Recent Articles

Identification of ${}^{145}{Tb}$ and ${}^{144}{Tb}$ and levels in the $N = 81$ nucleus, ${}^{145}{Gd}$

D. C. Sousa, K. S. Toth, C. R. Bingham, A. C. Kahler, and D. R. Zolnowski

Phys. Rev. C 25, 1012 (1982) - Published 1 February, 1982

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With the use of a helium gas-jet transport system the isotopes ${}^{145}{Tb}$ and ${}^{144}{Tb}$ were identified in a series of ${}^{10}B$ + ${}^{144}{Sm}$ irradiations. Nuclidic assignments were based on yields as a function of bombarding energy, $γ$ -ray coincidences with gadolinium $K$ x rays, and comparisons with data from in-beam $γ$ -ray studies. Thirteen transitions were observed to follow the decay of ${}^{145}{Tb}$ ( $T_{\frac{1}{2}} = 30 \pm 3$ sec). Nine of them were placed in a scheme incorporating six excited levels in ${}^{145}{Gd}$ , the lowest two of which, 27.3 and 748.7 keV, were previously known from ${}^{145}{Gd}^{m}$ decay. The nuclide ${}^{144}{Tb}$ ( $T_{\frac{1}{2}} = 5 \pm 1$ sec) was identified by observing the 742.9-keV $γ$ ray known from in-beam studies to be the $2^{+}$ (first-excited state)→ $0^{+}$ (ground state) transition in ${}^{144}{Gd}$ .

RADIOACTIVITY ${}^{145}{Tb}$ , ${}^{144}{Tb}$ , measured $T_{\frac{1}{2}}$ , $E_{γ}$ , $I_{γ}$ , $γ γ$ coin; ${}^{145}{Gd}$ , deduced levels, $J^{π}$ .

Relaxation of some fermion nonequilibrium momentum distributions

C. Toepffer and Cheuk-Yin Wong

Phys. Rev. C 25, 1018 (1982) - Published 1 February, 1982

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We study the time evolution of some momentum distributions for an infinite, dilute, and spatially homogeneous system of fermions by solving the Uehling-Uhlenbeck equation. The initial nonequilibrium distributions examined are (i) a Fermi sphere with an outer spherical shell, and (ii) a Fermi bisphere. It is found that the entropy of the system approaches its equilibrium value in a nearly exponential manner. Such a behavior allows an extraction of the relaxation times. The relaxation times decrease with increasing size of perturbation and depend on the shape of the perturbation. Deviations from equilibrium in the initial momentum distribution persist into the late stages of the relaxation process.

NUCLEAR REACTIONS Solution of Uehling-Uhlenbeck equation. Approach to thermal equilibrium in fermion system. Relaxation time.

Roothaan approach in the thermodynamic limit

G. Gutierrez and A. Plastino

Phys. Rev. C 25, 1028 (1982) - Published 1 February, 1982

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A systematic method for the solution of the Hartree-Fock equations in the thermodynamic limit is presented. The approach is seen to be a natural extension of the one usually employed in the finite-fermion case, i.e., that developed by Roothaan. The new techniques developed here are applied, as an example, to neutron matter, employing the so-called $V_{1}$ Bethe "homework" potential. The results obtained are, by far, superior to those that the ordinary plane-wave Hartree-Fock theory yields.

NUCLEAR STRUCTURE Hartree-Fock approach; nuclear and neutron matter.

Skyrme interaction and spectra of light nuclei

Ramesh C. Nayak

Phys. Rev. C 25, 1034 (1982) - Published 1 February, 1982

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The original three-body term in the Skyrme interaction is replaced by a two-body explicit density dependent term to reproduce simultaneously the excited and ground states of nuclei. Care has been taken to remove the spin instability of the Hartree-Fock ground state in nuclear matter and also the antipairing nature of the interaction inherent in the original Skyrme interaction. The spin-isospin dependent parameter introduced in the density dependent term is determined from the average asymmetry ratio and asymmetry energy. The modified Skyrme force is used to calculate the low-lying states of ${}^{18}O$ , ${}^{18}F$ , ${}^{42}{Ca}$ , ${}^{42}{Sc}$ , and ${}^{16}O$ , ${}^{40}{Ca}$ . In the light of these calculations the relative importance of the different Skyrme variants is studied.

