motion method in pairing-force theory.

Effective interaction for one-hole states in K isotopes

I. P. Johnstone

Phys. Rev. C 22, 2561 (1980) - Published 1 December, 1980

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One-hole states of $A = 39 - 47$ potassium isotopes are examined with a model space spanning the ${f_{\frac{7}{2}}}^{n} {(d_{\frac{3}{2}} s_{\frac{1}{2}})}^{- 1}$ and $f_{\frac{7}{2}}^{n - 1} p_{\frac{3}{2}} {d_{\frac{3}{2}}}^{- 1}$ configurations. The parameters of the neutron and particle-hole interaction are determined by least-squares fits to energy levels of Ca and K isotopes. The calculated spectra are in good agreement with experiment, and allow spin predictions to be made for the higher-mass K isotopes. The model wave functions are used to calculate magnetic moments and $M 1$ transition rates, and measurements which would be useful in determining certain matrix elements of the effective dipole operator are suggested.

NUCLEAR STRUCTURE Calculated one-hole spectra of K isotopes; effective interaction from least-squares fits; $M 1$ transitions and magnetic moments.

$\tilde{π} h_{\frac{9}{2}} \otimes \tilde{ν} i_{\frac{13}{2}}$ bands in doubly odd Tl isotopes including a proton-neutron residual interaction

A. J. Kreiner

Phys. Rev. C 22, 2570 (1980) - Published 1 December, 1980

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The level staggering in $\tilde{π} h_{\frac{9}{2}} \otimes \tilde{ν} i_{\frac{13}{2}}$ two-quasiparticle bands in doubly odd Tl isotopes, for $A ≳ 198$ , is shown to be related to the signature dependence of the Coriolis interaction even in the presence of a proton-neutron residual interaction obtained from ${}^{208}{Bi}$ . The study of the neutron number dependence of this system suggests the existence of new isomeric states in very neutron deficient Tl isotopes and also reveals a possible inadequacy of the residual force or of the model itself.

NUCLEAR STRUCTURE Two-quasiparticle bands in doubly odd Tl isotopes. Effects of a residual proton-neutron interaction.

Projected Hartree-Fock calculations for ${}^{52, 53}V$

Surender Saini and M. R. Gunye

Phys. Rev. C 22, 2575 (1980) - Published 1 December, 1980

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The structure of the low-lying nuclear states in neutron rich isotopes of vanadium ${}^{52, 53}V$ is investigated. The investigations are carried out in the framework of Hartree-Fock projection formalism by employing a realistic nucleon-nucleon interaction. All the valence nucleons outside the inert ${}^{40}{Ca}$ core are considered to be active in the configuration space of the full $fp$ shell. The energy levels, static electromagnetic moments, and the electromagnetic transition probabilities are evaluated from the band-mixing calculations, wherein the lowest few energetically close intrinsic states of the nuclei are taken into account. The results of the present calculations are in fair agreement with the available experimental data.

NUCLEAR STRUCTURE Vanadium isotopes: calculated energy levels, static moments, $B (E 2)$ and $B (M 1)$ . Hartree-Fock projection formalism, realistic nucleon-nucleon interaction, band mixing.

Instability in relativistic nuclear matter

Hirokazu Tezuka

Phys. Rev. C 22, 2585 (1980) - Published 1 December, 1980

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The stability of the Fermi gas state in the nuclear matter which satisfies the saturation property is considered relativistically. It is shown that the Fermi gas state is stable at very low density and at high density, but it is unstable against density fluctuation in the intermediate density region including the normal density.

NUCLEAR STRUCTURE Stability of nuclear matter satisfying nuclear saturation is studied for scalar meson condensation.