NUCLEAR STRUCTURE Ground and excited state properties of nuclei with modified Skyrme interaction, spectra of ${}^{18}O$ , ${}^{18}F$ , ${}^{42}{Ca}$ , ${}^{42}{Sc}$ , ${}^{16}O$ , ${}^{40}{Ca}$ .

Pair decay of the 15.1 MeV level of ${}^{12}C$

J. M. Enagonio, F. P. Calaprice, R. W. Dunford, and M. M. Lowry

Phys. Rev. C 25, 1047 (1982) - Published 1 February, 1982

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We have observed the $e^{+} e^{-}$ pair line from the decay of the 15.1 MeV level of ${}^{12}C$ . Pairs were detected using an intermediate image pair spectrometer. The use of this line as a calibration point for beta spectrometers is discussed.

RADIOACTIVITY ${}^{12}C$ ; observed $e^{+} e^{-}$ pair line from 15.1 MeV level. Intermediate image pair spectrometer.

Marked changes in ( $p$ , $t$ ) analyzing powers for the isotopes of Zr, Mo, Ru, and Pd and strong, sequential, two-step transfer processes in both ( $p$ , $t$ ) and ( $t$ , $p$ ) reactions

Y. Aoki, H. Iida, S. Kunori, K. Nagano, Y. Toba, and K. Yagi

Phys. Rev. C 25, 1050 (1982) - Published 1 February, 1982

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Drastic changes of $0_{g}^{+} \to 0_{g}^{+}$ ( $p$ , $t$ ) analyzing powers for the isotopes Zr, Mo, Ru, and Pd are explained in terms of interference between one-step and ( $p$ , $d$ )( $d$ , $t$ ) sequential transfer amplitudes of comparable magnitudes. Dependence of the analyzing powers on reaction $Q$ values, incident energies, and nuclear structures is interpreted from the interference. Analyzing powers for ( $t$ , $p$ ) reactions can be understood similarly. A test of time reversal invariance in nuclear reactions with use of the analyzing powers for ( $p$ , $t$ ) and ( $t$ , $p$ ) reactions is discussed.

NUCLEAR REACTIONS Vector analyzing power $A_{y} (θ)$ for g.s. ( $p$ , $t$ ) on ${}^{92}{Zr}$ , ${}^{94, 96, 98}{Mo}$ , ${}^{100, 102, 104}{Ru}$ , ${}^{104, 106, 108, 110}{Pd}$ , ${}^{138}{Ba}$ , $E_{p} = 22$ MeV, first- and second-order DWBA. Comparison with ( $\vec{t}$ , $p$ ).

Spin and parity of the 6.699 MeV level in ${}^{17}F$

S. Sen

Phys. Rev. C 25, 1054 (1982) - Published 1 February, 1982

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${}^{16}O$ ( $\vec{p}$ , $p$ ) ${}^{16}O$ measurements near $E_{p} = 6.482$ MeV and phase shift analysis of the data permits an unambiguous $J^{π} = \frac{5}{2^{+}}$ assignment to the narrow level at $E_{x} ({}^{17}F) = 6.699$ MeV that was previously listed as $\frac{3}{2^{-}}$ . The level parameters suggest correspondence to a predicted 5p-4h state at $E_{x} = 5.91$ MeV in $A = 17$ nuclei.

NUCLEAR REACTIONS ${}^{17}F$ ; measured ${}^{16}O$ ( $\vec{p}$ , $p$ ) ${}^{16}O$ , deduced $J^{π}$ , $Γ$ , $Γ_{p}$ .

Cross section for ${}^{12}C$ + ${}^{12}C$ → ${}^{12}C$ ( $O_{2}^{+}$ ) + ${}^{12}C$ (g.s.) using breathing mode doorways

M. U. Ahmed and William P. Beres

Phys. Rev. C 25, 1058 (1982) - Published 1 February, 1982

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A previously derived projection operator method is applied to the calculation of the cross section for ${}^{12}C$ + ${}^{12}C$ → ${}^{12}C$ ( $O_{2}^{+}$ ) + ${}^{12}C$ (g.s.) with a breathing mode model being used to describe the $O_{2}^{+}$ (7.68 MeV) state of ${}^{12}C$ . The relationship to processes leading to alpha particle channels is discussed. The cross section for ${}^{12}C$ + ${}^{12}C$ → ${}^{12}C$ ( $3^{-}$ ) + ${}^{12}C$ (g.s.) is also calculated and possible correlations with inelastic scattering to the $O_{2}^{+}$ and $2^{+}$ states of ${}^{12}C$ are discussed. The results for both $O_{2}^{+}$ and $3^{-}$ inelastic scattering are in reasonable agreement with experiment.

NUCLEAR REACTIONS ${}^{12}C$ + ${}^{12}C$ → ${}^{12}C$ ( $O_{2}^{+}$ ) + ${}^{12}C$ (g.s.) and ${}^{12}C$ + ${}^{12}C$ → ${}^{12}C$ ( $3^{-}$ ) + ${}^{12}C$ (g.s.), $E = 10 - 30$ MeV c.m., projection operator intermediate theory, calculated $σ$ (angle integrated $θ_{lab} = 15 ° to 25 °$ ).

Additional calculations of triton moments

D. F. Lally and J. S. Levinger

Phys. Rev. C 25, 1061 (1982) - Published 1 February, 1982

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The formalism of hyperspherical harmonics is used to calculate several moments of the triton photoeffect for a Volkov potential with Serber exchange. The accuracy of Clare's calculations of moments $σ_{0}$ and $σ_{1}$ is improved by including more terms in the hyperspherical harmonic expansion of the potential and of the ground state wave function. The moment $σ_{2} = 8.9 \times 10^{4}$ Me $V^{3}$ mb is calculated using one term in the hyperspherical harmonic expansions of the potential and wave function. We invert four moments and find reasonable agreement with Gorbunov's measurements of the ${}^{3}{He}$ photoeffect.

NUCLEAR REACTIONS Triton photoeffect, hyperspherical harmonics, moments of photoeffect, inversion of moments.

Identity between the widths from alpha decay and alpha elastic scattering

Luis Marquez

Phys. Rev. C 25, 1065 (1982) - Published 1 February, 1982

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We gave recently the general expression for the alpha decay width derived from the two body, complex energy eigenvalue theory. We show here that the width for alpha elastic scattering for the same state has the same expression. Our treatment for the alpha decay joins smoothly the quantum mechanics solution for the bound state problem and the one for the elastic scattering problem.

RADIOACTIVITY Derived theoretical expression for $α$ elastic scattering resonance width. It is the same as derived $α$ decay width.

Macroscopic description of isoscalar giant multipole resonances

J. Rayford Nix and Arnold J. Sierk

Phys. Rev. C 25, 1068 (1982) - Published 1 February, 1982

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We correct two mistakes that cancel each other in our previous derivation of a macroscopic expression for the isoscalar giant-resonance energy as a function of mass number and multipole degree, as well as discuss four additional effects that influence the energy.

NUCLEAR STRUCTURE Calculated isoscalar giant-resonance energy as function of mass number and multipole degree. Boltzmann equation, distorted Fermi surface, irrotational flow, surface and Coulomb energies, effective mass, pressure tensor, higher moments.

Comment on "Method for treating the spurious center-of-mass problem in a dynamically determined basis"

W. Plessas

Phys. Rev. C 25, 1070 (1982) - Published 1 February, 1982

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In a recent paper Miller and Vary came up with a new method for eliminating states with spurious center-of-mass excitation in multiparticle bound-state problems. This method is discussed in relation to a more general one—in the sense that it is also applicable to scattering problems—proposed previously by the present author.