Three-body resonances in the ${}^{6}{Li}$ nucleus

Yoshiko Matsui

Phys. Rev. C 22, 2591 (1980) - Published 1 December, 1980

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Six low-lying states of ${}^{6}{Li}$ have been studied by calculating the trajectories of the first two or three eigenvalues of the kernel of the Faddeev equation as the total energy $E$ increases from $- \infty$ to $\infty + i ε$ . In the separable-potential three-body ( $α NN$ ), model for ${}^{6}{Li}$ , the $N - N$ interaction is assumed to be a Yamaguchi-type-central plus tensor force for the triplet $s$ -wave part, and the central force alone for the singlet $s$ -wave part. On the other hand, the $p$ -wave interaction of the $α - N$ system is assumed to be Mitra-type-central plus the spin-orbit force. The integral equations are derived for the spectator functions of the wave function for each state of ${}^{6}{Li}$ in the $LS$ coupling scheme. Following the mathematical definition of $n$ -body resonance, the deformation of the integration contour is performed for the complex eigenvalues and the eigenvalue problems for these equations are solved to determine the binding energy or the resonance energy. The calculated energies of the ground state, the 1st, 2nd, 3rd, 4th, and 5th excited states are -5.558, -1.089, -0.8529, -2.342, 1.431, and -0.2074 MeV; the experimental values are -4.532, -2.347, -0.970, -0.22, 0.84, and 1.17 MeV. The level widths for the 1st, 4th, and 5th excited states are calculated from the trajectories of the eigenvalues obtained above.

NUCLEAR STRUCTURE ${}^{6}{Li}$ ; calculated levels, $J$ , $π$ , $Γ$ . Three-body, separable potential model.

Calculation of binding energies and isotope shifts in a long series of rubidium isotopes

X. Campi and M. Epherre

Phys. Rev. C 22, 2605 (1980) - Published 1 December, 1980

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Self-consistent mean-field calculations have been performed on nuclei with $Z = 36, 38$ . When compared to experimental values, the two neutron separation enegies and the mean-square-charge radii differences are in excellent agreement for isotopes with $N > 50$ , providing additional evidence for a region of strong deformation around $(Z, N) = (40, 60)$ . For isotopes with $N < 50$ the discrepancy between experiment and calculation can account for large zero-point quadrupole vibrations.

NUCLEAR STRUCTURE ${}^{76 - 106}{Sr}$ , ${}^{75 - 105}{Rb}$ , ${}^{74 - 104}{Kr}$ , calculated binding energies and mean-square-charge radii; Hartree-Fock method.

Second anomaly of the moment of inertia in the $N = 90$ isotones

Amand Faessler and M. Ploszajczak

Phys. Rev. C 22, 2609 (1980) - Published 1 December, 1980

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The second anomaly of the moment of inertia is studied in the framework of the cranked and particle-number-projected Hartree-Fock-Bogoliubov approach in the $N = 90$ isotones ${}_{66}^{156}{Dy}$ , ${}_{68}^{158}{Er}$ , and ${}_{70}^{160}{Yb}$ . Including the hexadecapole deformation one is able to explain the absence of the anomaly in ${}^{156}{Dy}$ , upbending in ${}^{158}{Er}$ , and backbending in ${}^{160}{Yb}$ as alignment of an $h_{\frac{11}{2}}$ proton pair.

NUCLEAR STRUCTURE High spin states, second backbending, cranked Hartree-Fock-Bogoliubov.

Microscopic description of the high-spin yrast spectra in some doubly even zinc, germanium, and selenium isotopes

S. K. Sharma

Phys. Rev. C 22, 2612 (1980) - Published 1 December, 1980

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A microscopic description of the yrast levels in some doubly even isotopes of Zn, Ge, and Se is attempted by carrying out Hartree-Fock-Bogoliubov calculations employing realistic effective interactions. The level energies, static quadrupole moments, reduced transition probabilities for $E 2$ transitions, as well as the occupation numbers for the spherical single-particle orbits are calculated for the yrast states. The overall agreement between the calculated and experimental results is reasonably good.