NUCLEAR REACTIONS Methods for eliminating spurious center-of-mass excitations.

Erratum: ${}^{2}H (α, p α) n$ reaction between 9.735 and 11.30 MeV

S. S. Dasgupta, R. J. Slobodrian, R. Roy, C. Rioux, and F. Lahlou

Phys. Rev. C 25, 1073 (1982) - Published 1 February, 1982

RAPID COMMUNICATION

Mass of ${}^{18}C$ from the double-charge-exchange reaction ${}^{48}{Ca}$ ( ${}^{18}O$ , ${}^{18}C$ ) ${}^{48}{Ti}$

F. Naulin, C. Détraz, M. Roy-Stéphan, M. Bernas, J. de Boer, D. Guillemaud, M. Langevin, F. Pougheon, and P. Roussel

Phys. Rev. C 25, 1074(R) (1982) - Published 1 February, 1982

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RAPID COMMUNICATION

Ground state mass of ${}^{81}{Kr}$ and the solar neutrino problem

R. T. Kouzes, M. M. Lowry, and C. L. Bennett

Phys. Rev. C 25, 1076(R) (1982) - Published 1 February, 1982

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The ${}^{81}{Br}$ ( ${}^{3}{He}$ , $t$ ) ${}^{81}{Kr}$ , reaction has been used to determine an improved value for the ground state mass of ${}^{81}{Kr}$ . A comparison is made with ${}^{51}V$ ( ${}^{3}{He}$ , $t$ ) ${}^{51}{Cr}$ and the implications for calibration of the proposed bromine solar neutrino detector are presented.

NUCLEAR REACTIONS ${}^{81}{Br}$ ( ${}^{3}{He}$ , $t$ ) ${}^{81}{Kr}$ , ${}^{51}V$ ( ${}^{3}{He}$ , $t$ ) ${}^{51}{Cr}$ , ${}^{87}{Rb}$ ( ${}^{3}{He}$ , $t$ ) ${}^{87}{Sr}$ , ${}^{85}{Rb}$ ( ${}^{3}{He}$ , $t$ ) ${}^{85}{Sr}$ , $E ({}^{3}{He}) = 24.7$ MeV; $Q$ values measured, ground state ${}^{81}{Kr}$ mass inferred.

RAPID COMMUNICATION

Experimental study of the $Σ$ -nucleon system through the reaction ${}^{2}H (K, π) Σ N$

M. May, R. E. Chrien, H. Palevsky, R. Sutter, S. Dytman, D. Marlow, P. Pile, F. Takeutchi, M. Deutsch, R. Cester, S. Bart, E. Hungerford, T. M. Williams, L. S. Pinsky, B. W. Mayes, and R. L. Stearns

Phys. Rev. C 25, 1079(R) (1982) - Published 1 February, 1982

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We report $Σ^{-} n$ mass spectra for the reaction ${}^{2}H (K^{-}, π^{+}) Σ^{-} n$ at $θ_{K π} = 20 °$ , momentum transfer $q = 294$ Mev/c. Upper limits on formation cross sections are given and appear to rule out the existence of $Σ^{-}$ neutron bound states. In addition, a missing mass spectrum for the reaction ${}^{2}H (K^{-} π^{-}) X$ , $θ_{K π} = 4 °$ , $q = 134$ MeV/c ( $X = Σ^{+} n, Σ^{\circ} p, or Λ p$ ), is shown and discussed.

NUCLEAR REACTIONS $Σ n$ mass spectrum $Σ$ neutron bound states, ( $K$ , $π$ ) reaction on deuterium, $Λ p$ mass spectrum.