NUCLEAR STRUCTURE Doubly even Zn, Ge, and Se isotopes: calculated yrast levels, static quadrupole moments, reduced transition probabilities for $E 2$ transitions, and occupation numbers for $p_{\frac{3}{2}}$ , $p_{\frac{1}{2}}$ , $f_{\frac{5}{2}}$ , and $g_{\frac{9}{2}}$ subshells. Hartree-Fock-Bogoliubov method with angular momentum projection.

Collective shape transition in the low-lying spectra of nuclei near $N = 28$ region

D. P. Ahalpara

Phys. Rev. C 22, 2619 (1980) - Published 1 December, 1980

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Deformed configuration mixing shell model calculations for the energy spectra and electromagnetic properties of low-lying collective states of ${}^{51}{Cr}$ , ${}^{53}{Fe}$ , ${}^{50}{Ti}$ , ${}^{52}{Cr}$ , ${}^{54}{Fe}$ , ${}^{53}{Cr}$ , and ${}^{55}{Fe}$ have been performed. For each of these nuclei these calculations give rise to a highly deformed band when a neutron is promoted from the predominantly ${(f_{\frac{7}{2}})}^{n}$ "spherical" ground intrinsic configuration to the unoccupied ( $pf$ ) orbits. The $K^{π}$ values of these excited bands are $\frac{1}{2^{-}}$ , $4^{+}$ , and $\frac{7}{2^{-}}$ for the nuclei having $N = 27, 28, and 29$ , respectively. The energy spectra and electromagnetic properties of these calculated excited bands are compared with those experimentally observed. Following high-spin members of the collective bands have been predicted by the calculations: $J = \frac{11}{2}, \frac{13}{2}, \frac{15}{2}, \frac{17}{2}, and \frac{19}{2}$ levels at 2.7, 3.8, 4.36, 5.94, and 6.47 MeV, respectively, in ${}^{51}{Cr}$ , $J = \frac{9}{2}, \frac{11}{2}, \frac{13}{2}, \frac{15}{2}, and \frac{17}{2}$ levels at 2.94, 3.67, 4.95, 6.01, and 7.47 MeV, respectively, in ${}^{53}{Fe}$ , $J = \frac{15}{2}, \frac{17}{2}, \frac{19}{2}, and \frac{21}{2}$ levels at 4.65, 5.77, 7.04, and 8.41 MeV, respectively, in ${}^{53}{Cr}$ , and $J = \frac{15}{2}, \frac{17}{2}, and \frac{19}{2}$ levels at 5.53, 6.92, and 8.33 MeV, respectively, in ${}^{55}{Fe}$ . In ${}^{50}{Ti}$ , ${}^{52}{Cr}$ , and ${}^{54}{Fe}$ the present model suggests an interesting possibility of $K = 3^{+}$ collective band lying close in energy to the recently observed $K = 4^{+}$ collective bands.

NUCLEAR STRUCTURE ${}^{50}{Ti}$ , ${}^{51, 52, 53}{Cr}$ , and ${}^{53, 54, 55}{Fe}$ . Calculated spectra, $B (E 2)$ and $B (M 1)$ transition strengths, $\frac{E 2}{M 1}$ mixing ratios, branching ratios and lifetimes in deformed configuration mixing shell model formalism in ${(fp)}^{n}$ model space. Modified Kuo-Brown interaction. Comparison with experiment and shell model and Nilsson model calculations.

RAPID COMMUNICATION

Cross sections for the reaction ${}^{16}O (γ, p_{0}) {}^{15}N$ at forward angles for $E_{γ} = 80$ MeV

B. Schoch, H. Göringer, P. Jennewein, F. Klein, G. Lührs, and F. Zettl

Phys. Rev. C 22, 2630(R) (1980) - Published 1 December, 1980

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Via the reaction ${}^{16}O (e, p_{0}) {}^{15}N$ cross sections for the transition ${}^{16}O (γ, p_{0}) {}^{15}N$ have been extracted at angles $θ_{p} = 5 ° - 40 °$ . Whereas a modified quasideuteron model fails to describe the data, a calculation of Gari and Hebach with the inclusion of spin currents comes close to the results.