RAPID COMMUNICATION

${}^{9}{Be}$ ( $\vec{p}$ , $π^{-}$ ) ${}^{10}C$ reaction in the 200-250 MeV proton energy range

G. J. Lolos, E. L. Mathie, P. L. Walden, G. Jones, E. G. Auld, and R. B. Taylor

Phys. Rev. C 25, 1082(R) (1982) - Published 1 February, 1982

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Measurements of the dependence on incident proton energy of the analyzing power $A_{y} (θ)$ for $\vec{p} π^{-}$ production on nuclei are reported for the ${}^{9}{Be}$ ( $\vec{p}$ , $π^{-}$ ) ${}^{10}C$ reaction leading to the ground state (g.s.) and the first three excited states of ${}^{10}C$ . For the transition to the g.s. the analyzing power shows little dependence on proton energy while for transitions leading to the ${}^{10}C_{3.35}$ * and ${}^{10}C_{6.60}$ * states it varies considerably with incident proton energy. Nuclear structure dependence of the $A_{y} (θ)$ is also observed for the first time in $\vec{p} π^{-}$ reactions.

NUCLEAR REACTIONS ${}^{9}{Be}$ ( $\vec{p}$ , $π^{-}$ ) ${}^{10}C$ measured $A_{y} (θ)$ for ${}^{10}C_{g . s .}$ , ${}^{10}C_{3.35}$ *, ${}^{10}C_{5.28}$ * and ${}^{10}C_{6.60}$ * transitions; $E_{\vec{p}} = 200, 225, 250$ MeV; calculated $Y_{0} (θ)$ .

RAPID COMMUNICATION

Energy dependence of the analyzing power for the ${}^{12}C$ ( $\vec{p}$ , $π^{+}$ ) ${}^{13}C$ reaction with polarized protons of 200 to 250 MeV

G. J. Lolos, P. L. Walden, E. L. Mathie, G. Jones, E. G. Auld, W. R. Falk, and R. B. Taylor

Phys. Rev. C 25, 1086(R) (1982) - Published 1 February, 1982

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The analyzing power angular distributions $A_{y} (θ)$ for the ${}^{13}C_{g . s .}$ as well as for several ${}^{13}C$ * excited state transitions from the ${}^{12}C$ ( $\vec{p}$ , $π^{+}$ ) ${}^{13}C$ reaction are reported as a function of incident proton energy from 200 to 250 MeV. For the first time in reactions of the type $A (\vec{p}, π^{+}) A + 1$ , a dramatic energy dependence is observed for the analyzing power. A dependence of the shape of the analyzing power on the nature of the excited nuclear state is also observed. The cross section for the ${}^{13}C_{g . s .}$ transition shows indication of backward peaking not observed at energies below 225 MeV.

NUCLEAR REACTIONS ${}^{12}C$ ( $\vec{p}$ , $π^{+}$ ) ${}^{13}C_{g . s .}$ and several excited states, polarized protons, $T_{p} = 200 - 250$ MeV; measured $A_{y} (θ)$ , $\frac{d σ}{d Ω} (θ)$ .

RAPID COMMUNICATION

${}^{9}{Be}$ ( ${}^{3}{He}$ , $\vec{p}$ ) ${}^{11}B$ polarization and implications for time-reversal invariance

R. A. Hardekopf, P. W. Keaton, P. W. Lisowski, and L. R. Veeser

Phys. Rev. C 25, 1090(R) (1982) - Published 1 February, 1982

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We have measured the polarization of protons from the ${}^{9}{Be}$ ( ${}^{3}{He}$ , $\vec{p}$ ) ${}^{11}B$ reaction between 35° and 50° at an incident bombarding energy of 13.6 MeV to check claims of time-reversal noninvariance. We find complete disagreement with other polarization measurements for the same energy and angular range, but our results are in agreement with earlier measurements of the analyzing power in the inverse reaction initiated with polarized protons. Consequently we maintain that this reaction and its inverse exhibit no evidence for a violation of time-reversal invariance.

NUCLEAR REACTIONS ${}^{9}{Be}$ ( ${}^{3}{He}$ , $\vec{p}$ ) ${}^{11}B$ ; $E = 13.6$ MeV; measured $P (θ)$ , $θ (lab) = 35 °, 40 °, 45 °, 50 °$ .