NUCLEAR REACTIONS ${}^{16}O (e, p_{0}) {}^{15}N$ , $E_{e} = 80$ MeV, measured $σ_{e} (E_{e}, θ)$ , deduced $σ_{γ} (E_{γ}, θ)$ ; BeO target.

RAPID COMMUNICATION

Forward-angle proton spectra in the continuum from the ${}^{58}{Ni} (p, x p)$ reaction at 100 MeV

A. A. Cowley, C. C. Chang, and H. D. Holmgren

Phys. Rev. C 22, 2633(R) (1980) - Published 1 December, 1980

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Forward-angle proton energy spectra in the continuum were measured for the reaction ${}^{58}{Ni} (p, x p)$ at 100 MeV with a plastic scintillator used as an active collimator. With this system it was possible to take measurements at angles as small as 8°. It was found that a previously observed broad peak in the continuum, which is suspected to appear as a result of a quasi-free nucleon-nucleon scattering, becomes even more pronounced as the scattering angle decreases. The active collimators were essential in eliminating contributions due to the penetration of collimator edges by elastically scattered protons. At small angles such effects can obscure the quasi-free peak.

NUCLEAR REACTION ${}^{58}{Ni} (p, x p)$ , $E_{p} = 100$ MeV; $θ_{L} = 8 ° - 25 °$ , measured $\frac{d^{2} σ}{d Ω d ε}$ .

RAPID COMMUNICATION

Hypervirial theorems and the Breit-type recoil correction for pionic atoms

J. L. Friar

Phys. Rev. C 22, 2636(R) (1980) - Published 1 December, 1980

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Hypervirial theorems are developed for the Klein-Gordon equation, which allow the Breit part of the pionic atom recoil correction (including the nuclear finite size) to be recast exactly into a form similar to the results for the Dirac equation. This form facilitates both numerical calculation and interpretation.

NUCLEAR STRUCTURE Pionic atoms, finite size, recoil correction, hypervirial theorems.

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Recent Issues

Pion reactions in deuterium and the muon-capture rate and weak form factors

Proton-proton bremsstrahlung at 200 MeV

Inelastic production of deuteron bag states

Angular momentum selection rule and the ${}^{9}{Be} (π^{+}, p) {}^{8}{Be}$ reaction at 50 MeV

Solvable model for pion-pion $S$ and $P$ waves derived from noncovariant perturbation theory

$β$ decay of ${}^{51}{Ca}$

Decay of mass-separated ${}^{78}{Zn}$

Equations-of-motion method and pairing correlations in odd- $A$ nuclei

Effective interaction for one-hole states in K isotopes

$\tilde{π} h_{\frac{9}{2}} \otimes \tilde{ν} i_{\frac{13}{2}}$ bands in doubly odd Tl isotopes including a proton-neutron residual interaction

Projected Hartree-Fock calculations for ${}^{52, 53}V$

Instability in relativistic nuclear matter

Three-body resonances in the ${}^{6}{Li}$ nucleus

Calculation of binding energies and isotope shifts in a long series of rubidium isotopes

Second anomaly of the moment of inertia in the $N = 90$ isotones

Microscopic description of the high-spin yrast spectra in some doubly even zinc, germanium, and selenium isotopes

Collective shape transition in the low-lying spectra of nuclei near $N = 28$ region

Cross sections for the reaction ${}^{16}O (γ, p_{0}) {}^{15}N$ at forward angles for $E_{γ} = 80$ MeV

Forward-angle proton spectra in the continuum from the ${}^{58}{Ni} (p, x p)$ reaction at 100 MeV

Hypervirial theorems and the Breit-type recoil correction for pionic atoms

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