RAPID COMMUNICATION

Energy dependence of the ratio of isovector effective interaction strengths $| \frac{J_{σ τ}}{J_{τ}} |$ from 0° ( $p$ , $n$ ) cross sections

T. N. Taddeucci, J. Rapaport, D. E. Bainum, C. D. Goodman, C. C. Foster, C. Gaarde, J. Larsen, C. A. Goulding, D. J. Horen, T. Masterson, and E. Sugarbaker

Phys. Rev. C 25, 1094(R) (1982) - Published 1 February, 1982

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Information concerning the ratio of the isovector effective interaction strengths $| \frac{J_{σ τ}}{J_{τ}} |$ may be obtained from the ratio of ( $p$ , $n$ ) Gamow-Teller and isobaric analog state 0° differential cross sections. We have examined 0° ( $p$ , $n$ ) data for the energy range 5-200 MeV and find that for energies larger than 50 MeV and for targets with $A = 7 - 42$ the product of the interaction-strength and distortion-factor ratios $| \frac{J_{σ τ}}{J_{τ}} | {(\frac{N_{σ τ}}{N_{τ}})}^{\frac{1}{2}}$ appears to be mass independent and linear as a function of bombarding energy.

NUCLEAR REACTIONS ${}^{7}{Li}$ , ${}^{13, 14}C$ , ${}^{26}{Mg}$ , ${}^{37}{Cl}$ , ${}^{41}{Ca}$ ( $p$ , $n$ ), measured $σ (θ = 0 °)$ , GT, IAS transitions, $E_{p} = 60 - 200$ MeV. Deduced energy dependence, interaction strength ratio $| \frac{J_{σ τ}}{J_{τ}} |$ .

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Recent Issues

Identification of ${}^{145}{Tb}$ and ${}^{144}{Tb}$ and levels in the $N = 81$ nucleus, ${}^{145}{Gd}$

Relaxation of some fermion nonequilibrium momentum distributions

Roothaan approach in the thermodynamic limit

Skyrme interaction and spectra of light nuclei

Pair decay of the 15.1 MeV level of ${}^{12}C$

Marked changes in ( $p$ , $t$ ) analyzing powers for the isotopes of Zr, Mo, Ru, and Pd and strong, sequential, two-step transfer processes in both ( $p$ , $t$ ) and ( $t$ , $p$ ) reactions

Spin and parity of the 6.699 MeV level in ${}^{17}F$

Cross section for ${}^{12}C$ + ${}^{12}C$ → ${}^{12}C$ ( $O_{2}^{+}$ ) + ${}^{12}C$ (g.s.) using breathing mode doorways

Additional calculations of triton moments

Identity between the widths from alpha decay and alpha elastic scattering

Macroscopic description of isoscalar giant multipole resonances

Comment on "Method for treating the spurious center-of-mass problem in a dynamically determined basis"

Erratum: ${}^{2}H (α, p α) n$ reaction between 9.735 and 11.30 MeV

Mass of ${}^{18}C$ from the double-charge-exchange reaction ${}^{48}{Ca}$ ( ${}^{18}O$ , ${}^{18}C$ ) ${}^{48}{Ti}$

Ground state mass of ${}^{81}{Kr}$ and the solar neutrino problem

Experimental study of the $Σ$ -nucleon system through the reaction ${}^{2}H (K, π) Σ N$

${}^{9}{Be}$ ( $\vec{p}$ , $π^{-}$ ) ${}^{10}C$ reaction in the 200-250 MeV proton energy range

Energy dependence of the analyzing power for the ${}^{12}C$ ( $\vec{p}$ , $π^{+}$ ) ${}^{13}C$ reaction with polarized protons of 200 to 250 MeV

${}^{9}{Be}$ ( ${}^{3}{He}$ , $\vec{p}$ ) ${}^{11}B$ polarization and implications for time-reversal invariance

Energy dependence of the ratio of isovector effective interaction strengths $| \frac{J_{σ τ}}{J_{τ}} |$ from 0° ( $p$ , $n$ ) cross sections

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